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7–2C What is the difference between streamlined and blunt bodies? Is a tennis ball a streamlined or blunt body
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7–3C What is drag? What causes it? Why do we usually try to minimize it
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7–4C What is lift? What causes it? Does wall shear contribute to the lift
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7–5C During flow over a given body, the drag force, the upstream velocity, and the fluid density are measured. Explain how you would detennine the drag coefficient. What area would you use in calculations
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7–6C Define frontal area of a body subjected to external flow. When is it appropriate to use the frontal area in drag and lift calculations
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7–7C What is the difference between skin friction drag and pressure drag? Which is usually more significant for slender bodies such as airfoils
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7–8C What is the effect of surface roughness on the friction drag coefficient in laminar and turbulent flows
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7–9C What is the effect of streamlining on (a) friction drag and (b) pressure drag? Does the total drag acting on a body necessarily decrease as a result of streamlining? Explain.
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7–10C What is flow separation? What causes it? What is the effect of flow separation on the drag coefficient?
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7–11C What does the friction coefficient represent in flow over a flat plate? How is it related to the drag force acting on the plate
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7–12C Consider laminar flow over a flat plate. Will the friction coefficient change with distance from the leading edge? How about the heat transfer coefficient
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7–13C How are the average friction and heat transfer coefficients determined in flow over a flat plate
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7–14 Engine oil at 80°C flows over a 6-m-long flat plate whose temperature is 30°C with a velocity of 3 m/s. Determine the total drag force and the rate of heat transfer over the entire plate per unit width
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7–15 The local atmospheric pressure in Denver, Colorado (elevation 1610 m), is 83.4 kPa. Air at this pressure and at 30°C flows with a velocity of 6 m/s over a 2.5-m 8-m flat plate whose temperature is 120°C. Determine the rate of heat transfer from the plate if the air flows parallel to the (a) 8-m-long side and (b) the 2.5-m side
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7–16 During a cold winter day, wind at 55 km/h is blowing parallel to a 4-m-high and 10-m-long wall of a house. If the air outside is at 5°C and the surface temperature of the wall is 12°C, determine the rate of heat loss from that wall by convection. What would your answer be if the wind velocity was doubled?
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7–17 Reconsider Problem 7–16. Using EES (or other) software, investigate the effects of wind velocity and outside air temperature on the rate of heat loss from the wall by convection. Let the wind velocity vary from 10 km/h to 80 km/h and the outside air temperature from 0ºC to 10ºC. Plot the rate of heat loss as a function of the wind velocity and of the outside temperature, and discuss the results
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7–18E Air at 60°F flows over a 10-ft-long flat plate at 7 ft/s. Determine the local friction and heat transfer coefficients at intervals of 1 ft, and plot the results against the distance from the leading edge
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7–19E Reconsider Problem 7–18. Using EES (or other) software, evaluate the local friction and heat transfer coefficients along the plate at intervals of 0.1 ft, and plot them against the distance from the leading edge
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7–20 Consider a hot automotive engine, which can be approximated as a 0.5-m-high, 0.40-m-wide, and 0.8-m-long rectangular block. The bottom surface of the block is at a temperature of 80°C and has an emissivity of 0.95. The ambient air is at 20°C, and the road surface is at 25°C. Determine the rate of heat transfer from the bottom surface of the engine block by convection and radiation as the car travels at a velocity of 80 km/h. Assume the flow to be turbulent over the entire surface because of the constant agitation of the engine block
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7–21 The forming section of a plastics plant puts out a continuous sheet of plastic that is 1.2 m wide and 2 mm thick at a rate of 15 m/min. The temperature of the plastic sheet is 90°C when it is exposed to the surrounding air, and the sheet is subjected to air flow at 30°C at a velocity of 3 m/s on both sides along its surfaces normal to the direction of motion of the sheet. The width of the air cooling section is such that a fixed point on the plastic sheet passes through that section in 2 s. Determine the rate of heat transfer from the plastic sheet to the air.
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7–22 The top surface of the passenger car of a train moving at a velocity of 70 km/h is 2.8 m wide and 8 m long. The top surface is absorbing solar radiation at a rate of 200 W/m2, and the temperature of the ambient air is 30°C. Assuming the roof of the car to be perfectly insulated and the radiation heat exchange with the surroundings to be small relative to convection, determine the equilibrium temperature of the top surface of the car.
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7–23 Reconsider Problem 7–22. Using EES (or other) software, investigate the effects of the train velocity and the rate of absorption of solar radiation on the equilibrium temperature of the top surface of the car. Let the train velocity vary from 10 km/h to 120 km/h and the rate of solar absorption from 100 W/m2 to 500 W/m2. Plot the equilibrium temperature as functions of train velocity and solar radiation absorption rate, and discuss the results
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7–24 A 15-cm 15-cm circuit board dissipating 15 W of power uniformly is cooled by air, which approaches the circuit board at 20°C with a velocity of 5 m/s. Disregarding any heat transfer from the back surface of the board, determine the surface temperature of the electronic components (a) at the leading edge and (b) at the end of the board. Assume the flow to be turbulent since the electronic components are expected to act as turbulators
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7–25 Consider laminar flow of a fluid over a flat plate maintained at a constant temperature. Now the free-stream velocity of the fluid is doubled. Determine the change in the drag force on the plate and rate of heat transfer between the fluid and the plate. Assume the flow to remain laminar
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7–26E Consider a refrigeration truck traveling at 55 mph at a location where the air temperature is 80°F. The refrigerated compartment of the truck can be considered to be a 9-ft-wide, 8-ft-high, and 20-ft-long rectangular box. The refrigeration system of the truck can provide 3 tons of refrigeration (i.e., it can remove heat at a rate of 600 Btu/min). The outer surface of the truck is coated with a low-emissivity material, and thus radiation heat transfer is very small. Determine the average temperature of the outer surface of the refrigeration compartment of the truck if the refrigeration system is observed to be operating at half the capacity. Assume the air flow over the entire outer surface to be turbulent and the heat transfer coefficient at the front and rear surfaces to be equal to that on side surfaces
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7–27 Solar radiation is incident on the glass cover of a solar collector at a rate of 700 W/m2. The glass transmits 88 percent of the incident radiation and has an emissivity of 0.90. The entire hot water needs of a family in summer can be met by two collectors 1.2 m high and 1 m wide. The two collectors are attached to each other on one side so that they appear like a single collector 1.2 m 2 m in size. The temperature of the glass cover is measured to be 35°C on a day when the surrounding air temperature is 25°C and the wind is blowing at 30 km/h. The effective sky temperature for radiation exchange between the glass cover and the open sky is -40°C. Water enters the tubes attached to the absorber plate at a rate of 1 kg/min. Assuming the back surface of the absorber plate to be heavily insulated and the only heat loss to occur through the glass cover, determine (a) the total rate of heat loss from the collector, (b) the collector efficiency, which is the ratio of the amount of heat transferred to the water to the solar energy incident on the collector, and (c) the temperature rise of water as it flows through the collector.
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7–28 A transformer that is 10 cm long, 6.2 cm wide, and 5 cm high is to be cooled by attaching a 10 cm 6.2 cm wide polished aluminum heat sink (emissivity 0.03) to its top surface. The heat sink has seven fins, which are 5 mm high, 2 mm thick, and 10 cm long. A fan blows air at 25°C parallel to the passages between the fins. The heat sink is to dissipate 20 Wof heat and the base temperature of the heat sink is not to exceed 60°C. Assuming the fins and the base plate to be nearly isothermal and the radiation heat transfer to be negligible, determine the minimum free-stream velocity the fan needs to supply to avoid overheating.
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7–29 Repeat Problem 7–28 assuming the heat sink to be black-anodized and thus to have an effective emissivity of 0.90. Note that in radiation calculations the base area (10 cm 6.2 cm) is to be used, not the total surface area
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7–30 An array of power transistors, dissipating 6 Wof power each, are to be cooled by mounting them on a 25-cm x 25-cm square aluminum plate and blowing air at 35°C over the plate with a fan at a velocity of 4 m/s. The average temperature of the plate is not to exceed 65°C. Assuming the heat transfer from the back side of the plate to be negligible and disregarding radiation, determine the number of transistors that can be placed on this plate.
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7–31 Repeat Problem 7–30 for a location at an elevation of 1610 m where the atmospheric pressure is 83.4 kPa.
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7–32 Air at 25°C and 1 atm is flowing over a long flat plate with a velocity of 8 m/s. Determine the distance from the leading edge of the plate where theflow becomes turbulent, and the thickness of the boundary layer at that location
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7–33 Repeat Problem 7–32 for water
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7–34 The weight of a thin flat plate 50 cm 50 cm in size is balanced by a counterweight that has a mass of 2 kg, as shown in the figure. Now a fan is turned on, and air at 1 atm and 25°C flows downward over both surfaces of the plate with a freestream velocity of 10 m/s. Determine the mass of the counterweight that needs to be added in order to balance the plate in this case.
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7–35C Consider laminar flow of air across a hot circular cylinder. At what point on the cylinder will the heat transfer be highest? What would your answer be if the flow were turbulent
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7–36C In flow over cylinders, why does the drag coefficient suddenly drop when the flow becomes turbulent? Isn’t turbulence supposed to increase the drag coefficient instead of decreasing it
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7–37C In flow over blunt bodies such as a cylinder, how does the pressure drag differ from the friction drag
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7–38C Why is flow separation in flow over cylinders delayed in turbulent flow
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7–39 A long 8-cm-diameter steam pipe whose external surface temperature is 90°C passes through some open area that is not protected against the winds. Determine the rate of heat loss from the pipe per unit of its length when the airis at 1 atm pressure and 7°C and the wind is blowing across the pipe at a velocity of 50 km/h
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7–40 Astainless steel ball (p=8055 kg/m3, Cp 480 J/kg · °C) of diameter D 15 cm is removed from the oven at a uniform temperature of 350°C. The ball is then subjected to the flow of air at 1 atm pressure and 30°C with a velocity of 6 m/s. The surface temperature of the ball eventually drops to 250°C. Determine the average convection heat transfer coefficient during this cooling process and estimate how long this process has taken
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7–41 Reconsider Problem 7–40. Using EES (or other) software, investigate the effect of air velocity on the average convection heat transfer coefficient and the cooling time. Let the air velocity vary from 1 m/s to 10 m/s. Plot the heat transfer coefficient and the cooling time as a function of air velocity, and discuss the results
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7–42E Aperson extends his uncovered arms into the windy air outside at 54°F and 20 mph in order to feel nature closely. Initially, the skin temperature of the arm is 86°F. Treating the arm as a 2-ft-long and 3-in.-diameter cylinder, determine the rate of heat loss from the arm.
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7–43E Reconsider Problem 7–42E. Using EES (or other) software, investigate the effects of air temperature and wind velocity on the rate of heat loss from the arm. Let the air temperature vary from 20°F to 80°F and the wind velocity from 10 mph to 40 mph. Plot the rate of heat loss as a function of air temperature and of wind velocity, and discuss the results
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7–44 An average person generates heat at a rate of 84 W while resting. Assuming one-quarter of this heat is lost from the head and disregarding radiation, determine the average surface temperature of the head when it is not covered and is subjected to winds at 10°C and 35 km/h. The head can be approximated as a 30-cm-diameter sphere.
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7–45 Consider the flow of a fluid across a cylinder maintained at a constant temperature. Now the free-stream velocity of the fluid is doubled. Determine the change in the drag force on the cylinder and the rate of heat transfer between the fluid and the cylinder.
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7–46 A6-mm-diameter electrical transmission line carries an electric current of 50 Aand has a resistance of 0.002 ohm per meter length. Determine the surface temperature of the wire during a windy day when the air temperature is 10°C and the wind is blowing across the transmission line at 40 km/h.
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7–47 Reconsider Problem 7–46. Using EES (or other) software, investigate the effect of the wind velocity on the surface temperature of the wire. Let the wind velocity vary from 10 km/h to 80 km/h. Plot the surface temperature as a function of wind velocity, and discuss the results
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7–48 Aheating system is to be designed to keep the wings of an aircraft cruising at a velocity of 900 km/h above freezing temperatures during flight at 12,200-m altitude where the standard atmospheric conditions are -55.4°C and 18.8 kPa. Approximating the wing as a cylinder of elliptical cross section whose minor axis is 30 cm and disregarding radiation, determine the average convection heat transfer coefficient on the wing surface and the average rate of heat transfer per unit surface area
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7–49 A long aluminum wire of diameter 3 mm is extruded at a temperature of 370°C. The wire is subjected to cross air flow at 30°C at a velocity of 6 m/s. Determine the rate of heat transfer from the wire to the air per meter length when it is first exposed to the air.
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7–50E Consider a person who is trying to keep cool on a hot summer day by turning a fan on and exposing his entire body to air flow. The air temperature is 85°F and the fan is blowing air at a velocity of 6 ft/s. If the person is doing light work and generating sensible heat at a rate of 300 Btu/h, determine the average temperature of the outer surface (skin or clothing) of the person. The average human body can be treated as a 1-ftdiameter cylinder with an exposed surface area of 18 ft2. Disregard any heat transfer by radiation. What would your answer be if the air velocity were doubled?
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7–51 An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 10 percent of the electrical energy it consumes into light while converting the remaining 90 percent into heat. (A fluorescent lightbulb will give the same amount of light while consuming only one-fourth of the electrical energy, and it will last 10 times longer than an incandescent lightbulb.) The glass bulb of the lamp heats up very quickly as a result of absorbing all that heat and dissipating it to the surroundings by convection and radiation. Consider a 10-cm-diameter 100-Wlightbulb cooled by a fan that blows air at 25°C to the bulb at a velocity of 2 m/s. The surrounding surfaces are also at 25°C, and the emissivity of the glass is 0.9. Assuming 10 percent of the energy passes through the glass bulb as light with negligible absorption and the rest of the energy is absorbed and dissipated by the bulb itself, determine the equilibrium temperature of the glass bulb.
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7–52 During a plant visit, it was noticed that a 12-m-long section of a 10-cm-diameter steam pipe is completely exposed to the ambient air. The temperature measurements indicate that the average temperature of the outer surface of the steam pipe is 75°C when the ambient temperature is 5°C. There are also light winds in the area at 10 km/h. The emissivity of the outer surface of the pipe is 0.8, and the average temperature of the surfaces surrounding the pipe, including the sky, is estimated to be 0°C. Determine the amount of heat lost from the steam during a 10-h-long work day. Steam is supplied by a gas-fired steam generator that has an efficiency of 80 percent, and the plant pays $0.54/therm of natural gas (1 therm 105,500 kJ). If the pipe is insulated and 90 percent of the heat loss is saved, determine the amount of money this facility will save a year as a result of insulating the steam pipes. Assume the plant operates every day of the year for 10 h. State your assumptions.
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7–53 Reconsider Problem 7–52. There seems to be some uncertainty about the average temperature of the surfaces surrounding the pipe used in radiation calculations, and you are asked to determine if it makes any significant difference in overall heat transfer. Repeat the calculations for average surrounding and surface temperatures of -20°C and 25°C, respectively, and determine the change in the values obtained
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7–54E A 12-ft-long, 1.5-kW electrical resistance wire is made of 0.1-in.-diameter stainless steel (k 8.7 Btu/h · ft · °F). The resistance wire operates in an environment at 85°F. Determine the surface temperature of the wire if it is cooled by a fan blowing air at a velocity of 20 ft/s.
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7–55 The components of an electronic system are located in a 1.5-m-long horizontal duct whose cross section is 20 cm 20 cm. The components in the duct are not allowed to come into direct contact with cooling air, and thus are cooled by air at 30°C flowing over the duct with a velocity of 200 m/min. Ifthe surface temperature of the duct is not to exceed 65°C, determine the total power rating of the electronic devices that can be mounted into the duct.
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7–56 Repeat Problem 7–55 for a location at 4000-m altitude where the atmospheric pressure is 61.66 kPa
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7–57 A0.4-W cylindrical electronic component with diameter 0.3 cm and length 1.8 cm and mounted on a circuit board is cooled by air flowing across it at a velocity of 150 m/min. If the air temperature is 40°C, determine the surface temperature of the component
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7–58 Consider a 50-cm-diameter and 95-cm-long hot water tank. The tank is placed on the roof of a house. The water inside the tank is heated to 80ºC by a flat-plate solar collector during the day. The tank is then exposed to windy air at 18ºC with an average velocity of 40 km/h during the night. Estimate the temperature of the tank after a 45-mm period. Assume the tank surface to be at the same temperature as the water inside, and the heat transfer coefficient on the top and bottom surfaces to be the same as that on the side surface
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7–59 Reconsider Problem 7–58. Using EES (or other) software, plot the temperature of the tank as a function of the cooling time as the time varies from 30 mm to 5 h, and discuss the results
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7–60 A1.8-m-diameter spherical tank of negligible thickness contains iced water at 0ºC. Air at 25ºC flows over the tank with a velocity of 7 m/s. Determine the rate of heat transfer to the tank and the rate at which ice melts. The heat of fusion of water at 0ºC is 333.7 kJ/kg.
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7-61 A 10-cm-diameter, 30-cm-high cylindrical bottle contains cold water at 3ºC. The bottle is placed in windy air at 27ºC. The water temperature is measured to be 11ºC after 45 minutes of cooling. Disregarding radiation effects and heat transfer from the top and bottom surfaces, estimate the average wind velocity.
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7–62C In flow across tube banks, why is the Reynolds number based on the maximum velocity instead of the uniform approach velocity
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7–63C In flow across tube banks, how does the heat transfer coefficient vary with the row number in the flow direction? How does it vary with in the transverse direction for a given row number
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7–64 Combustion air in a manufacturing facility is to be preheated before entering a furnace by hot water at 90ºC flowing through the tubes of a tube bank located in a duct. Air enters the duct at 15ºC and 1 atm with a mean velocity of 3.8 m/s, and flows over the tubes in normal direction. The outer diameter of the tubes is 2.1 cm, and the tubes are arranged in-line with longitudinal and transverse pitches of SL = ST = 5 cm. There are eight rows in the flow direction with eight tubes in each row. Determine the rate of heat transfer per unit length of the tubes, and the pressure drop across the tube bank
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7–65 Repeat Problem 7–64 for staggered arrangement with SL = ST = 5 cm
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7–66 Air is to be heated by passing it over a bank of 3-m-long tubes inside which steam is condensing at 100ºC. Air approaches the tube bank in the normal direction at 20ºC and 1 atm with a mean velocity of 5.2 m/s. The outer diameter of the tubes is 1.6 cm, and the tubes are arranged staggered with longitudinal and transverse pitches of SL = ST = 4 cm. There are 20 rows in the flow direction with 10 tubes in each row. Determine (a) the rate of heat transfer, (b) and pressure drop across the tube bank, and (c) the rate of condensation of steam inside the tubes
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7–67 Repeat Problem 7–66 for in-line arrangement with SL = ST = 5 cm
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7–68 Exhaust gases at 1 atm and 300ºC are used to preheat water in an industrial facility by passing them over a bank of tubes through which water is flowing at a rate of 6 kg/s. The mean tube wall temperature is 80ºC. Exhaust gases approach the tube bank in normal direction at 4.5 m/s. The outer diameter of the tubes is 2.1 cm, and the tubes are arranged in-line with longitudinal and transverse pitches of SL = ST = 8 cm. There are 16 rows in the flow direction with eight tubes in each row. Using the properties of air for exhaust gases, determine (a) the rate of heat transfer per unit length of tubes, (b) and pressure drop across the tube bank, and (c) the temperature rise of water flowing through the tubes per unit length of tubes
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7–69 Water at 15ºC is to be heated to 65ºC by passing it over a bundle of 4-m-long 1-cm-diameter resistance heater rods maintained at 90ºC. Water approaches the heater rod bundle in normal direction at a mean velocity of 0.8 m/s. The rods arc arranged in-line with longitudinal and transverse pitches of SL = 4 cm and ST = 3 cm. Determine the number of tube rows NL in the flow direction needed to achieve the indicated temperature rise.
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7–70 Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20ºC. Air approaches the tube bank in the normal direction at 0ºC and 1 atm with a mean velocity of 4 m/s. The tubes are arranged in-line with longitudinal and transverse pitches of SL = ST = 1.5 cm. There are 30 rows in the flow direction with 15 tubes in each row. Determine (a) the refrigeration capacity of this system and (b) and pressure drop across the tube bank.
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7–71 Repeat Problem 7–70 by solving it for staggered arrangement with SL = ST = 1.5 cm, and compare the performance of the evaporator for the in-line and staggered arrangements
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7–72 Atube bank consists of 300 tubes at a distance of 6 cm between the centerlines of any two adjacent tubes. Air approaches the tube bank in the normal direction at 40ºC and 1 atm with a mean velocity of 7 m/s. There are 20 rows in the flow direction with 15 tubes in each row with an average surface temperature of 140ºC. For an outer tube diameter of 2 cm, determine the average heat transfer coefficient.
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7–73C What is thermal insulation? How does a thermal insulator differ in purpose from an electrical insulator and from a sound insulator
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7–74C Does insulating cold surfaces save energy? Explain.
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7–75C What is the R-value of insulation? How is it determined? Will doubling the thickness of flat insulation double its R-value
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7–76C How does the R-value of an insulation differ from its thermal resistance
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7–77C Why is the thermal conductivity of superinsulation orders of magnitude lower than the thermal conductivities of ordinary insulations
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7–78C Someone suggests that one function of hair is to insulate the head. Do you agree with this suggestion
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7–79C Name five different reasons for using insulation in industrial facilities
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7–80C What is optimum thickness of insulation? How is it determined
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7–81 What is the thickness of flat R-8 (in SI units) insulation whose thermal conductivity is 0.04 W/m · °C
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7–82E What is the thickness of flat R-20 (in English units) insulation whose thermal conductivity is 0.02 Btu/h · ft · °F
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7–83 Hot water at 110°C flows in a cast iron pipe (k 52 W/m · °C) whose inner radius is 2.0 cm and thickness is 0.3 cm. The pipe is to be covered with adequate insulation so that the temperature of the outer surface of the insulation does not exceed 30°C when the ambient temperature is 22°C. Taking the heat transfer coefficients inside and outside the pipe to be hi 80 W/m2 · °C and ho 22 W/m2 · °C, respectively, determine the thickness of fiber glass insulation (k 0.038 W/m · °C) that needs to be installed on the pipe.
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7–84 Reconsider Problem 7–83. Using EES (or other) software, plot the thickness of the insulation as a function of the maximum temperature of the outer surface of insulation in the range of 24ºC to 48ºC. Discuss the results
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7–85 Consider a furnace whose average outer surface temperature is measured to be 90°C when the average surrounding air temperature is 27°C. The furnace is 6 m long and 3 m in diameter. The plant operates 80 h per week for 52 weeks per year. You are to insulate the furnace using fiberglass insulation (kins 0.038 W/m · °C) whose cost is $10/m2 per cm of thickness for materials, plus $30/m2 for labor regardless of thickness. The combined heat transfer coefficient on the outer surface is estimated to be ho 30 W/m2 · °C. The furnace uses natural gas whose unit cost is $0.50/therm input (1 therm 105,500 kJ), and the efficiency of the furnace is 78 percent. The management is willing to authorize the installation of the thickest insulation (in whole cm) that will pay for itself (materials and labor) in one year. That is, the total cost of insulation should be roughly equal to the drop in the fuel cost of the furnace for one year. Determine the thickness of insulation to be used and the money saved per year. Assume the surface temperature of the furnace and the heat transfer coefficient are to remain constant.
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7–85 Repeat Problem 7–85 for an outer surface temperature of 75°C for the furnace
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7–87E Steam at 400°F is flowing through a steel pipe (k 8.7 Btu/h · ft · °F) whose inner and outer diameters are 3.5 in. and 4.0 in., respectively, in an environment at 60°F. The pipe is insulated with 1-in.-thick fiberglass insulation (k 0.020 Btu/h · ft · °F), and the heat transfer coefficients on the inside and the outside of the pipe are 30 Btu/h · ft2 · °F and 5 Btu/h · ft2 · °F, respectively. It is proposed to add another 1-in.-thick layer of fiberglass insulation on top of the existing one to reduce the heat losses further and to save energy and money. The total cost of new insulation is $7 per ft length of the pipe, and the net fuel cost of energy in the steam is $0.01 per 1000 Btu (therefore, each 1000 Btu reduction in the heat loss will save the plant $0.01). The policy of the plant is to implement energy conservation measures that pay for themselves within two years. Assuming continuous operation (8760 h/year), determine if the proposed additional insulation is justified
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7–88 The plumbing system of a plant involves a section of a plastic pipe (k 0.16 W/m · °C) of inner diameter 6 cm and outer diameter 6.6 cm exposed to the ambient air. You are to insulate the pipe with adequate weather-jacketed fiberglass insulation (k 0.035 W/m · °C) to prevent freezing of water in the pipe. The plant is closed for the weekends for a period of 60 h, and the water in the pipe remains still during that period. The ambient temperature in the area gets as low as -10°C in winter, and the high winds can cause heat transfer coefficients as high as 30 W/m2 · °C. Also, the water temperature in the pipe can be as cold as 15°C, and water starts freezing when its temperature drops to 0°C. Disregarding the convection resistance inside the pipe, determine the thickness of insulation that will protect the water from freezing under worst conditions
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7–89 Repeat Problem 7–88 assuming 20 percent of the water in the pipe is allowed to freeze without jeopardizing safety.
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7–90 Consider a house that is maintained at 22°C at all times. The walls of the house have R-3.38 insulation in SI units (i.e., an L/k value or a thermal resistance of 3.38 m2 · °C/W). During a cold winter night, the outside air temperature is 4°C and wind at 50 km/h is blowing parallel to a 3-m-high and 8-m-long wall of the house. If the heat transfer coefficient on the interior surface of the wall is 8 W/m2 · °C, determine the rate of heat loss from that wall of the house. Draw the thermal resistance network and disregard radiation heat transfer.
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7–91 An automotive engine can be approximated as a 0.4-mhigh, 0.60-m-wide, and 0.7-m-long rectangular block. The bottom surface of the block is at a temperature of 75°C and has an emissivity of 0.92. The ambient air is at 5°C, and the road surface is at 10°C. Determine the rate of heat transfer from the bottom surface of the engine block by convection and radiation as the car travels at a velocity of 60 km/h. Assume the flow to be turbulent over the entire surface because of the constant agitation of the engine block. How will the heat transfer be affected when a 2-mm-thick gunk (k 3 W/m · °C) has formed at the bottom surface as a result of the dirt and oil collected at that surface over time? Assume the metal temperature under the gunk still to be 75°C.
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7–92E The passenger compartment of a minivan traveling at 60 mph can be modeled as a 3.2-ft-high, 6-ft-wide, and 11-ftlong rectangular box whose walls have an insulating value of R-3 (i.e., a wall thickness–to–thermal conductivity ratio of 3h· ft2 · °F/Btu). The interior of a minivan is maintained at an average temperature of 70°F during a trip at night while the outside air temperature is 90°F. The average heat transfer coefficient on the interior surfaces of the van is 1.2 Btu/h · ft2 · °F. The air flow over the exterior surfaces can be assumed to be turbulent because of the intense vibrations involved, and the heat transfer coefficient on the front and back surfaces can be taken to be equal to that on the top surface. Disregarding any heat gain or loss by radiation, determine the rate of heat transfer from the ambient air to the van.
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7–93 Consider a house that is maintained at a constant temperature of 22°C. One of the walls of the house has three single-pane glass windows that are 1.5 m high and 1.2 m long. The glass (k 0.78 W/m · °C) is 0.5 cm thick, and the heat transfer coefficient on the inner surface of the glass is 8W/m2 · C. Now winds at 60 km/h start to blow parallel to the surface of this wall. If the air temperature outside is -2°C, determine the rate of heat loss through the windows of this wall. Assume radiation heat transfer to be negligible
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7–94 Consider a person who is trying to keep cool on a hot summer day by turning a fan on and exposing his body to air flow. The air temperature is 32°C, and the fan is blowing air at a velocity of 5 m/s. The surrounding surfaces are at 40°C, and the emissivity of the person can be taken to be 0.9. If the person is doing light work and generating sensible heat at a rate of 90 W, determine the average temperature of the outer surface (skin or clothing) of the person. The average human body can be treated as a 30-cm-diameter cylinder with an exposed surface area of 1.7 m2.
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7–95 Four power transistors, each dissipating 12 W, are mounted on a thin vertical aluminum plate (k 237 W/m · °C) 22 cm 22 cm in size. The heat generated by the transistors is to be dissipated by both surfaces of the plate to the surrounding air at 20°C, which is blown over the plate by a fan at a velocity of 250 m/min. The entire plate can be assumed to be nearly isothermal, and the exposed surface area of the transistor can be taken to be equal to its base area. Determine the temperature of the aluminum plate
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7–96 A3-m-internal-diameter spherical tank made of 1-cmthick stainless steel (k 15 W/m · °C) is used to store iced water at 0°C. The tank is located outdoors at 30°C and is subjected to winds at 25 km/h. Assuming the entire steel tank to be at 0°C and thus its thermal resistance to be negligible, determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a 24-h period. The heat of fusion of water at atmospheric pressure is hif 333.7 kJ/kg. Disregard any heat transfer by radiation.
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7–97 Repeat Problem 7–96, assuming the inner surface of the tank to be at 0°C but by taking the thermal resistance of the tank and heat transfer by radiation into consideration. Assume the average surrounding surface temperature for radiation exchange to be 15°C and the outer surface of the tank to have an emissivity of 0.9.
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7–98E Atransistor with a height of 0.25 in. and a diameter of 0.22 in. is mounted on a circuit board. The transistor is cooled by air flowing over it at a velocity of 500 ft/min. If the air temperature is 120°F and the transistor case temperature is not to exceed 180°F, determine the amount of power this transistor can dissipate safely.
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7–99 The roof of a house consists of a 15-cm-thick concrete slab (k 2 W/m · °C) 15 m wide and 20 m long. The convection heat transfer coefficient on the inner surface of the roof is 5 W/m2 · °C. On a clear winter night, the ambient air is reported to be at 10°C, while the night sky temperature is 100 K. The house and the interior surfaces of the wall are maintained at a constant temperature of 20°C. The emissivity of both surfaces of the concrete roof is 0.9. Considering both radiation and convection heat transfer, determine the rate of heat transfer through the roof when wind at 60 km/h is blowing over the roo
f. If the house is heated by a furnace burning natural gas with an efficiency of 85 percent, and the price of natural gas is $0.60/therm (1 therm 105,500 kJ of energy content), determine the money lost through the roof that night during a 14-h period.
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7–100 Steam at 250°C flows in a stainless steel pipe (k 15 W/m · °C) whose inner and outer diameters are 4 cm and 4.6 cm, respectively. The pipe is covered with 3.5-cm-thick glass wool insulation (k 0.038 W/m · °C) whose outer surface has an emissivity of 0.3. Heat is lost to the surrounding air and surfaces at 3°C by convection and radiation. Taking the heat transfer coefficient inside the pipe to be 80 W/m2 · °C, determine the rate of heat loss from the steam per unit length of the pipe when air is flowing across the pipe at 4 m/s.
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7–101 The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is -196°C. Therefore, nitrogen is commonly used in low-temperature scientific studies, since the temperature of liquid nitrogen in a tank open to the atmosphere will remain constant at 196°C until it is depleted. Any heat transfer to the tank will result in the evaporation of some liquid nitrogen, which has a heat of vaporization of 198 kJ/kg and a density of 810 kg/m3 at 1 atm. Consider a 4-m-diameter spherical tank that is initially filled with liquid nitrogen at 1 atm and -196°C. The tank is exposed to 20°C ambient air and 40 km/h winds. The temperature of the thin-shelled spherical tank is observed to be almost the same as the temperature of the nitrogen inside. Disregarding any radiation heat exchange, determine the rate of evaporation of the liquid nitrogen in the tank as a result of heat transfer from the ambient air if the tank is (a) not insulated, (b) insulated with 5-cm-thick fiberglass insulation (k 0.035 W/m · °C), and (c) insulated with 2-cm-thick superinsulation that has an effective thermal conductivity of 0.00005 W/m · °C.
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7–102 Repeat Problem 7–101 for liquid oxygen, which has a boiling temperature of -183°C, a heat of vaporization of 213 kJ/kg, and a density of 1140 kg/m3 at 1 atm pressure
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7–103 A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. The board is impregnated with copper fillings and has an effective thermal conductivity of 16 W/m ·°C. All the heat generated in the chips is conducted across the circuit board and is dissipated from the back side of the board to the ambient air at 30°C, which is forced to flow over the surface by a fan at a free-stream velocity of 400 m/min. Determine the temperatures on the two sides of the circuit board.
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7–104E It is well known that cold air feels much colder in windy weather than what the thermometer reading indicates because of the “chilling effect” of the wind. This effect is due to the increase in the convection heat transfer coefficient with increasing air velocities. The equivalent windchill temperature in °F is given by (1993 ASHRAE Handbook of Fundamentals, Atlanta, GA, p. 8.15)
where V is the wind velocity in mph and Tambient is the ambient air temperature in °F in calm air, which is taken to be air with light winds at speeds up to 4 mph. The constant 91.4°F in the above equation is the mean skin temperature of a resting person in a comfortable environment. Windy air at a temperature Tambient and velocity will feel as cold as calm air at a temperature Tequiv. The equation above is valid for winds up to 43 mph. Winds at higher velocities produce little additional chilling effect. Determine the equivalent wind chill temperature of an environment at 10°F at wind speeds of 10, 20, 30, and 40 mph. Exposed flesh can freeze within one minute at a temperature below 25°F in calm weather. Does a person need to be concerned about this possibility in any of the cases above?
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7–l05E Reconsider Problem 7–104E. Using EES (or other) software, plot the equivalent wind chill temperatures in ºF as a function of wind velocity in the range of 4 mph to 100 mph for ambient temperatures of 20ºF, 40ºF and 60ºF. Discuss the results.
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