Heat Transfer - Yunus Cengel - 2ed - Chapter 15- Solutions

15–1C What invention started the electronic age? Why did the invention of the transistor mark the beginning of a revolution in that age
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15–2C What is an integrated circuit? What is its significance in the electronics era? What do the initials MSI, LSI, and VLSI stand for?
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15–3C When electric current I passes through an electrical element having a resistance R, why is heat generated in the element? How is the amount of heat generation determined
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15–4C Consider a TV that is wrapped in the blankets from all sides except its screen. Explain what will happen when the TV is turned on and kept on for a long time, and why. What will happen if the TV is kept on for a few minutes only
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15–5C Consider an incandescent light bulb that is completely wrapped in a towel. Explain what will happen when the light is turned on and kept on. (P.S. Do not try this at home!)
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15–6C A businessman ties a large cloth advertisement banner in front of his car such that it completely blocks the airflow to the radiator. What do you think will happen when he starts the car and goes on a trip?
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15–7C Which is more likely to break: a car or a TV? Why
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15–8C Why do electronic components fail under prolonged use at high temperatures
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15–9 The temperature of the case of a power transistor that is dissipating 12 W is measured to be 60°C. If the junction-tocase thermal resistance of this transistor is specified by the manufacturer to be 5°C/W, determine the junction temperature of the transistor.
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15–10 Power is supplied to an electronic component from a 12-V source, and the variation in the electric current, the junction temperature, and the case temperatures with time are observed. When everything is stabilized, the current is observed to be 0.15 Aand the temperatures to be 80°C and 55°C at the junction and the case, respectively. Calculate the junction-tocase thermal resistance of this component
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15–11 A logic chip used in a computer dissipates 6 W of power in an environment at 55°C and has a heat transfer surface area of 0.32 cm2. Assuming the heat transfer from the surface to be uniform, determine (a) the amount of heat this chip dissipates during an 8-h work day, in kWh, and (b) the heat flux on the surface of the chip, in W/cm2
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15–12 A 15 –cm x 20-cm circuit board houses 90 closely spaced logic chips, each dissipating 0.1 W, on its surface. If the heat transfer from the back surface of the board is negligible, determine (a) the amount of heat this circuit board dissipates during a 10-h period, in kWh, and (b) the heat flux on the surface of the circuit board, in W/cm2.
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15–13E A resistor on a circuit board has a total thermal resistance of 130°F/W. If the temperature of the resistor is not to exceed 360°F, determine the power at which it can operate safely in an ambient at 120°F
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15–14 Consider a 0.1-kΩ resistor whose surface-to-ambient thermal resistance is 300°C/W. If the voltage drop across the resistor is 7.5 V and its surface temperature is not to exceed 150°C, determine the power at which it can operate safely in an ambient at 30°C.
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15–15 Reconsider Problem 15–14. Using EES (or other) software, plot the power at which the resistor can operate safely as a function of the ambient temperature as the temperature varies from 20ºC to 40ºC, and discuss the results.
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15–16C Why is a chip in a chip carrier bonded to a lead frame instead of the plastic case of the chip carrier
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15–17C Draw a schematic of a chip carrier, and explain how heat is transferred from the chip to the medium outside of the chip carrier
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15–18C What does the junction-to-case thermal resistance represent? On what does it depend for a chip carrier
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15–19C What is a hybrid chip carrier? What are the advantages of hybrid electronic packages
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15–20C What is a PCB? Of what is the board of a PCB made? What does the “device-to-PCB edge” thermal resistance in conduction-cooled systems represent? Why is this resistance relatively high
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15–21C What are the three types of printed circuit boards? What are the advantages and disadvantages of each type
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15–22C What are the desirable characteristics of the materials used in the fabrication of the circuit boards
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15–23C What is an electronic enclosure? What is the primary function of the enclosure of an electronic system? Of what materials are the enclosures made?
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15–24C Consider an electronics box that consumes 120 Wof power when plugged in. How is the heating load of this box determined
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15–25C Why is the development of superconducting materials generating so much excitement among designers of electronic equipment
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15–26C How is the duty cycle of an electronic system defined? How does the duty cycle affect the design and selection of a cooling technique for a system
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15–27C What is temperature cycling? How does it affect the reliability of electronic equipment
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15–28C What is the ultimate heat sink for (a) a TV, (b) an airplane, and (c) a ship? For each case, what is the range of temperature variation of the ambient
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15–29C What is the ultimate heat sink for (a) a VCR, (b) a spacecraft, and (c) a communication system on top of a mountain? For each case, what is the range of temperature variation of the ambient?
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15–30C How are the electronics of short-range and longrange missiles cooled
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15–31C What is dynamic temperature? What causes it? How is it determined? At what velocities is it significant
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15–32C How are the electronics of a ship or submarine cooled
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15–33C How are the electronics of the communication systems at remote areas cooled
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15–34C How are the electronics of high-power microwave equipment such as radars cooled
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15–35C How are the electronics of a space vehicle cooled
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15–36 Consider an airplane cruising in the air at a temperature of -25°C at a velocity of 850 km/h. Determine the temperature rise of air at the nose of the airplane as a result of the ramming effect of the air.
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15–37 The temperature of air in high winds is measured by a thermometer to be 12°C. Determine the true temperature of air if the wind velocity is 90 km/h.
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15–38 Reconsider Problem 15–37. Using EES (or other) software, plot the true temperature of air as a function of the wind velocity as the velocity varies from 20 km/h to 120 km/h, and discuss the results
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15–39 Air at 25°C is flowing in a channel at a velocity of (a) 1, (b) 10, (c) 100, and (d) 1000 m/s. Determine the temperature that a stationary probe inserted into the channel will read for each case
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15–40 An electronic device dissipates 2 W of power and has a surface area of 5 cm2. If the surface temperature of the device is not to exceed the ambient temperature by more than 50°C, determine a suitable cooling technique for this device. Use Figure 15–17
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15–41E Astand-alone circuit board, 6 in. x 8 in. in size, dissipates 20 Wof power. The surface temperature of the board is not to exceed 165°F in an 85°F environment. Using Figure 15–17 as a guide, select a suitable cooling mechanism.
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15–42C What are the major considerations in the selection of a cooling technique for electronic equipment
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15–43C What is thermal resistance? To what is it analogous in electrical circuits? Can thermal resistance networks be analyzed like electrical circuits? Explain
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15–44C If the rate of heat conduction through a medium and the thermal resistance of the medium are known, how can the temperature difference between the two sides of the medium be determined
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15–45C Consider a wire of electrical resistance R, length L, and cross-sectional area A through which electric current I is flowing. How is the voltage drop across the wire determined? What happens to the voltage drop when L is doubled while I is held constant? Now consider heat conduction at a rate of Q · through the same wire having a thermal resistance of R. How is the temperature drop across the wire determined? What happens to the temperature drop when L is doubled while Q · is held constant?
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15–46C What is a heat frame? How does it enhance heat transfer along a PCB? Which components on a PCB attached to a heat frame operate at the highest temperatures: those at the middle of the PCB or those near the edge
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15–47C What is constriction resistance in heat flow? To what is it analogous in fluid flow through tubes and electric current flow in wires
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15–48C What does the junction-to-case thermal resistance of an electronic component represent? In practice, how is this value determined? How can the junction temperature of a component be determined when the case temperature, the power dissipation of the component, and the junction-to-case thermal resistance are known
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15–49C What does the case-to-ambient thermal resistance of an electronic component represent? In practice, how is this value determined? How can the case temperature of a component be determined when the ambient temperature, the power dissipation of the component, and the case-to-ambient thermal resistance are known
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15–50C Consider an electronic component whose junction-tocase thermal resistance Rjunction-case is provided by the manufacturer and whose case-to-ambient thermal resistance Rcase-ambient is determined by the thermal designer. When the power dissipation of the component and the ambient temperature are known, explain how the junction temperature can be determined. When Rjunction-case is greater than Rcase-ambient, will the case temperature be closer to the junction or ambient temperature
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15–51C Why is the rate of heat conduction along a PCB very low? How can heat conduction from the mid-parts of a PCB to its outer edges be improved? How can heat conduction across the thickness of the PCB be improved
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15–52C Why is the warping of epoxy boards that are coppercladded on one side a major concern? What is the cause of this warping? How can the warping of PCBs be avoided
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15–53C Why did the thermal conduction module receive so much attention from thermal designers of electronic equipment? How does the design of TCM differ from traditional chip carrier design? Why is the cavity in the TCM filled with helium instead of air
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15–54 Consider a chip dissipating 0.8 W of power in a DIP with 18 pin leads. The materials and the dimensions of various sections of this electronic device are given in the table.


 If the temperature of the leads is 50°C, estimate the temperature at the junction of the chip.
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15–55 A fan blows air at 25°C over a 2-W plastic DIP with 16 leads mounted on a PCB at a velocity of 300 m/min. Using data from Figure 15–23, determine the junction temperature of the electronic device. What would the junction temperature be if the fan were to fail
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15–56 Heat is to be conducted along a PCB with copper cladding on one side. The PCB is 12 cm long and 12 cm wide, and the thicknesses of the copper and epoxy layers are 0.06 mm and 0.5 mm, respectively. Disregarding heat transfer from the side surfaces, determine the percentages of heat conduction along the copper (k 386 W/m · °C) and epoxy (k 0.26 W/m · °C) layers. Also, determine the effective thermal conductivity of the PCB.
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15–57 Reconsider Problem 15–56. Using EES (or other) software, investigate the effect of the thickness of the copper layer on the percentage of heat conducted along the copper layer and the effective thermal conductivity of the PCB. Let the thickness vary from 0.02 mm to 0.10 mm. Plot the percentage of heat conducted along the copper layer and the effective thermal conductivity as a function of the thickness of the copper layer, and discuss the results
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15–58 The heat generated in the circuitry on the surface of a silicon chip (k 130 W/m · °C) is conducted to the ceramic substrate to which it is attached. The chip is 6 mm 6 mm in size and 0.5-mm thick and dissipates 3Wof power. Determine the temperature difference between the front and back surfaces of the chip in steady operation
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15–59E Consider a 6-in. 7-in. glass–epoxy laminate (k 0.15 Btu/h · ft ·°F) whose thickness is 0.05 in. Determine the thermal resistance of this epoxy layer for heat flow (a) along the 7-in.-long side and (b) across its thickness
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15–60 Consider a 15–cm x 18-cm glass–epoxy laminate (k 0.26 W/m ·°C) whose thickness is 1.4 mm. In order to reduce the thermal resistance across its thickness, cylindrical copper fillings (k 386 W/m · °C) of diameter 1 mm are to be planted throughout the board with a center-to-center distance of 3 mm. Determine the new value of the thermal resistance of the epoxy board for heat conduction across its thickness as a result of this modification
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15–61 Reconsider Problem 15–60. Using EES (or other) software, investigate the effects of the thermal conductivity and the diameter of the filling material on the thermal resistance of the epoxy board. Let the thermal conductivity vary from 10 W/m · 0C to 400 W/m · 0C and the diameter from 0.5 mm to 2.0 mm. Plot the thermal resistance as functions of the thermal conductivity and the diameter, and discuss the results
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15–62 A 12-cm 15–cm circuit board dissipating 45 W of heat is to be conduction-cooled by a 1.5-mm-thick copper heat frame (k 386 W/m · °C) 12 cm x 17 cm in size. The epoxy laminate (k 0.26 W/m · °C) has a thickness of 2 mm and is attached to the heat frame with conductive epoxy adhesive (k 1.8 W/m · °C) of thickness 0.12 mm. The PCB is attached to a heat sink by clamping a 5-mm-wide portion of the edge to the heat sink from both ends. The temperature of the heat frame at this point is 30°C. Heat is uniformly generated on the PCB at a rate of 3 Wper 1-cm x 12-cm strip. Considering only onehalf of the PCB board because of symmetry, determine the maximum surface temperature on the PCB and the temperature distribution along the heat frame.
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15–63 Consider a 15–cm x 20-cm double-sided circuit board dissipating a total of 30 Wof heat. The board consists of a 3-mm-thick epoxy layer (k 0.26 W/m · °C) with 1-mm-diameter aluminum wires (k 237 W/m · °C) inserted along the 20-cm-long direction, as shown in Figure P15–63. The distance between the centers of the aluminum wires is 2 mm. The circuit board is attached to a heat sink from both ends, and the temperature of the board at both ends is 30°C. Heat is considered to be uniformly generated on both sides of the epoxy layer of the PCB. Considering only a portion of the PCB because of symmetry, determine the magnitude and location of the maximum temperature that occurs in the PCB.
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15–64 Repeat Problem 15–63, replacing the aluminum wires by copper wires (k 386 W/m · °C)
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15–65 Repeat Problem 15–63 for a center-to-center distance of 4 mm instead of 2 mm between the wires
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15–66 Consider a thermal conduction module with 80 chips, each dissipating 4 W of power. The module is cooled by water at 18°C flowing through the cold plate on top of the module. The thermal resistances in the path of heat flow are Rchip 12°C/W between the junction and the surface of the chip, Rint 9°C/W between the surface of the chip and the outer surface of the thermal conduction module, and Rext 7°C/W between the outer surface of the module and the cooling water. Determine the junction temperature of the chip
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15–67 Consider a 0.3-mm-thick epoxy board (k 0.26 W/m · °C) that is 15 cm 20 cm in size. Now a 0.1-mm-thick layer of copper (k 386 W/m ·°C) is attached to the back surface of the PCB. Determine the effective thermal conductivity of the PCB along its 20-cm-long side. What fraction of the heat conducted along that side is conducted through copper
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15–68 A 0.5-mm-thick copper plate (k 386 W/m · °C) is sandwiched between two 3-mm-thick epoxy boards (k 0.26 W/m · °C) that are 12 cm x 18 cm in size. Determine the effective thermal conductivity of the PCB along its 18-cm-long side. What fraction of the heat conducted along that side is conducted through copper?
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15–69E A 6-in. x 8-in. x 0.06-in. copper heat frame is used to conduct 20 W of heat generated in a PCB along the 8-in.-long side toward the ends. Determine the temperature difference between the midsection and either end of the heat frame.
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15–70 A12-W power transistor is cooled by mounting it on an aluminum bracket (k 237 W/m · °C) that is attached to a liquid-cooled plate by 0.2-mm-thick epoxy adhesive (k 1.8 W/m · °C), as shown in Figure P15–70. The thermal resistance of the plastic washer is given as 2.5°C/W. Preliminary calculations show that about 20 percent of the heat is dissipated by convection and radiation, and the rest is conducted to the liquid-cooled plate. If the temperature of the cold plate is 50°C, determine the temperature of the transistor case.
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15–71C A student puts his books on top of a VCR, completely blocking the air vents on the top surface. What do you think will happen as the student watches a rented movie played by that VCR
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15–72C Can a low-power electronic system in space be cooled by natural convection? Can it be cooled by radiation? Explain
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15–73C Why are there several openings on the various surfaces of a TV, VCR, and other electronic enclosures? What happens if a TV or VCR is enclosed in a cabinet with no free air space around
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15–74C Why should radiation heat transfer always be considered in the analysis of natural convection–cooled electronic equipment
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15–75C How does atmospheric pressure affect natural convection heat transfer? What are the best and worst orientations for heat transfer from a square surface
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15–76C What is view factor? How does it affect radiation heat transfer between two surfaces
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15–77C What is emissivity? How does it affect radiation heat transfer between two surfaces?
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15–78C For most effective natural convection cooling of a PCB array, should the PCBs be placed horizontally or vertically? Should they be placed close to each other or far from each other
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15–79C Why is radiation heat transfer from the components on the PCBs in an enclosure negligible
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15–80 Consider a sealed 20-cm-high electronic box whose base dimensions are 35 cm x 50 cm that is placed on top of a stand in a room at 30°C. The emissivity of the outer surface of the box is 0.85. If the electronic components in the box dissipate a total of 100 Wof power and the outer surface temperature of the box is not to exceed 65°C, determine if this box can be cooled by natural convection and radiation alone. Assume the heat transfer from the bottom surface of the box to the stand to be negligible, and the temperature of the surrounding surfaces to be the same as the air temperature of the room.
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15–81 Repeat Problem 15–80, assuming the box is mounted on a wall instead of a stand such that it is 0.5 m high. Again, assume heat transfer from the bottom surface to the wall to be negligible
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15–82E A 0.15-W small cylindrical resistor mounted on a circuit board is 0.5 in. long and has a diameter of 0.15 in. The view of the resistor is largely blocked by the circuit board facing it, and the heat transfer from the connecting wires is negligible. The air is free to flow through the parallel flow passages between the PCBs as a result of natural convection currents. If the air temperature in the vicinity of the resistor is 130°F, determine the surface temperature of the resistor.
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15–83 A14-cm x 20-cm PCB has electronic components on one side, dissipating a total of 7 W. The PCB is mounted in a rack vertically (height 14 cm) together with other PCBs. If the surface temperature of the components is not to exceed 90°C, determine the maximum temperature of the environment in which this PCB can operate safely at sea level. What would your answer be if this rack is located at a location at 3000 m altitude where the atmospheric pressure is 70.12 kPa?
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15–84 Acylindrical electronic component whose diameter is 2 cm and length is 4 cm is mounted on a board with its axis in the vertical direction and is dissipating 3 W of power. The emissivity of the surface of the component is 0.8, and the temperature of the ambient air is 30°C. Assuming the temperature of the surrounding surfaces to be 20°C, determine the average surface temperature of the component under combined natural convection and radiation cooling
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15–85 Repeat Problem 15–84, assuming the component is oriented horizontally
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15–86 Reconsider Problem 15–84. Using EES (or other) software, investigate the effects of surface emissivity and ambient temperature on the average surface temperature of the component. Let the emissivity vary from 0.1 to 1.0 and the ambient temperature from 15ºC to 35ºC. Take the temperature of the surrounding surfaces to be 10ºC smaller than the ambient air temperature. Plot the average surface temperature as functions of the emissivity and the ambient air temperature, and discuss the results
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15–87 Consider a power transistor that dissipates 0.1 W of power in an environment at 30°C. The transistor is 0.4 cm long and has a diameter of 0.4 cm. Assuming heat to be transferred uniformly from all surfaces, determine (a) the heat flux on the surface of the transistor, in W/cm2, and (b) the surface temperature of the transistor for a combined convection and radiation heat transfer coefficient of 18 W/m2 · °C
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15–88 The components of an electronic system dissipating 150 W are located in a 1-m-long horizontal duct whose cross section is 15 cm x 15 cm. The components in the duct are cooled by forced air, which enters at 30°C at a rate of 0.4 m3/min and leaves at 45°C. The surfaces of the sheet metal duct are not painted, and thus radiation heat transfer from the outer surfaces is negligible. If the ambient air temperature is 25°C, determine (a) the heat transfer from the outer surfaces of the duct to the ambient air by natural convection and (b) the average temperature of the duct.
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15–89 Repeat Problem 15–88 for a circular horizontal duct of diameter 10 cm
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15–90 Reconsider Problem 15–88. Using EES (or other) software, investigate the effects of the volume flow rate of air and the side-length of the duct on heat transfer by natural convection and the average temperature of the duct. Let the flow rate vary from 0.1 m3/min to 0.5 m3/min, and the side-length from 10 cm to 20 cm. Plot the heat transfer rate by natural convection and the average duct temperature as functions of flow rate and side-length, and discuss the results
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15–91 Repeat Problem 15–88, assuming that the fan fails and thus the entire heat generated inside the duct must be rejected to the ambient air by natural convection from the outer surfaces of the duct
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15–92 A 20-cm x 20-cm circuit board containing 81 square chips on one side is to be cooled by combined natural convection and radiation by mounting it on a vertical surface in a room at 25°C. Each chip dissipates 0.08 W of power, and the emissivity of the chip surfaces is 0.65. Assuming the heat transfer from the back side of the circuit board to be negligible and the temperature of the surrounding surfaces to be the same as the air temperature of the room, determine the surface temperature of the chips
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15–93 Repeat Problem 15–92, assuming the circuit board to be positioned horizontally with (a) chips facing up and (b) chips facing down.
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15–94C Why is radiation heat transfer in forced-air-cooled systems disregarded
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15–95C If an electronic system can be cooled adequately by either natural convection or forced-air convection, which would you prefer? Why
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15–96C Why is forced convection cooling much more effective than natural convection cooling
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15–97C Consider a forced-air-cooled electronic system dissipating a fixed amount of power. How will increasing the flow rate of air affect the surface temperature of the components? Explain. How will it affect the exit temperature of the air
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15–98C To what do internal and external flow refer in forced convection cooling? Give an example of a forced-air-cooled electronic system that involves both types of flow
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15–99C For a specified power dissipation and air inlet temperature, how does the convection heat transfer coefficient affect the surface temperature of the electronic components? Explain
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15–100C How does high altitude affect forced convection heat transfer? How would you modify your forced-air cooling system to operate at high altitudes safely
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15–101C What are the advantages and disadvantages of placing the cooling fan at the inlet or at the exit of an electronic box
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15–102C How is the volume flow rate of air in a forced-aircooled electronic system that has a constant-speed fan established? If a few more PCBs are added to the box while keeping the fan speed constant, will the flow rate of air through the system change? Explain
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15–103C What happens if we attempt to cool an electronic system with an undersized fan? What about if we do that with an oversized fan
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15–104 Consider a hollow-core PCB that is 15 cm high and 20 cm long, dissipating a total of 30 W. The width of the air gap in the middle of the PCB is 0.25 cm. The cooling air enters the core at 30°C at a rate of 1 L/s. Assuming the heat generated to be uniformly distributed over the two side surfaces of the PCB, determine (a) the temperature at which the air leaves the hollow core and (b) the highest temperature on the inner surface of the core.
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15–105 Repeat Problem 15–104 for a hollow-core PCB dissipating 45 W
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15–106 Reconsider Problem 15–104. Using EES (or other) software, investigate the effects of the power rating of the PCB and the volume flow rate of the air on the exit temperature of the air and the maximum temperature on the inner surface of the core. Let the power vary from 20 W to 60 W and the flow rate from 0.5 L/s to 2.5 L/s. Plot the air exit temperature and the maximum surface temperature of the core as functions of power and flow rate, and discuss the results
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15–107E Atransistor with a height of 0.25 in. and a diameter of 0.2 in. is mounted on a circuit board. The transistor is cooled by air flowing over it at a velocity of 400 ft/min. If the air temperature is 140°F and the transistor case temperature is not to exceed 175°F, determine the amount of power this transistor can dissipate safely.
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15–108 A desktop computer is to be cooled by a fan. The electronic components of the computer consume 75 W of power under full-load conditions. The computer is to operate in environments at temperatures up to 45°C and at elevations up to 3400 m where the atmospheric pressure is 66.63 kPa. The exit temperature of air is not to exceed 60°C to meet reliability requirements. Also, the average velocity of air is not to exceed 110 m/min at the exit of the computer case, where the fan is installed to keep the noise level down. Determine the flow rate of the fan that needs to be installed and the diameter of the casing of the fan
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15–109 Repeat Problem 15–108 for a computer that consumes 100 W of power
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15–110 A computer cooled by a fan contains eight PCBs, each dissipating 12 W of power. The height of the PCBs is 12 cm and the length is 18 cm. The clearance between the tips of the components on the PCB and the back surface of the adjacent PCB is 0.3 cm. The cooling air is supplied by a 15-W fan mounted at the inlet. If the temperature rise of air as it flows through the case of the computer is not to exceed 15°C, determine (a) the flow rate of the air that the fan needs to deliver, (b) the fraction of the temperature rise of air due to the heat generated by the fan and its motor, and (c) the highest allowable inlet air temperature if the surface temperature of the components is not to exceed 90°C anywhere in the system.
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15–111 An array of power transistors, each dissipating 2 W of power, is to be cooled by mounting them on a 20-cm x 20-cm square aluminum plate and blowing air over the plate with a fan at 30°C with a velocity of 3 m/s. The average temperature of the plate is not to exceed 60°C. Assuming the heat transfer from the back side of the plate to be negligible, determine the number of transistors that can be placed on this plate.
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15–112 Repeat Problem 15–111 for a location at an elevation of 1610 m where the atmospheric pressure is 83.4 kPa
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15–113 Reconsider Problem 15–111. Using EES (or other) software, investigate the effects of air velocity and the maximum plate temperature on the number of transistors. Let the air velocity vary from 1 rn/s to 8 m/s and the maximum plate temperature from 40ºC to 80ºC. Plot the number of transistors as functions of air velocity and maximum plate temperature, and discuss the results
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15–114 An enclosure contains an array of circuit boards, 15 cm high and 20 cm long. The clearance between the tips of the components on the PCB and the back surface of the adjacent PCB is 0.3 cm. Each circuit board contains 75 square chips on one side, each dissipating 0.15 W of power. Air enters the space between the boards through the 0.3-cm 15–cm cross section at 40°C with a velocity of 300 m/min. Assuming the heat transfer from the back side of the circuit board to be negligible, determine the exit temperature of the air and the highest surface temperature of the chips
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15–115 The components of an electronic system dissipating 120 W are located in a 1-m-long horizontal duct whose cross section is 20 cm 20 cm. The components in the duct are cooled by forced air, which enters at 30°C at a rate of 0.5 m3/min. Assuming 80 percent of the heat generated inside is transferred to air flowing through the duct and the remaining 20 percent is lost through the outer surfaces of the duct, determine (a) the exit temperature of air and (b) the highest component surface temperature in the duct
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15–116 Repeat Problem 15–115 for a circular horizontal duct of diameter 10 cm.
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15–117C If an electronic system can be cooled adequately by either forced-air cooling or liquid cooling, which one would you prefer? Why
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15–118C Explain how direct and indirect liquid cooling systems differ from each other
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15–119C Explain how closed-loop and open-loop liquid cooling systems operate
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15–120C What are the properties of a liquid ideally suited for cooling electronic equipment
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15–121 Acold plate that supports 10 power transistors, each dissipating 40 W, is to be cooled with water. It is specified that the temperature rise of the water not exceed 4°C and the velocity of water remain under 0.5 m/s. Assuming 25 percent of the heat generated is dissipated from the components to the surroundings by convection and radiation, and the remaining 75 percent is removed by the cooling water, determine the mass flow rate of water needed and the diameter of the pipe to satisfy the restriction imposed on the flow velocity. Also, determine the case temperature of the devices if the total case-to-liquid thermal resistance is 0.04°C/W and the water enters the cold plate at 25°C
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15–122 Reconsider Problem 15–121. Using EES (or other) software, investigate the effect of the maximum temperature rise of the water on the mass flow rate of water, the diameter of the pipe, and the case temperature. Let the maximum temperature rise vary from 1ºC to 10ºC. Plot the mass flow rate, the diameter, and the case temperature as a function of the temperature rise, and discuss the results
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15–123E Water enters the tubes of a cold plate at 95°F with an average velocity of 60 ft/min and leaves at 105°F. The diameter of the tubes is 0.25 in. Assuming 15 percent of the heat generated is dissipated from the components to the surroundings by convection and radiation, and the remaining 85 percent is removed by the cooling water, determine the amount of heat generated by the electronic devices mounted on the cold plate.
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15–124 Asealed electronic box is to be cooled by tap water flowing through channels on two of its sides. It is specified that the temperature rise of the water not exceed 3°C. The power dissipation of the box is 2 kW, which is removed entirely by water. If the box operates 24 h a day, 365 days a year, determine the mass flow rate of water flowing through the box and the amount of cooling water used per year
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15–125 Repeat Problem 15–124 for a power dissipation of 3 kW.
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15–126C What are the desirable characteristics of a liquid used in immersion cooling of electronic devices
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15–127C How does an open-loop immersion cooling system operate? How does it differ from closed-loop cooling systems
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15–128C How do immersion cooling systems with internal and external cooling differ? Why are externally cooled systems limited to relatively low-power applications
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15–129C Why is boiling heat transfer used in the cooling of very high-power electronic devices instead of forced air or liquid cooling
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15–130 A logic chip used in a computer dissipates 4 W of power and has a heat transfer surface area of 0.3 cm2. If the surface of the chip is to be maintained at 70°C while being cooled by immersion in a dielectric fluid at 20°C, determine the necessary heat transfer coefficient and the type of cooling mechanism that needs to be used to achieve that heat transfer coefficient
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15–131 A 6-W chip having a surface area of 0.5 cm2 is cooled by immersing it into FC86 liquid that is maintained at a temperature of 25°C. Using the boiling curve in Figure 15–63, estimate the temperature of the chip surface.
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15–132 A logic chip cooled by immersing it in a dielectric liquid dissipates 3.5 Wof power in an environment at 50°C and has a heat transfer surface area of 0.8 cm2. The surface temperature of the chip is measured to be 95°C. Assuming the heat transfer from the surface to be uniform, determine (a) the heat flux on the surface of the chip, in W/cm2; (b) the heat transfer coefficient on the surface of the chip, in W/m2 · °C; and (c) the thermal resistance between the surface of the chip and the cooling medium, in °C/W.
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15–133 Reconsider Problem 15–132. Using EES (or other) software, investigate the effect of chip power on the heat flux, the heat transfer coefficient, and the convection resistance on chip surface. Let the power vary from 2 W to 10 W. Plot the heat flux, the heat transfer coefficient, and the thermal resistance as a function of power dissipated, and discuss the results
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15–134 A computer chip dissipates 5 W of power and has a heat transfer surface area of 0.4 cm2. If the surface of the chip is to be maintained at 55°C while being cooled by immersion in a dielectric fluid at 10°C, determine the necessary heat transfer coefficient and the type of cooling mechanism that needs to be used to achieve that heat transfer coefficient
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15–135 A 3-W chip having a surface area of 0.2 cm2 is cooled by immersing it into FC86 liquid that is maintained at a temperature of 45°C. Using the boiling curve in Figure 15–63, estimate the temperature of the chip surface.
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15–136 Alogic chip having a surface area of 0.3 cm2 is to be cooled by immersing it into FC86 liquid that is maintained at a temperature of 35°C. The surface temperature of the chip is not to exceed 60°C. Using the boiling curve in Figure 15–63, estimate the maximum power that the chip can dissipate safely
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15–137 A 2-kW electronic device that has a surface area of 120 cm2 is to be cooled by immersing it in a dielectric fluid with a boiling temperature of 60°C contained in a 1-m x 1-m x 1-m cubic enclosure. Noting that the combined natural convection and the radiation heat transfer coefficients in air are typically about 10 W/m2 · °C, determine if the heat generated inside can be dissipated to the ambient air at 20°C by natural convection and radiation. If it cannot, explain what modification you could make to allow natural convection cooling. Also, determine the heat transfer coefficients at the surface of the electronic device for a surface temperature of 80°C. Assume the liquid temperature remains constant at 60°C throughout the enclosure.
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15–138C Several power transistors are to be cooled by mounting them on a water-cooled metal plate. The total power dissipation, the mass flow rate of water through the tube, and the water inlet temperature are fixed. Explain what you would do for the most effective cooling of the transistors
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15–139C Consider heat conduction along a vertical copper bar whose sides are insulated. One person claims that the bar should be oriented such that the hot end is at the bottom and the cold end is at the top for better heat transfer, since heat rises. Another person claims that it makes no differences to heat conduction whether heat is conducted downward or upward, and thus the orientation of the bar is irrelevant. With which person do you agree
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15–140 Consider a 15–cm 15–cm multilayer circuit board dissipating 22.5 W of heat. The board consists of four layers of 0.1-mm-thick copper (k 386 W/m · °C) and three layers of 0.5-mm-thick glass–epoxy (k 0.26 W/m · °C) sandwiched together, as shown in Figure P15–140. The circuit board is attached to a heat sink from both ends, and the temperature of the board at those ends is 35°C. Heat is considered to be uniformly generated in the epoxy layers of the PCB at a rate of 0.5 W per 1-cm x 15–cm epoxy laminate strip (or 1.5 W per 1-cm x 15–cm strip of the board). Considering only a portion of the PCB because of symmetry, determine the magnitude and location of the maximum temperature that occurs in the PCB. Assume heat transfer from the top and bottom faces of the PCB to be negligible.
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15–141 Repeat Problem 15–140, assuming that the board consists of a single 1.5-mm-thick layer of glass–epoxy, with no copper layers
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15–142 The components of an electronic system that is dissipating 150 W are located in a 1-m-long horizontal duct whose cross section is 10 cm 10 cm. The components in the duct are cooled by forced air, which enters at 30°C and 50 m/min and leaves at 45°C. The surfaces of the sheet metal duct are not painted, and so radiation heat transfer from the outer surfaces is negligible. If the ambient air temperature is 30°C, determine (a) the heat transfer from the outer surfaces of the duct to the ambient air by natural convection, (b) the average temperature of the duct, and (c) the highest component surface temperature in the duct
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15–143 Two 10-Wpower transistors are cooled by mounting them on the two sides of an aluminum bracket (k 237 W/m · °C) that is attached to a liquid-cooled plate by 0.2-mm-thick epoxy adhesive (k 1.8 W/m · °C), as shown in Figure P15–143. The thermal resistance of each plastic washer is given as 2°C/W, and the temperature of the cold plate is 40°C. The surface of the aluminum plate is untreated, and thus radiation heat transfer from it is negligible because of the low emissivity of aluminum surfaces. Disregarding heat transfer from the 0.3-cm-wide edges of the aluminum plate, determine the surface temperature of the transistor case. Also, determine the fraction of heat dissipation to the ambient air by natural convection and to the cold plate by conduction. Take the ambient temperature to be 25°C
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15–144E Afan blows air at 70°F and a velocity of 500 ft/min over a 1.5-Wplastic DIPwith 24 leads mounted on a PCB. Using data from Figure 15–23, determine the junction temperature of the electronic device. What would the junction temperature be if the fan were to fail
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15–145 A15–cm 18-cm double-sided circuit board dissipating a total of 18 W of heat is to be conduction-cooled by a 1.2-mm-thick aluminum core plate (k 237 W/m · °C) sandwiched between two epoxy laminates (k 0.26 W/m · °C). Each epoxy layer has a thickness of 0.5 mm and is attached to the aluminum core plate with conductive epoxy adhesive (k 1.8 W/m · °C) of thickness 0.1 mm. Heat is uniformly generated on each side of the PCB at a rate of 0.5 W per 1-cm x 15–cm epoxy laminate strip. All of the heat is conducted along the 18-cm side since the PCB is cooled along the two 15–cm-long edges. Considering only part of the PCB board because of symmetry, determine the maximum temperature rise across the 9-cm distance between the center and the sides of the PCB.
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15–146 Ten power transistors, each dissipating 2 W, are attached to a 7-cm x 7-cm x 0.2-cm aluminum plate with a square cutout in the middle in a symmetrical arrangement, as shown in Figure P15–146. The aluminum plate is cooled from two sides by liquid at 40°C. If 70 percent of the heat generated by the transistors is estimated to be conducted through the aluminum plate, determine the temperature rise across the 1-cmwide section of the aluminum plate between the transistors and the heat sink
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15–147 The components of an electronic system are located in a 1.2-m-long horizontal duct whose cross section is 10 cm x 20 cm. The components in the duct are not allowed to come into direct contact with cooling air, and so are cooled by air flowing over the duct at 30°C with a velocity of 250 m/min. The duct is oriented such that air strikes the 10-cm-high side of the duct normally. If the surface temperature of the duct is not to exceed 60°C, determine the total power rating of the electronic devices that can be mounted in the duct. What would your answer be if the duct is oriented such that air strikes the 20-cm-high side normally?
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15–148 Repeat Problem 15–147 for a location at an altitude of 5000 m, where the atmospheric pressure is 54.05 kPa
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15–149E Acomputer that consumes 65 Wof power is cooled by a fan blowing air into the computer enclosure. The dimensions of the computer case are 6 in. x 20 in. x 24 in., and all surfaces of the case are exposed to the ambient, except for the base surface. Temperature measurements indicate that the case is at an average temperature of 95°F when the ambient temperature and the temperature of the surrounding walls are 80°F. If the emissivity of the outer surface of the case is 0.85, determine the fraction of heat lost from the outer surfaces of the computer case.
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Heat Transfer - Yunus Cengel - 2ed - Chapter 14- Solutions

14–1C How does mass transfer differ from bulk fluid flow? Can mass transfer occur in a homogeneous medium
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14–2C How is the concentration of a commodity defined? How is the concentration gradient defined? How is the diffusion rate of a commodity related to the concentration gradient
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14–3C Give examples for (a) liquid-to-gas, (b) solid-toliquid, (c) solid-to-gas, and (d) gas-to-liquid mass transfer
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14–4C Someone suggests that thermal (or heat) radiation can also be viewed as mass radiation since, according to Einstein’s formula, an energy transfer in the amount of E corresponds to a mass transfer in the amount of m E/c2. What do you think
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14–5C What is the driving force for (a) heat transfer, (b) electric current flow, (c) fluid flow, and (d) mass transfer
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14–6C What do (a) homogeneous reactions and (b) heterogeneous reactions represent in mass transfer? To what do they correspond in heat transfer?
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14–7C Both Fourier’s law of heat conduction and Fick’s law of mass diffusion can be expressed as Q · kA(dT/dx). What do the quantities Q · , k, A, and Trepresent in (a) heat conduction and (b) mass diffusion
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14–8C Mark these statements as being True or False for a binary mixture of substances A and B. (a) The density of a mixture is always equal to the sum of the densities of its constituents. (b) The ratio of the density of component A to the density of component B is equal to the mass fraction of component A. (c) If the mass fraction of component A is greater than 0.5, then at least half of the moles of the mixture are component A. (d) If the molar masses of A and B are equal to each other, then the mass fraction of A will be equal to the mole fraction of A. (e) If the mass fractions of A and B are both 0.5, then the molar mass of the mixture is simply the arithmetic average of the molar masses of A and B.
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14–9C Mark these statements as being True or False for a binary mixture of substances A and B. (a) The molar concentration of a mixture is always equal to the sum of the molar concentrations of its constituents. (b) The ratio of the molar concentration of A to the molar concentration of B is equal to the mole fraction of component A. (c) If the mole fraction of component A is greater than 0.5, then at least half of the mass of the mixture is component A. (d) If both Aand Bare ideal gases, then the pressure fraction of A is equal to its mole fraction. (e) If the mole fractions of A and B are both 0.5, then the molar mass of the mixture is simply the arithmetic average of the molar masses of A and B
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14–10C Fick’s law of diffusion is expressed on the mass and mole basis as m · diff, A = -pADAB(dwA/dx) and N · diff, A = -CADAB(dyA/dx), respectively. Are the diffusion coefficients DAB in the two relations the same or different
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14–11C How does the mass diffusivity of a gas mixture change with (a) temperature and (b) pressure
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14–12C At a given temperature and pressure, do you think the mass diffusivity of air in water vapor will be equal to the mass diffusivity of water vapor in air? Explain
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14–13C At a given temperature and pressure, do you think the mass diffusivity of copper in aluminum will be equal to the mass diffusivity of aluminum in copper? Explain
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14–14C In a mass production facility, steel components are to be hardened by carbon diffusion. Would you carry out the hardening process at room temperature or in a furnace at a high temperature, say 900°C? Why
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14–15C Someone claims that the mass and the mole fractions for a mixture of CO2 and N2O gases are identical. Do you agree? Explain
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14–16 The composition of moist air is given on a molar basis to be 78 percent N2, 20 percent O2, and 2 percent water vapor. Determine the mass fractions of the constituents of air.
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14–17E Agas mixture consists of 5 lbm of O2, 8 lbm of N2, and 10 lbm of CO2. Determine (a) the mass fraction of each component, (b) the mole fraction of each component, and (c) the average molar mass of the mixture
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14–18 Agas mixture consists of 8 kmol of H2 and 2 kmol of N2. Determine the mass of each gas and the apparent gas constant of the mixture.
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14–19 The molar analysis of a gas mixture at 290 K and 250 kPa is 65 percent N2, 20 percent O2, and 15 percent CO2. Determine the mass fraction and partial pressure of each gas
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14–20 Determine the binary diffusion coefficient of CO2 in air at (a) 200 K and 1 atm, (b) 400 K and 0.8 atm, and (c) 600 K and 3 atm
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14–21 Repeat Problem 14–20 for O2 in N2
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14–22E The relative humidity of air at 80°F and 14.7 psia is increased from 30 percent to 90 percent during a humidification process at constant temperature and pressure. Determine the percent error involved in assuming the density of air to have remained constant.
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14–23 The diffusion coefficient of hydrogen in steel is given as a function of temperature as DAB = 1.65 x 10-6 exp(–4630/T) (m 2/s) where T is in K. Determine the diffusion coefficients from 200 K to 1200 K in 200 K increments and plot the results
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14–24 Reconsider Problem 14–23. Using EES (or other) software, plot the diffusion coefficient as a function of the temperature in the range of 200 K to 1200 K.
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14–25C Write three boundary conditions for mass transfer (on a mass basis) for species A at x 0 that correspond to specified temperature, specified heat flux, and convection boundary conditions in heat transfer
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14–26C What is an impermeable surface in mass transfer? How is it expressed mathematically (on a mass basis)? To what does it correspond in heat transfer
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14–27C Consider the free surface of a lake exposed to the atmosphere. If the air at the lake surface is saturated, will the mole fraction of water vapor in air at the lake surface be the same as the mole fraction of water in the lake (which is nearly 1)
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14–28C When prescribing a boundary condition for mass transfer at a solid–gas interface, why do we need to specify the side of the surface (whether the solid or the gas side)? Why did we not do it in heat transfer
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14–29C Using properties of saturated water, explain how you would determine the mole fraction of water vapor at the surface of a lake when the temperature of the lake surface and the atmospheric pressure are specified
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14–30C Using solubility data of a solid in a specified liquid, explain how you would determine the mass fraction of the solid in the liquid at the interface at a specified temperature
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14–31C Using solubility data of a gas in a solid, explain how you would determine the molar concentration of the gas in the solid at the solid–gas interface at a specified temperature
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14–32C Using Henry’s constant data for a gas dissolved in a liquid, explain how you would determine the mole fraction of the gas dissolved in the liquid at the interface at a specified temperature
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14–33C What is permeability? How is the permeability of a gas in a solid related to the solubility of the gas in that solid
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14–34E Determine the mole fraction of the water vapor at the surface of a lake whose temperature at the surface is 60°F, and compare it to the mole fraction of water in the lake. Take the atmospheric pressure at lake level to be 13.8 psia
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14–35 Determine the mole fraction of dry air at the surface of a lake whose temperature is 15°C. Take the atmospheric pressure at lake level to be 100 kPa.
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14–36 Reconsider Problem 14–35. Using EES (or other) software, plot the mole fraction of dry air at the surface of the lake as a function of the lake temperature as the temperatue varies from 5°C to 25°C, and discuss the results
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14–37 Consider a rubber plate that is in contact with nitrogen gas at 298 K and 250 kPa. Determine the molar and mass densities of nitrogen in the rubber at the interface.
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14–38 A wall made of natural rubber separates O2 and N2 gases at 25°C and 500 kPa. Determine the molar concentrations of O2 and N2 in the wall
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14–39 Consider a glass of water in a room at 20°C and 97 kPa. If the relative humidity in the room is 100 percent and the water and the air are in thermal and phase equilibrium, determine (a) the mole fraction of the water vapor in the air and (b) the mole fraction of air in the water
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14–40E Water is sprayed into air at 80°F and 14.3 psia, and the falling water droplets are collected in a container on the floor. Determine the mass and mole fractions of air dissolved in the water
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14–41 Consider a carbonated drink in a bottle at 27°C and 130 kPa. Assuming the gas space above the liquid consists of a saturated mixture of CO2 and water vapor and treating the drink as water, determine (a) the mole fraction of the water vapor in the CO2 gas and (b) the mass of dissolved CO2 in a 200-ml drink.
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14–42C Write down the relations for steady one-dimensional heat conduction and mass diffusion through a plane wall, and identify the quantities in the two equations that correspond to each other
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14–43C Consider steady one-dimensional mass diffusion through a wall. Mark these statements as being True or False. (a) Other things being equal, the higher the density of the wall, the higher the rate of mass transfer. (b) Other things being equal, doubling the thickness of the wall will double the rate of mass transfer. (c) Other things being equal, the higher the temperature, the higher the rate of mass transfer. (d) Other things being equal, doubling the mass fraction of the diffusing species at the high concentration side will double the rate of mass transfer
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14–44C Consider one-dimensional mass diffusion of species A through a plane wall of thickness L. Under what conditions will the concentration profile of species A in the wall be a straight line
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14–45C Consider one-dimensional mass diffusion of species A through a plane wall. Does the species A content of the wall change during steady mass diffusion? How about during transient mass diffusion
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14–46 Helium gas is stored at 293 K in a 3-m-outer-diameter spherical container made of 5-cm-thick Pyrex. The molar concentration of helium in the Pyrex is 0.00073 kmol/m3 at the inner surface and negligible at the outer surface. Determine the mass flow rate of helium by diffusion through the Pyrex container.
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14–47 Athin plastic membrane separates hydrogen from air. The molar concentrations of hydrogen in the membrane at the inner and outer surfaces are determined to be 0.065 and 0.003 kmol/m3, respectively. The binary diffusion coefficient of hydrogen in plastic at the operation temperature is 5.3 x 10-10 m2/s. Determine the mass flow rate of hydrogen by diffusion through the membrane under steady conditions if the thickness of the membrane is (a) 2 mm and (b) 0.5 mm
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14–48 The solubility of hydrogen gas in steel in terms of its mass fraction is given as w = 2.09 x 10-4 exp(–3950/T) where is the partial pressure of hydrogen in bars and T is the temperature in K. If natural gas is transported in a 1-cmthick, 3-m-internal-diameter steel pipe at 500 kPa pressure and the mole fraction of hydrogen in the natural gas is 8 percent, determine the highest rate of hydrogen loss through a 100-mlong section of the pipe at steady conditions at a temperature of293 K if the pipe is exposed to air. Take the diffusivity of hydrogen in steel to be 2.9 x 10-13 m2/s.
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14–49 Reconsider Problem 14–48. Using EES (or other) software, plot the highest rate of hydrogen loss as a function of the mole fraction of hydrogen in natural gas as the mole fraction varies from 5 to 15 percent, and discuss the results
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14–50 Helium gas is stored at 293 K and 500 kPa in a 1-cmthick, 2-m-inner-diameter spherical tank made of fused silica (SiO2). The area where the container is located is well ventilated. Determine (a) the mass flow rate of helium by diffusion through the tank and (b) the pressure drop in the tank in one week as a result of the loss of helium gas
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14–51 You probably have noticed that balloons inflated with helium gas rise in the air the first day during a party but they fall down the next day and act like ordinary balloons filled with air. This is because the helium in the balloon slowly leaks out through the wall while air leaks in by diffusion. Consider a balloon that is made of 0.1-mm-thick soft rubber and has a diameter of 15 cm when inflated. The pressure and temperature inside the balloon are initially 110 kPa and 25°C. The permeability of rubber to helium, oxygen, and nitrogen at 25°C are 9.4 x 10-13, 7.05 x 10-13, and 2.6 x 10-13 kmol/m · s · bar, respectively. Determine the initial rates of diffusion of helium, oxygen, and nitrogen through the balloon wall and the mass fraction of helium that escapes the balloon during the first 5 h assuming the helium pressure inside the balloon remains nearly constant. Assume air to be 21 percent oxygen and 79 percent nitrogen by mole numbers and take the room conditions to be 100 kPa and 25°C.
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14–52 Reconsider the balloon discussed in Problem 14–51. Assuming the volume to remain constant and disregarding the diffusion of air into the balloon, obtain a relation for the variation of pressure in the balloon with time. Using the results obtained and the numerical values given in the problem, determine how long it will take for the pressure inside the balloon to drop to 100 kPa
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14–53 Pure N2 gas at 1 atm and 25°C is flowing through a 10-m-long, 3-cm-inner diameter pipe made of 1-mm-thick rubber. Determine the rate at which N2 leaks out of the pipe if the medium surrounding the pipe is (a) a vacuum and (b) atmospheric air at 1 atm and 25°C with 21 percent O2 and 79 percent N2.
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14–54C Consider a tank that contains moist air at 3 atm and whose walls are permeable to water vapor. The surrounding air at 1 atm pressure also contains some moisture. Is it possible for the water vapor to flow into the tank from surroundings? Explain
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14–55C Express the mass flow rate of water vapor through a wall of thickness L in terms of the partial pressure of water vapor on both sides of the wall and the permeability of the wall to the water vapor
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14–56C How does the condensation or freezing of water vapor in the wall affect the effectiveness of the insulation in the wall? How does the moisture content affect the effective thermal conductivity of soil
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14–57C Moisture migration in the walls, floors, and ceilings of buildings is controlled by vapor barriers or vapor retarders. Explain the difference between the two, and discuss which is more suitable for use in the walls of residential buildings
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14–58C What are the adverse effects of excess moisture on the wood and metal components of a house and the paint on the walls
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14–59C Why are the insulations on the chilled water lines always wrapped with vapor barrier jackets
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14–60C Explain how vapor pressure of the ambient air is determined when the temperature, total pressure, and relative humidity of the air are given
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14–61 The diffusion of water vapor through plaster boards and its condensation in the wall insulation in cold weather are of concern since they reduce the effectiveness of insulation. Consider a house that is maintained at 20°C and 60 percent relative humidity at a location where the atmospheric pressure is 97 kPa. The inside of the walls is finished with 9.5-mm-thick gypsum wallboard. Taking the vapor pressure at the outer side of the wallboard to be zero, determine the maximum amount of water vapor that will diffuse through a 3-m x 8-m section of a wall during a 24-h period. The permeance of the 9.5-mm-thick gypsum wallboard to water vapor is 2.86 x 10-9 kg/s · m2 · Pa
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14–62 Reconsider Problem 14–61. In order to reduce the migration of water vapor through the wall, it is proposed to use a 0.2-mm-thick polyethylene film with a permeance of 2.3 x 10-12 kg/s · m2 · Pa. Determine the amount of water vapor that will diffuse through the wall in this case during a 24-h period.
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14–63 The roof of a house is 15 m x 8 m and is made of a 20-cm-thick concrete layer. The interior of the house is maintained at 25°C and 50 percent relative humidity and the local atmospheric pressure is 100 kPa. Determine the amount of water vapor that will migrate through the roof in 24 h if the average outside conditions during that period are 3°C and 30 percent relative humidity. The permeability of concrete to water vapor is 24.7 x 10-12 kg/s · m · Pa
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14–64 Reconsider Problem 14–63. Using EES (or other) software, investigate the effects of temperature and relative humidity of air inside the house on the amount of water vapor that will migrate through the roo
f. Let the temperature vary from 15°C to 30°C and the relative humidity from 30 to 70 percent. Plot the amount of water vapor that will migrate as functions of the temperature and the relative humidity, and discuss the results
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14–65 Reconsider Problem 14–63. In order to reduce the migration of water vapor, the inner surface of the wall is painted with vapor retarder latex paint whose permeance is 26 x 10-12 kg/s · m2 · Pa. Determine the amount of water vapor that will diffuse through the roof in this case during a 24-h period
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14–66 Aglass of milk left on top of a counter in the kitchen at 25°C, 88 kPa, and 50 percent relative humidity is tightly sealed by a sheet of 0.009-mm-thick aluminum foil whose permeance is 2.9 x 10-12 kg/s · m2 · Pa. The inner diameter of the glass is 12 cm. Assuming the air in the glass to be saturated at all times, determine how much the level of the milk in the glass will recede in 12 h.
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14–67C In transient mass diffusion analysis, can we treat the diffusion of a solid into another solid of finite thickness (such as the diffusion of carbon into an ordinary steel component) as a diffusion process in a semi-infinite medium? Explain
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14–68C Define the penetration depth for mass transfer, and explain how it can be determined at a specified time when the diffusion coefficient is known
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14–69C When the density of a species A in a semi-infinite medium is known at the beginning and at the surface, explain how you would determine the concentration of the species A at a specified location and time
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14–70 A steel part whose initial carbon content is 0.12 percent by mass is to be case-hardened in a furnace at 1150 K by exposing it to a carburizing gas. The diffusion coefficient of carbon in steel is strongly temperature dependent, and at the furnace temperature it is given to be DAB = 7.2 x 10-12 m2/s. Also, the mass fraction of carbon at the exposed surface of the steel part is maintained at 0.011 by the carbon-rich environment in the furnace. If the hardening process is to continue until the mass fraction of carbon at a depth of 0.7 mm is raised to 0.32 percent, determine how long the part should be held in the furnace.
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14–71 Repeat Problem 14–70 for a furnace temperature of 500 K at which the diffusion coefficient of carbon in steel is DAB = 2.1 x 10-20 m2/s
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14–72 Apond with an initial oxygen content of zero is to be oxygenated by forming a tent over the water surface and filling the tent with oxygen gas at 25°C and 130 kPa. Determine the mole fraction of oxygen at a depth of 2 cm from the surface after 12 h.
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14–73 A long nickel bar with a diameter of 5 cm has been stored in a hydrogen-rich environment at 358 K and 300 kPa for a long time, and thus it contains hydrogen gas throughout uniformly. Now the bar is taken into a well-ventilated area so that the hydrogen concentration at the outer surface remains at almost zero at all times. Determine how long it will take for the hydrogen concentration at the center of the bar to drop by hal
f. The diffusion coefficient of hydrogen in the nickel bar at the room temperature of 298 K can be taken to be DAB = 1.2 x 10-12 m2/s.
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14–74C Define the following terms: mass-average velocity, diffusion velocity, stationary medium, and moving medium
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14–75C What is diffusion velocity? How does it affect the mass-average velocity? Can the velocity of a species in a moving medium relative to a fixed reference point be zero in a moving medium? Explain
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14–76C What is the difference between mass-average velocity and mole-average velocity during mass transfer in a moving medium? If one of these velocities is zero, will the other also necessarily be zero? Under what conditions will these two velocities be the same for a binary mixture
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14–77C Consider one-dimensional mass transfer in a moving medium that consists of species A and B with p= pA + pB = constant. Mark these statements as being True or False. (a) The rates of mass diffusion of species A and B are equal in magnitude and opposite in direction. (b) DAB = DBA. (c) During equimolar counterdiffusion through a tube, equal numbers of moles of A and B move in opposite directions, and thus a velocity measurement device placed in the tube will read zero. (d) The lid of a tank containing propane gas (which is heavier than air) is left open. If the surrounding air and the propane in the tank are at the same temperature and pressure, no propane will escape the tank and no air will enter
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14–78C What is Stefan flow? Write the expression for Stefan’s law and indicate what each variable represents
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14–79E The pressure in a pipeline that transports helium gas at a rate of 5 lbm/s is maintained at 14.5 psia by venting helium to the atmosphere through a -in. internal diameter tube that extends 30 ft into the air. Assuming both the helium and the atmospheric air to be at 80°F, determine (a) the mass flow rate of helium lost to the atmosphere through an individual tube, (b) the mass flow rate of air that infiltrates into the pipeline, and (c) the flow velocity at the bottom of the tube where it is attached to the pipeline that will be measured by an anemometer in steady operation.
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14–80E Repeat Problem 14–79E for a pipeline that transports carbon dioxide instead of helium
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14–81 Atank with a 2-cm thick shell contains hydrogen gas at the atmospheric conditions of 25°C and 90 kPa. The charging valve of the tank has an internal diameter of 3 cm and extends 8 cm above the tank. If the lid of the tank is left open so that hydrogen and air can undergo equimolar counterdiffusion through the 10-cm-long passageway, determine the mass flow rate of hydrogen lost to the atmosphere through the valve at the initial stages of the process.
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14–82 Reconsider Problem 14–81. Using EES (or other) software, plot the mass flow rate of hydrogen lost as a function of the diameter of the charging valve as the diameter varies from 1 cm to 5 cm, and discuss the results
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14–83E A1-in.-diameter Stefan tube is used to measure the binary diffusion coefficient of water vapor in air at 70°F and 13.8 psia. The tube is partially filled with water with a distance from the water surface to the open end of the tube of 10 in. Dry air is blown over the open end of the tube so that water vapor rising to the top is removed immediately and the concentration of vapor at the top of the tube is zero. During 10 days of continuous operation at constant pressure and temperature, the amount of water that has evaporated is measured to be 0.0015 lbm. Determine the diffusion coefficient of water vapor in air at 70°F and 13.8 psia
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14–84 An 8-cm-internal-diameter, 30-cm-high pitcher half filled with water is left in a dry room at 15°C and 87 kPa with its top open. If the water is maintained at 15°C at all times also, determine how long it will take for the water to evaporate completely.
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14–85 Alarge tank containing ammonia at 1 atm and 25°C is vented to the atmosphere through a 3-m-long tube whose internal diameter is 1 cm. Determine the rate of loss of ammonia and the rate of infiltration of air into the tank.
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14–86C Heat convection is expressed by Newton’s law of cooling as Q = hA(Ts - T∞). Express mass convection in an analogous manner on a mass basis, and identify all the quantities in the expression and state their units.
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14–87C What is a concentration boundary layer? How is it defined for flow over a plate
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14–88C What is the physical significance of the Schmidt number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Schmidt number of 1 indicate
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14–89C What is the physical significance of the Sherwood number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Sherwood number of 1 indicate for a plain fluid layer
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14–90C What is the physical significance of the Lewis number? How is it defined? What does a Lewis number of 1 indicate
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14–91C In natural convection mass transfer, the Grashof number is evaluated using density difference instead of temperature difference. Can the Grashof number evaluated this way be used in heat transfer calculations also
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14–92C Using the analogy between heat and mass transfer, explain how the mass transfer coefficient can be determined from the relations for the heat transfer coefficient
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14–93C It is well known that warm air in a cooler environment rises. Now consider a warm mixture of air and gasoline (C8H18) on top of an open gasoline can. Do you think this gas mixture will rise in a cooler environment
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14–94C Consider two identical cups of coffee, one with no sugar and the other with plenty of sugar at the bottom. Initially, both cups are at the same temperature. If left unattended, which cup of coffee will cool faster
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14–95C Under what conditions will the normalized velocity, thermal, and concentration boundary layers coincide during flow over a flat plate
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14–96C What is the relation ( f/2) Re = Nu = Sh known as? Under what conditions is it valid? What is the practical importance of it
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14–97C What is the name of the relation f/2 = St Pr2/3 = StmassSc2/3 and what are the names of the variables in it? Under what conditions is it valid? What is the importance of it in engineering
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14–98C What is the relation hheat =pCphmass known as? For what kind of mixtures is it valid? What is the practical importance of it
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14–99C What is the low mass flux approximation in mass transfer analysis? Can the evaporation of water from a lake be treated as a low mass flux process
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14–100E Consider a circular pipe of inner diameter D = 0.5 in. whose inner surface is covered with a thin layer of liquid water as a result of condensation. In order to dry the pipe, air at 540 R and 1 atm is forced to flow through it with an average velocity of 4 ft/s. Using the analogy between heat and mass transfer, determine the mass transfer coefficient inside the pipe for fully developed flow.
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14–101 The average heat transfer coefficient for air flow over an odd-shaped body is to be determined by mass transfer measurements and using the Chilton–Colburn analogy between heat and mass transfer. The experiment is conducted by blowing dry air at 1 atm at a free stream velocity of 2 m/s over a body covered with a layer of naphthalene. The surface area of the body is 0.75 m2, and it is observed that 100 g of naphthalene has sublimated in 45 min. During the experiment, both the body and the air were kept at 25°C, at which the vapor pressure and mass diffusivity of naphthalene are 11 Pa and DAB = 0.61 x 10-5 m2/s, respectively. Determine the heat transfer coefficient under the same flow conditions over the same geometry.
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14–102 Consider a 15-cm-internal-diameter, 10-m-long circular duct whose interior surface is wet. The duct is to be dried by forcing dry air at 1 atm and 15°C through it at an average velocity of 3 m/s. The duct passes through a chilled room, and it remains at an average temperature of 15°C at all times. Determine the mass transfer coefficient in the duct
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14–103 Reconsider Problem 14–102. Using EES (or other) software, plot the mass transfer coefficient as a function of the air velocity as the velocity varies from 1 m/s to 8 m/s, and discuss the results
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14–104 Dry air at 15°C and 92 kPa flows over a 2-m-long wet surface with a free stream velocity of 4 m/s. Determine the average mass transfer coefficient.
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14–105 Consider a 5-m x 5-m wet concrete patio with an average water film thickness of 0.3 mm. Now wind at 50 km/h is blowing over the surface. If the air is at 1 atm, 15°C, and 35 percent relative humidity, determine how long it will take for the patio to dry completely.
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14–106E A2-in.-diameter spherical naphthalene ball is suspended in a room at 1 atm and 80°F. Determine the average mass transfer coefficient between the naphthalene and the air if air is forced to flow over naphthalene with a free stream velocity of 15 ft/s. The Schmidt number of naphthalene in air at room temperature is 2.35.
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14–107 Consider a 3-mm-diameter raindrop that is falling freely in atmospheric air at 25°C. Taking the temperature of the raindrop to be 9°C, determine the terminal velocity of the raindrop at which the drag force equals the weight of the drop and the average mass transfer coefficient at that time
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14–108 In a manufacturing facility, wet brass plates coming out of a water bath are to be dried by passing them through a section where dry air at 1 atm and 25°C is blown parallel to their surfaces. If the plates are at 20°C and there are no dry spots, determine the rate of evaporation from both sides of a plate.
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14–109E Air at 80°F, 1 atm, and 30 percent relative humidity is blown over the surface of a 15-in. x 15-in. square pan filled with water at a free stream velocity of 10 ft/s. If the water is maintained at a uniform temperature of 80°F, determine the rate of evaporation of water and the amount of heat that needs to be supplied to the water to maintain its temperature constant
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14–110E Repeat Problem 14–109E for temperature of 60°F for both the air and water.
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14–111C Does a mass transfer process have to involve heat transfer? Describe a process that involves both heat and mass transfer
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14–112C Consider a shallow body of water. Is it possible for this water to freeze during a cold and dry night even when the ambient air and surrounding surface temperatures never drop to 0°C? Explain.
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14–113C During evaporation from a water body to air, under what conditions will the latent heat of vaporization be equal to convection heat transfer from the air
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14–114 Jugs made of porous clay were commonly used to cool water in the past. Asmall amount of water that leaks out keeps the outer surface of the jug wet at all times, and hot and relatively dry air flowing over the jug causes this water to evaporate. Part of the latent heat of evaporation comes from the water in the jug, and the water is cooled as a result. If the environment conditions are 1 atm, 30°C, and 35 percent relative humidity, determine the temperature of the water when steady conditions are reached.
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14–115 Reconsider Problem 14–114. Using EES (or other) software, plot the water temperature as a function of the relative humidity of air as the relative humidity varies from 10 to 100 percent, and discuss the results
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14–116E During a hot summer day, a 2-Lbottle drink is to be cooled by wrapping it in a cloth kept wet continually and blowing air to it with a fan. If the environment conditions are 1 atm, 80°F, and 30 percent relative humidity, determine the temperature of the drink when steady conditions are reached
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14–117 A glass bottle washing facility uses a wellagitated hot water bath at 55°C with an open top that is placed on the ground. The bathtub is 1 m high, 2 m wide, and 4 m long and is made of sheet metal so that the outer side surfaces are also at about 55°C. The bottles enter at a rate of 800 per minute at ambient temperature and leave at the water temperature. Each bottle has a mass of 150 g and removes 0.6 g of water as it leaves the bath wet. Makeup water is supplied at 15°C. If the average conditions in the plant are 1 atm, 25°C, and 50 percent relative humidity, and the average temperature of the surrounding surfaces is 15°C, determine (a) the amount of heat and water removed by the bottles themselves per second; (b) the rate of heat loss from the top surface of the water bath by radiation, natural convection, and evaporation; (c) the rate of heat loss from the side surfaces by natural convection and radiation; and (d) the rate at which heat and water must be supplied to maintain steady operating conditions. Disregard heatloss through the bottom surface of the bath and take the emissivities of sheet metal and water to be 0.61 and 0.95, respectively.
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14–118 Repeat Problem 14–117 for a water bath temperature of 50°C
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14–119 One way of increasing heat transfer from the head on a hot summer day is to wet it. This is especially effective in windy weather, as you may have noticed. Approximating the head as a 30-cm-diameter sphere at 30°C with an emissivity of 0.95, determine the total rate of heat loss from the head at ambient air conditions of 1 atm, 25°C, 40 percent relative humidity, and 25 km/h winds if the head is (a) dry and (b) wet. Take the surrounding temperature to be 25°C.
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14–120 A2-m-deep 20-m x 20-m heated swimming pool is maintained at a constant temperature of 30°C at a location where the atmospheric pressure is 1 atm. If the ambient air is at 20°C and 60 percent relative humidity and the effective sky temperature is 0°C, determine the rate of heat loss from the top surface of the pool by (a) radiation, (b) natural convection, and (c) evaporation. (d) Assuming the heat losses to the ground to be negligible, determine the size of the heater
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14–121 Repeat Problem 14–120 for a pool temperature of 25°C.
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14–122C Mark these statements as being True or False. (a) The units of mass diffusivity, heat diffusivity, and momentum diffusivity are all the same. (b) If the molar concentration (or molar density) C of a mixture is constant, then its density p must also be constant. (c) If the mass-average velocity of a binary mixture is zero, then the mole-average velocity of the mixture must also be zero. (d) If the mole fractions of A and B of a mixture are both 0.5, then the molar mass of the mixture is simply the arithmetic average of the molar masses of A and B
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14–123 Using Henry’s law, show that the dissolved gases in a liquid can be driven off by heating the liquid.
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14–124 Show that for an ideal gas mixture maintained at a constant temperature and pressure, the molar concentration C of the mixture remains constant but this is not necessarily the case for the density p of the mixture
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14–125E Agas mixture in a tank at 600 R and 20 psia consists of 1 lbm of CO2 and 3 lbm of CH4. Determine the volume of the tank and the partial pressure of each gas
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14–126 Dry air whose molar analysis is 78.1 percent N2, 20.9 percent O2, and 1 percent Ar flows over a water body until it is saturated. If the pressure and temperature of air remain constant at 1 atm and 25°C during the process, determine (a) the molar analysis of the saturated air and (b) the density of air before and after the process. What do you conclude from your results
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14–127 Consider a glass of water in a room at 25°C and 100 kPa. If the relative humidity in the room is 70 percent and the water and the air are at the same temperature, determine (a) the mole fraction of the water vapor in the room air, (b) the mole fraction of the water vapor in the air adjacent to the water surface, and (c) the mole fraction of air in the water near the surface.
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14–128 The diffusion coefficient of carbon in steel is given as DAB = 2.67 x 10-5 exp(–17,400/T)m 2/s where T is in K. Determine the diffusion coefficient from 300 K to 1500 K in 100 K increments and plot the results
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14–129 Acarbonated drink is fully charged with CO2 gas at 17°C and 600 kPa such that the entire bulk of the drink is in thermodynamic equilibrium with the CO2–water vapor mixture. Now consider a 2-Lsoda bottle. If the CO2 gas in that bottle were to be released and stored in a container at 25°C and 100 kPa, determine the volume of the container.
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14–130 Consider a brick house that is maintained at 20°C and 60 percent relative humidity at a location where the atmospheric pressure is 85 kPa. The walls of the house are made of 20-cm thick brick whose permeance is 23 x 10-9 kg/s · m2 · Pa. Taking the vapor pressure at the outer side of the wallboard to be zero, determine the maximum amount of water vapor that will diffuse through a 4-m x 7-m section of a wall during a 24-h period
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14–131E Consider a masonry cavity wall that is built around 6-in.-thick concrete blocks. The outside is finished with 4-in. face brick with -in. cement mortar between the bricks and concrete blocks. The inside finish consists of -in. gypsum wallboard separated from the concrete block by -in.-thick air space. The thermal and vapor resistances of various components for a unit wall area are as follows:

The indoor conditions are 70°F and 65 percent relative humidity while the outdoor conditions are 32°F and 40 percent relative humidity. Determine the rates of heat and water vapor transfer through a 9-ft x 25-ft section of the wall.
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14–132 The oxygen needs of fish in aquariums are usually met by forcing air to the bottom of the aquarium by a compressor. The air bubbles provide a large contact area between the water and the air, and as the bubbles rise, oxygen and nitrogen gases in the air dissolve in water while some water evaporates into the bubbles. Consider an aquarium that is maintained at room temperature of 25°C at all times. The air bubbles are observed to rise to the free surface of water in 2 s. If the air entering the aquarium is completely dry and the diameter of the air bubbles is 4 mm, determine the mole fraction of water vapor at the center of the bubble when it leaves the aquarium. Assume no fluid motion in the bubble so that water vapor propagates in the bubble by diffusion only.
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14–133 Oxygen gas is forced into an aquarium at 1 atm and 25°C, and the oxygen bubbles are observed to rise to the free surface in 2 s. Determine the penetration depth of oxygen into water from a bubble during this time period.
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14–134 Consider a 30-cm-diameter pan filled with water at 15°C in a room at 20°C, 1 atm, and 30 percent relative humidity. Determine (a) the rate of heat transfer by convection, (b) the rate of evaporation of water, and (c) the rate of heat transfer to the water needed to maintain its temperature at 15°C. Disregard any radiation effects
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14–135 Repeat Problem 14–134 assuming a fan blows air over the water surface at a velocity of 3 m/s. Take the radius of the pan to be the characteristic length
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14–136 Naphthalene is commonly used as a repellent against moths to protect clothing during storage. Consider a 1-cmdiameter spherical naphthalene ball hanging in a closet at 25°C and 1 atm. Considering the variation of diameter with time, determine how long it will take for the naphthalene to sublimate completely. The density and vapor pressure of naphthalene at 25°C are 0.11 Pa and 1100 kg/m3 and 11 Pa, respectively, and the mass diffusivity of naphthalene in air at 25°C is DAB = 0.61 x 10-5 m2/s.
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14–137E Aswimmer extends his wet arms into the windy air outside at 1 atm, 40°F, 50 percent relative humidity, and 20 mph. If the average skin temperature is 80°F, determine the rate at which water evaporates from both arms and the corresponding rate of heat transfer by evaporation. The arm can be modeled as a 2-ft-long and 3-in.-diameter cylinder with adiabatic ends
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14–138 Athick part made of nickel is put into a room filled with hydrogen at 3 atm and 85°C. Determine the hydrogen concentration at a depth of 2-mm from the surface after 24 h.
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14–139 Amembrane made of 0.1-mm-thick soft rubber separates pure O2 at 1 atm and 25°C from air at 1.2 atm pressure. Determine the mass flow rate of O2 through the membrane per unit area and the direction of flow
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14–140E The top section of an 8-ft-deep 100-ft x 100-ft heated solar pond is maintained at a constant temperature of 80°F at a location where the atmospheric pressure is 1 atm. If the ambient air is at 70°F and 100 percent relative humidity and wind is blowing at an average velocity of 40 mph, determine the rate of heat loss from the top surface of the pond by (a) forced convection, (b) radiation, and (c) evaporation. Take the average temperature of the surrounding surfaces to be 60°F
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14–141E Repeat Problem 14–140E for a solar pond surface temperature of 90°F.
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