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13–2C Classify heat exchangers according to construction type and explain the characteristics of each type
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13–3C When is a heat exchanger classified as being compact? Do you think a double-pipe heat exchanger can be classified as a compact heat exchanger
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13–4C How does a cross-flow heat exchanger differ from a counter-flow one? What is the difference between mixed and unmixed fluids in cross-flow
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13–5C What is the role of the baffles in a shell-and-tube heat exchanger? How does the presence of baffles affect the heat transfer and the pumping power requirements? Explain
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13–6C Draw a 1-shell-pass and 6-tube-passes shell-and-tube heat exchanger. What are the advantages and disadvantages of using 6 tube passes instead of just 2 of the same diameter
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13–7C Draw a 2-shell-passes and 8-tube-passes shell-andtube heat exchanger. What is the primary reason for using so many tube passes
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13–8C What is a regenerative heat exchanger? How does a static type of regenerative heat exchanger differ from a dynamic type?
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13–9C What are the heat transfer mechanisms involved during heat transfer from the hot to the cold fluid?
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13–10C Under what conditions is the thermal resistance of the tube in a heat exchanger negligible
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13–11C Consider a double-pipe parallel-flow heat exchanger of length L. The inner and outer diameters of the inner tube are D1 and D2, respectively, and the inner diameter of the outer tube is D3. Explain how you would determine the two heat transfer surface areas Ai and Ao. When is it reasonable to assume Ai Ao As
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13–12C Is the approximation hi ho h for the convection heat transfer coefficient in a heat exchanger a reasonable one when the thickness of the tube wall is negligible
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13–13C Under what conditions can the overall heat transfer coefficient of a heat exchanger be determined from U (1/hi 1/ho) 1
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13–14C What are the restrictions on the relation UAs UiAi UoAo for a heat exchanger? Here As is the heat transfer surface area and U is the overall heat transfer coefficient
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13–15C In a thin-walled double-pipe heat exchanger, when is the approximation U hi a reasonable one? Here U is the overall heat transfer coefficient and hi is the convection heat transfer coefficient inside the tube
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13–16C What are the common causes of fouling in a heat exchanger? How does fouling affect heat transfer and pressure drop
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13–17C How is the thermal resistance due to fouling in a heat exchanger accounted for? How do the fluid velocity and temperature affect fouling
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13–18 Adouble-pipe heat exchanger is constructed of a copper (k 380 W/m · °C) inner tube of internal diameter Di 1.2 cm and external diameter Do 1.6 cm and an outer tube of diameter 3.0 cm. The convection heat transfer coefficient is reported to be hi 700 W/m2 · °C on the inner surface of the tube and ho 1400 W/m2 · °C on its outer surface. For a fouling factor Rf, i 0.0005 m2 · °C/W on the tube side and Rf, o 0.0002 m2 · °C/W on the shell side, determine (a) the thermal resistance of the heat exchanger per unit length and (b) the overall heat transfer coefficients Ui and Uo based on the inner and outer surface areas of the tube, respectively
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13–19 Reconsider Problem 13–18. Using EES (or other) software, investigate the effects of pipe conductivity and heat transfer coefficients on the thermal resistance of the heat exchanger. Let the thermal conductivity vary from 10 W/m · ºC to 400 W/m · ºC, the convection heat transfer coefficient from 500 W/m2 · ºC to 1500 W/m2 · ºC on the inner surface, and from 1000 W/m2 · ºC to 2000 W/m2 · ºC on the outer surface. Plot the thermal resistance of the heat exchanger as functions of thermal conductivity and heat transfer coefficients, and discuss the results
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13–20 Water at an average temperature of 107°C and an average velocity of 3.5 m/s flows through a 5-m-long stainless steel tube (k 14.2 W/m · °C) in a boiler. The inner and outer diameters of the tube are Di 1.0 cm and Do 1.4 cm, respectively. If the convection heat transfer coefficient at the outer surface of the tube where boiling is taking place is ho 8400 W/m2 · °C, determine the overall heat transfer coefficient Ui of this boiler based on the inner surface area of the tube
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13–21 Repeat Problem 13–20, assuming a fouling factor Rf, i 0.0005 m2 · °C/W on the inner surface of the tube
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13–22 Reconsider Problem 13–21. Using EES (or other) software, plot the overall heat transfer coefficient based on the inner surface as a function of fouling factor Fi as it varies from 0.0001 m2 · ºC/Wto 0.0008 m2 · ºC/W, and discuss the results
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13–23 A long thin-walled double-pipe heat exchanger with tube and shell diameters of 1.0 cm and 2.5 cm, respectively, is used to condense refrigerant 134a by water at 20°C. The refrigerant flows through the tube, with a convection heat transfer coefficient of hi 5000 W/m2 · °C. Water flows through the shell at a rate of 0.3 kg/s. Determine the overall heat transfer coefficient of this heat exchanger.
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13–24 Repeat Problem 13–23 by assuming a 2-mm-thick layer of limestone (k 1.3 W/m · °C) forms on the outer surface of the inner tube
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13–25 Reconsider Problem 13–24. Using EES (or other) software, plot the overall heat transfer coefficient as a function of the limestone thickness as it varies from 1 mm to 3 mm, and discuss the results
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13–26E Water at an average temperature of 140°F and an average velocity of 8 ft/s flows through a thin-walled -in.diameter tube. The water is cooled by air that flows across the tube with a velocity of V ∞= 12 ft/s at an average temperature of 80°F. Determine the overall heat transfer coefficient.
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13–27C What are the common approximations made in the analysis of heat exchangers?
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13–28C Under what conditions is the heat transfer relation
valid for a heat exchanger
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13–29C What is the heat capacity rate? What can you say about the temperature changes of the hot and cold fluids in a heat exchanger if both fluids have the same capacity rate? What does a heat capacity of infinity for a fluid in a heat exchanger mean
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13–30C Consider a condenser in which steam at a specified temperature is condensed by rejecting heat to the cooling water. If the heat transfer rate in the condenser and the temperature rise of the cooling water is known, explain how the rate of condensation of the steam and the mass flow rate of the cooling water can be determined. Also, explain how the total thermal resistance R of this condenser can be evaluated in this case
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13–31C Under what conditions will the temperature rise of the cold fluid in a heat exchanger be equal to the temperature drop of the hot fluid?
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13–32C In the heat transfer relation Q · UAs Tlm for a heat exchanger, what is Tlm called? How is it calculated for a parallel-flow and counter-flow heat exchanger
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13–33C How does the log mean temperature difference for a heat exchanger differ from the arithmetic mean temperature difference (AMTD)? For specified inlet and outlet temperatures, which one of these two quantities is larger
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13–34C The temperature difference between the hot and cold fluids in a heat exchanger is given to be T1 at one end and T2 at the other end. Can the logarithmic temperature difference Tlm of this heat exchanger be greater than both T1 and T2? Explain
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13–35C Can the logarithmic mean temperature difference Tlm of a heat exchanger be a negative quantity? Explain
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13–36C Can the outlet temperature of the cold fluid in a heat exchanger be higher than the outlet temperature of the hot fluid in a parallel-flow heat exchanger? How about in a counter-flow heat exchanger? Explain
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13–37C For specified inlet and outlet temperatures, for what kind of heat exchanger will the Tlm be greatest: double-pipe parallel-flow, double-pipe counter-flow, cross-flow, or multipass shell-and-tube heat exchanger
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13–38C In the heat transfer relation Q · UAsF Tlm for a heat exchanger, what is the quantity F called? What does it represent? Can F be greater than one
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13–39C When the outlet temperatures of the fluids in a heat exchanger are not known, is it still practical to use the LMTD method? Explain.
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13–40C Explain how the LMTD method can be used to determine the heat transfer surface area of a multipass shell-andtube heat exchanger when all the necessary information, including the outlet temperatures, is given
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13–41 Steam in the condenser of a steam power plant is to be condensed at a temperature of 50°C (hfg 2305 kJ/kg) with cooling water (Cp 4180 J/kg ·°C) from a nearby lake, which enters the tubes of the condenser at 18°C and leaves at 27°C. The surface area of the tubes is 58 m2, and the overall heat transfer coefficient is 2400 W/m2 · °C. Determine the mass flow rate of the cooling water needed and the rate of condensation of the steam in the condenser.
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13–42 Adouble-pipe parallel-flow heat exchanger is to heat water (Cp 4180 J/kg · °C) from 25°C to 60°C at a rate of 0.2 kg/s. The heating is to be accomplished by geothermal water (Cp 4310 J/kg · °C) available at 140°C at a mass flow rate of 0.3 kg/s. The inner tube is thin-walled and has a diameter of 0.8 cm. If the overall heat transfer coefficient of the heat exchanger is 550 W/m2 · °C, determine the length of the heat exchanger required to achieve the desired heating
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13–43 Reconsider Problem 13–42. Using EES (or other) software, investigate the effects of temperature and mass flow rate of geothermal water on the length of the heat exchanger. Let the temperature vary from 100ºC to 200ºC, and the mass flow rate from 0.1 kg/s to 0.5 kg/s. Plot the length of the heat exchanger as functions of temperature and mass flow rate, and discuss the results
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13–44E A 1-shell-pass and 8-tube-passes heat exchanger is used to heat glycerin (Cp 0.60 Btu/lbm · °F) from 65°F to 140°F by hot water (Cp 1.0Btu/lbm · °F) that enters the thinwalled 0.5-in.-diameter tubes at 175°F and leaves at 120°F. The total length of the tubes in the heat exchanger is 500 ft. The convection heat transfer coefficient is 4 Btu/h · ft2 · °F on the glycerin (shell) side and 50 Btu/h · ft2 · °F on the water (tube) side. Determine the rate of heat transfer in the heat exchanger (a) before any fouling occurs and (b) after fouling with a fouling factor of 0.002 h · ft2 · °F/Btu occurs on the outer surfaces of the tubes.
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13–45 Atest is conducted to determine the overall heat transfer coefficient in a shell-and-tube oil-to-water heat exchanger that has 24 tubes of internal diameter 1.2 cm and length 2 m in a single shell. Cold water (Cp 4180 J/kg ·°C) enters the tubes at 20°C at a rate of 5 kg/s and leaves at 55°C. Oil (Cp 2150 J/kg · °C) flows through the shell and is cooled from 120°C to 45°C. Determine the overall heat transfer coefficient Ui of this heat exchanger based on the inner surface area of the tubes.
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13–46 Adouble-pipe counter-flow heat exchanger is to cool ethylene glycol (Cp 2560 J/kg · °C) flowing at a rate of 3.5kg/s from 80°C to 40°C by water(Cp 4180 J/kg · °C) that enters at 20°C and leaves at 55°C. The overall heat transfer coefficient based on the inner surface area of the tube is 250 W/m2 · °C. Determine (a) the rate of heat transfer, (b) the mass flow rate of water, and (c) the heat transfer surface area on the inner side of the tube.
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13–47 Water (Cp 4180 J/kg · °C) enters the 2.5-cminternal-diameter tube of a double-pipe counter-flow heat exchanger at 17°C at a rate of 3 kg/s. It is heated by steam condensing at 120°C (hfg 2203 kJ/kg) in the shell. If the overall heat transfer coefficient of the heat exchanger is 1500 W/m2 · °C, determine the length of the tube required in order to heat the water to 80°C
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13–48 A thin-walled double-pipe counter-flow heat exchanger is to be used to cool oil (Cp 2200 J/kg · °C) from 150°C to 40°C at a rate of 2 kg/s by water (Cp 4180 J/kg · °C) that enters at 22°C at a rate of 1.5 kg/s. The diameter of the tube is 2.5 cm, and its length is 6 m. Determine the overall heat transfer coefficient of this heat exchanger
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13–49 Reconsider Problem 13–48. Using EES (or other) software, investigate the effects of oil exit temperature and water inlet temperature on the overall heat transfer coefficient of the heat exchanger. Let the oil exit temperature vary from 30ºC to 70ºC and the water inlet temperature from 5ºC to 25ºC. Plot the overall heat transfer coefficient as functions of the two temperatures, and discuss the results
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13–50 Consider a water-to-water double-pipe heat exchanger whose flow arrangement is not known. The temperature measurements indicate that the cold water enters at 20°C and leaves at 50°C, while the hot water enters at 80°C and leaves at 45°C. Do you think this is a parallel-flow or counter-flow heat exchanger? Explain
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13–51 Cold water (Cp 4180 J/kg · °C) leading to a shower enters a thin-walled double-pipe counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (Cp 4190 J/kg · °C) that enters at 100°C at a rate of 3 kg/s. If the overall heat transfer coefficient is 1210 W/m2 ·°C, determine the rate of heat transfer and the heat transfer surface area of the heat exchanger
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13–52 Engine oil (Cp 2100 J/kg · °C) is to be heated from 20°C to 60°C at a rate of 0.3 kg/s in a 2-cm-diameter thinwalled copper tube by condensing steam outside at a temperature of 130°C (hfg 2174 kJ/kg). For an overall heat transfer coefficient of 650 W/m2 · °C, determine the rate of heat transfer and the length of the tube required to achieve it.
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13–53E Geothermal water (Cp 1.03 Btu/lbm · °F) is to be used as the heat source to supply heat to the hydronic heating system of a house at a rate of 30 Btu/s in a double-pipe counter-flow heat exchanger. Water (Cp 1.0 Btu/lbm · °F) is heated from 140°F to 200°F in the heat exchanger as the geothermal water is cooled from 310°F to 180°F. Determine the mass flow rate of each fluid and the total thermal resistance of this heat exchanger
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13–54 Glycerin (Cp 2400 J/kg · °C) at 20°C and 0.3 kg/s is to be heated by ethylene glycol (Cp 2500 J/kg · °C) at 60°C in a thin-walled double-pipe parallel-flow heat exchanger. The temperature difference between the two fluids is 15°C at the outlet of the heat exchanger. If the overall heat transfer coefficient is 240 W/m2 · °C and the heat transfer surface area is 3.2 m2, determine (a) the rate of heat transfer, (b) the outlet temperature of the glycerin, and (c) the mass flow rate of the ethylene glycol
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13–55 Air (Cp 1005 J/kg · °C) is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at 95 kPa and 20°C at a rate of 0.8 m3/s. The combustion gases (Cp 1100 J/kg · °C) enter at 180°C at a rate of 1.1 kg/s and leave at 95°C. The product of the overall heat transfer coefficient and the heat transfer surface area is AU 1200 W/°C. Assuming both fluids to be unmixed, determine the rate of heat transfer and the outlet temperature of the air.
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13–56 A shell-and-tube heat exchanger with 2-shell passes and 12-tube passes is used to heat water (Cp 4180 J/kg · °C) in the tubes from 20°C to 70°C at a rate of 4.5 kg/s. Heat is supplied by hot oil (Cp 2300 J/kg · °C) that enters the shell side at 170°C at a rate of 10 kg/s. For a tube-side overall heat transfer coefficient of 600 W/m2 · °C, determine the heat transfer surface area on the tube side.
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13–57 Repeat Problem 13–56 for a mass flow rate of 2 kg/s for water
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13–58 Ashell-and-tube heat exchanger with 2-shell passes and 8-tube passes is used to heat ethyl alcohol (Cp 2670 J/kg · °C) in the tubes from 25°C to 70°C at a rate of 2.1 kg/s. The heating is to be done by water (Cp 4190J/kg ·°C) that enters the shell side at 95°C and leaves at 45°C. If the overall heat transfer coefficient is 950 W/m2 · °C, determine the heat transfer surface area of the heat exchanger.
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13–59 Ashell-and-tube heat exchanger with 2-shell passes and 12-tube passes is used to heat water (Cp 4180 J/kg · °C) with ethylene glycol (Cp 2680 J/kg · °C). Water enters the tubes at 22°C at a rate of 0.8 kg/s and leaves at 70°C. Ethylene glycol enters the shell at 110°C and leaves at 60°C. If the overall heat transfer coefficient based on the tube side is 280 W/m2 · °C, determine the rate of heat transfer and the heat transfer surface area on the tube side.
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13–60 Reconsider Problem 13–59. Using EES (or other) software, investigate the effect of the mass flow rate of water on the rate of heat transfer and the tube-side surface area. Let the mass flow rate vary from 0.4 kg/s to 2.2 kg/s. Plot the rate of heat transfer and the surface area as a function of the mass flow rate, and discuss the results
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13–61E Steam is to be condensed on the shell side of a 1-shell-pass and 8-tube-passes condenser, with 50 tubes in each pass at 90°F (hfg 1043 Btu/lbm). Cooling water (Cp 1.0 Btu/lbm · °F) enters the tubes at 60°F and leaves at 73°F. The tubes are thin-walled and have a diameter of 3/4 in. and length of 5 ft per pass. If the overall heat transfer coefficient is 600 Btu/h · ft2 · °F, determine (a) the rate of heat transfer, (b) the rate of condensation of steam, and (c) the mass flow rate of cold water.
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13–62E Reconsider Problem 13–61E. Using EES (or other) software, investigate the effect of the condensing steam temperature on the rate of heat transfer, the rate of condensation of steam, and the mass flow rate of cold water. Let the steam temperature vary from 80ºF to 120ºF. Plot the rate of heat transfer, the condensation rate of steam, and the mass flow rate of cold water as a function of steam temperature, and discuss the results
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13–63 Ashell-and-tube heat exchanger with 1-shell pass and 20–tube passes is used to heat glycerin (Cp 2480 J/kg · °C) in the shell, with hot water in the tubes. The tubes are thinwalled and have a diameter of 1.5 cm and length of 2 m per pass. The water enters the tubes at 100°C at a rate of 5 kg/s and leaves at 55°C. The glycerin enters the shell at 15°C and leaves at 55°C. Determine the mass flow rate of the glycerin and the overall heat transfer coefficient of the heat exchanger
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13–64 In a binary geothermal power plant, the working fluid isobutane is to be condensed by air in a condenser at 75°C (hfg 255.7 kJ/kg) at a rate of 2.7 kg/s. Air enters the condenser at 21ºC and leaves at 28ºC. The heat transfer surface area based on the isobutane side is 24 m2. Determine the mass flow rate of air and the overall heat transfer coefficient
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13–65 Hot exhaust gases of a stationary diesel engine are to be used to generate steam in an evaporator. Exhaust gases (Cp 1051 J/kg · ºC) enter the heat exchanger at 550ºC at a rate of 0.25 kg/s while water enters as saturated liquid and evaporates at 200ºC (hfg 1941 kJ/kg). The heat transfer surface area of the heat exchanger based on water side is 0.5 m2 and overall heat transfer coefficient is 1780 W/m2 · ºC. Determine the rate of heat transfer, the exit temperature of exhaust gases, and the rate of evaporation of water
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13–66 Reconsider Problem 13–65. Using EES (or other) software, investigate the effect of the exhaust gas inlet temperature on the rate of heat transfer, the exit temperature of exhaust gases, and the rate of evaporation of water. Let the temperature of exhaust gases vary from 300ºC to 600ºC. Plot the rate of heat transfer, the exit temperature of exhaust gases, and the rate of evaporation of water as a function of the temperature of the exhaust gases, and discuss the results
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13–67 In a textile manufacturing plant, the waste dyeing water (Cp 4295 J/g · ºC) at 75°C is to be used to preheat fresh water (Cp 4180 J/kg · ºC) at 15ºC at the same flow rate in a double-pipe counter-flow heat exchanger. The heat transfer surface area of the heat exchanger is 1.65 m2 and the overall heat transfer coefficient is 625 W/m2 · ºC. If the rate of heat transfer in the heat exchanger is 35 kW, determine the outlet temperature and the mass flow rate of each fluid stream.
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13–68C Under what conditions is the effectiveness–NTU method definitely preferred over the LMTD method in heat exchanger analysis
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13–69C What does the effectiveness of a heat exchanger represent? Can effectiveness be greater than one? On what factors does the effectiveness of a heat exchanger depend
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13–70C For a specified fluid pair, inlet temperatures, and mass flow rates, what kind of heat exchanger will have the highest effectiveness: double-pipe parallel-flow, double-pipe counter-flow, cross-flow, or multipass shell-and-tube heat exchanger
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13–71C Explain how you can evaluate the outlet temperatures of the cold and hot fluids in a heat exchanger after its effectiveness is determined
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13–72C Can the temperature of the hot fluid drop below the inlet temperature of the cold fluid at any location in a heat exchanger? Explain
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13–73C Can the temperature of the cold fluid rise above the inlet temperature of the hot fluid at any location in a heat exchanger? Explain
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13–74C Consider a heat exchanger in which both fluids have the same specific heats but different mass flow rates. Which fluid will experience a larger temperature change: the one with the lower or higher mass flow rate
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13–75C Explain how the maximum possible heat transfer rate Q · max in a heat exchanger can be determined when the mass flow rates, specific heats, and the inlet temperatures of the two fluids are specified. Does the value of Q · max depend on the type of the heat exchanger
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13–76C Consider two double-pipe counter-flow heat exchangers that are identical except that one is twice as long as the other one. Which heat exchanger is more likely to have a higher effectiveness
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13–77C Consider a double-pipe counter-flow heat exchanger. In order to enhance heat transfer, the length of the heat exchanger is now doubled. Do you think its effectiveness will also double
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13–78C Consider a shell-and-tube water-to-water heat exchanger with identical mass flow rates for both the hot and cold water streams. Now the mass flow rate of the cold water is reduced by hal
f. Will the effectiveness of this heat exchanger increase, decrease, or remain the same as a result of this modification? Explain. Assume the overall heat transfer coefficient and the inlet temperatures remain the same
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13–79C Under what conditions can a counter-flow heat exchanger have an effectiveness of one? What would your answer be for a parallel-flow heat exchanger
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13–80C How is the NTU of a heat exchanger defined? What does it represent? Is a heat exchanger with a very large NTU (say, 10) necessarily a good one to buy?
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13–81C Consider a heat exchanger that has an NTU of 4. Someone proposes to double the size of the heat exchanger and thus double the NTU to 8 in order to increase the effectiveness of the heat exchanger and thus save energy. Would you support this proposal
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13–82C Consider a heat exchanger that has an NTU of 0.1. Someone proposes to triple the size of the heat exchanger and thus triple the NTU to 0.3 in order to increase the effectiveness of the heat exchanger and thus save energy. Would you support this proposal
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13–83 Air (Cp 1005 J/kg · °C) enters a cross-flow heat exchanger at 10°C at a rate of 3 kg/s, where it is heated by a hot water stream (Cp 4190 J/kg ·°C) that enters the heat exchanger at 95°C at a rate of 1 kg/s. Determine the maximum heat transfer rate and the outlet temperatures of the cold and the hot water streams for that case
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13–84 Hot oil (Cp 2200 J/kg · °C) is to be cooled by water (Cp 4180 J/kg · °C) in a 2-shell-pass and 12-tube-pass heat exchanger. The tubes are thin-walled and are made of copper with a diameter of 1.8 cm. The length of each tube pass in the heat exchanger is 3 m, and the overall heat transfer coefficient is 340 W/m2 · °C. Water flows through the tubes at a total rate of 0.1 kg/s, and the oil through the shell at a rate of 0.2 kg/s. The water and the oil enter at temperatures 18°C and 160°C, respectively. Determine the rate of heat transfer in the heat exchanger and the outlet temperatures of the water and the oil.
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13–85 Consider an oil-to-oil double-pipe heat exchanger whose flow arrangement is not known. The temperature measurements indicate that the cold oil enters at 20°C and leaves at 55°C, while the hot oil enters at 80°C and leaves at 45°C. Do you think this is a parallel-flow or counter-flow heat exchanger? Why? Assuming the mass flow rates of both fluids to be identical, determine the effectiveness of this heat exchanger
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13–86E Hot water enters a double-pipe counter-flow waterto-oil heat exchanger at 220°F and leaves at 100°F. Oil enters at 70°F and leaves at 150°F. Determine which fluid has the smaller heat capacity rate and calculate the effectiveness of this heat exchanger
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13–87 A thin-walled double-pipe parallel-flow heat exchanger is used to heat a chemical whose specific heat is 1800 J/kg · °C with hot water (Cp 4180 J/kg · °C). The chemical enters at 20°C at a rate of 3 kg/s, while the water enters at 110°C at a rate of 2 kg/s. The heat transfer surface area of the heat exchanger is 7 m2 and the overall heat transfer coefficient is 1200 W/m2 · °C. Determine the outlet temperatures of the chemical and the water.
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13–88 Reconsider Problem 13–87. Using EES (or other) software, investigate the effects of the inlet temperatures of the chemical and the water on their outlet temperatures. Let the inlet temperature vary from 10ºC to 50ºC for the chemical and from 80ºC to 150ºC for water. Plot the outlet temperature of each fluid as a function of the inlet temperature of that fluid, and discuss the results
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13–89 A cross-flow air-to-water heat exchanger with an effectiveness of 0.65 is used to heat water (Cp 4180 J/kg · °C) with hot air (Cp 1010 J/kg ·°C). Water enters the heat exchanger at 20°C at a rate of 4 kg/s, while air enters at 100°C at a rate of 9 kg/s. If the overall heat transfer coefficient based on the water side is 260 W/m2 · °C, determine the heat transfer surface area of the heat exchanger on the water side. Assume both fluids are unmixed.
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13–90 Water (Cp 4180 J/kg · °C) enters the 2.5-cminternal-diameter tube of a double-pipe counter-flow heat exchanger at 17°C at a rate of 3 kg/s. Water is heated by steam condensing at 120°C (hfg 2203 kJ/kg) in the shell. If the overall heat transfer coefficient of the heat exchanger is 900 W/m2 · °C, determine the length of the tube required in order to heat the water to 80°C using (a) the LMTD method and (b) the –NTU method
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13–91 Ethanol is vaporized at 78°C (hfg 846 kJ/kg) in a double-pipe parallel-flow heat exchanger at a rate of 0.03 kg/s by hot oil (Cp 2200J/kg ·°C) that enters at 120°C. If the heat transfer surface area and the overall heat transfer coefficients are 6.2 m2 and 320 W/m2 · °C, respectively, determine the outlet temperature and the mass flow rate of oil using (a) the LMTD method and (b) the –NTU method
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13–92 Water (Cp 4180 J/kg · °C) is to be heated by solarheated hot air (Cp 1010 J/kg · °C) in a double-pipe counterflow heat exchanger. Air enters the heat exchanger at 90°C at a rate of 0.3 kg/s, while water enters at 22°C at a rate of 0.1 kg/s. The overall heat transfer coefficient based on the inner side of the tube is given to be 80 W/m2 · °C. The length of the tube is 12 m and the internal diameter of the tube is 1.2 cm. Determine the outlet temperatures of the water and the air
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13–93 Reconsider Problem 13–92. Using EES (or other) software, investigate the effects of the mass flow rate of water and the tube length on the outlet temperatures of water and air. Let the mass flow rate vary from 0.05 kg/s to 1.0 kg/s and the tube length from 5 m to 25 m. Plot the outlet temperatures of the water and the air as the functions of the mass flow rate and the tube length, and discuss the results
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13–94E A thin-walled double-pipe heat exchanger is to be used to cool oil (Cp 0.525 Btu/lbm · °F) from 300°F to 105°F at a rate of 5 lbm/s by water (Cp 1.0 Btu/lbm · °F) that enters at 70°F at a rate of 3 lbm/s. The diameter of the tube is 1 in. and its length is 20 ft. Determine the overall heat transfer coefficient of this heat exchanger using (a) the LMTD method and (b) the –NTU method
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13–95 Cold water (Cp 4180 J/kg · °C) leading to a shower enters a thin-walled double-pipe counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (Cp 4190 J/kg · °C) that enters at 100°C at a rate of 3 kg/s. If the overall heat transfer coefficient is 950 W/m2 · °C, determine the rate of heat transfer and the heat transfer surface area of the heat exchanger using the –NTU method.
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13–96 Reconsider Problem 13–95. Using EES (or other) software, investigate the effects of the inlet temperature of hot water and the heat transfer coefficient on the rate of heat transfer and surface area. Let the inlet temperature vary from 60ºC to 120ºC and the overall heat transfer coefficient from 750 W/m2 · °C to 1250 W/m2 · °C. Plot the rate of heat transfer and surface area as functions of inlet temperature and the heat transfer coefficient, and discuss the results
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13–97 Glycerin (Cp 2400 J/kg · °C) at 20°C and 0.3 kg/s is to be heated by ethylene glycol (Cp 2500 J/kg · °C) at 60°C and the same mass flow rate in a thin-walled doublepipe parallel-flow heat exchanger. If the overall heat transfer coefficient is 380 W/m2 · °C and the heat transfer surface area is 5.3 m2, determine (a) the rate of heat transfer and (b) the outlet temperatures of the glycerin and the glycol
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13–98 A cross-flow heat exchanger consists of 40 thinwalled tubes of 1-cm diameter located in a duct of 1 m 1 m cross-section. There are no fins attached to the tubes. Cold water (Cp 4180 J/kg · °C) enters the tubes at 18°C with an average velocity of 3 m/s, while hot air (Cp 1010 J/kg · °C) enters the channel at 130°C and 105 kPa at an average velocity of 12 m/s. If the overall heat transfer coefficient is 130 W/m2 · °C, determine the outlet temperatures of both fluids and the rate of heat transfer.
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13–99 A shell-and-tube heat exchanger with 2-shell passes and 8-tube passes is used to heat ethyl alcohol (Cp 2670 J/kg · °C) in the tubes from 25°C to 70°C at a rate of 2.1 kg/s. The heating is to be done by water (Cp 4190 J/kg ·°C) that enters the shell at 95°C and leaves at 60°C. If the overall heat transfer coefficient is 800 W/m2 · °C, determine the heat transfer surface area of the heat exchanger using (a) the LMTD method and (b) the –NTU method.
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13–100 Steam is to be condensed on the shell side of a 1-shell-pass and 8-tube-passes condenser, with 50 tubes in each pass, at 30°C (hfg 2430 kJ/kg). Cooling water (Cp 4180 J/kg · °C) enters the tubes at 15°C at a rate of 1800 kg/h. The tubes are thin-walled, and have a diameter of 1.5 cm and length of 2 m per pass. If the overall heat transfer coefficient is 3000 W/m2 · °C, determine (a) the rate of heat transfer and (b) the rate of condensation of steam.
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13–101 Reconsider Problem 13–100. Using EES (or other) software, investigate the effects of the condensing steam temperature and the tube diameters on the rate of heat transfer and the rate of condensation of steam. Let the steam temperature vary from 20ºC to 70ºC and the tube diameter from 1.0 cm to 2.0 cm. Plot the rate of heat transfer and the rate of condensation as functions of steam temperature and tube diameter, and discuss the results
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13–102 Cold water (Cp 4180 J/kg · °C) enters the tubes of a heat exchanger with 2-shell-passes and 13–tube-passes at 20°C at a rate of 3 kg/s, while hot oil (Cp 2200 J/kg · °C) enters the shell at 130°C at the same mass flow rate. The overall heat transfer coefficient based on the outer surface of the tube is 300 W/m2 · °C and the heat transfer surface area on that side is 20 m2. Determine the rate of heat transfer using (a) the LMTD method and (b) the –NTU method.
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13–103C Aheat exchanger is to be selected to cool a hot liquid chemical at a specified rate to a specified temperature. Explain the steps involved in the selection process
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13–104C There are two heat exchangers that can meet the heat transfer requirements of a facility. One is smaller and cheaper but requires a larger pump, while the other is larger and more expensive but has a smaller pressure drop and thus requires a smaller pump. Both heat exchangers have the same life expectancy and meet all other requirements. Explain which heat exchanger you would choose under what conditions
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13–105C There are two heat exchangers that can meet the heat transfer requirements of a facility. Both have the same pumping power requirements, the same useful life, and the same price tag. But one is heavier and larger in size. Under what conditions would you choose the smaller one
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13–106 Aheat exchanger is to cool oil (Cp 2200 J/kg · °C) at a rate of 13 kg/s from 120°C to 50°C by air. Determine the heat transfer rating of the heat exchanger and propose a suitable type.
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13–107 A shell-and-tube process heater is to be selected to heat water (Cp 4190 J/kg · °C) from 20°C to 90°C by steam flowing on the shell side. The heat transfer load of the heater is 600 kW. If the inner diameter of the tubes is 1 cm and the velocity of water is not to exceed 3 m/s, determine how many tubes need to be used in the heat exchanger.
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13–108 Reconsider Problem 13–107. Using EES (or other) software, plot the number of tube passes as a function of water velocity as it varies from 1 m/s to 8 m/s, and discuss the results
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13–109 The condenser of a large power plant is to remove 500 MW of heat from steam condensing at 30°C (hfg 2430 kJ/kg). The cooling is to be accomplished by cooling water (Cp 4180 J/kg · °C) from a nearby river, which enters the tubes at 18°C and leaves at 26°C. The tubes of the heat exchanger have an internal diameter of 2 cm, and the overall heat transfer coefficient is 3500 W/m2 · °C. Determine the total length of the tubes required in the condenser. What type of heat exchanger is suitable for this task?
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13–110 Repeat Problem 13–109 for a heat transfer load of 300 MW.
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13–111 Hot oil is to be cooled in a multipass shell-and-tube heat exchanger by water. The oil flows through the shell, with a heat transfer coefficient of ho 35 W/m2 · °C, and the water flows through the tube with an average velocity of 3 m/s. The tube is made of brass (k 110 W/m · °C) with internal and external diameters of 1.3 cm and 1.5 cm, respectively. Using water properties at 25°C, determine the overall heat transfer coefficient of this heat exchanger based on the inner surface
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13–112 Repeat Problem 13–111 by assuming a fouling factor Rf, o 0.0004 m2 · °C/W on the outer surface of the tube
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13–113 Cold water (Cp 4180 J/kg · °C) enters the tubes of a heat exchanger with 2-shell passes and 20–tube passes at 20°C at a rate of 3 kg/s, while hot oil (Cp 2200 J/kg · °C) enters the shell at 130°C at the same mass flow rate and leaves at 60°C. If the overall heat transfer coefficient based on the outer surface of the tube is 300 W/m2 · °C, determine (a) the rate of heat transfer and (b) the heat transfer surface area on the outer side of the tube.
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13–114E Water (Cp 1.0 Btu/lbm · °F) is to be heated by solar-heated hot air (Cp 0.24 Btu/lbm · °F) in a double-pipe counter-flow heat exchanger. Air enters the heat exchanger at 190°F at a rate of 0.7 lbm/s and leaves at 135°F. Water enters at 70°F at a rate of 0.35 lbm/s. The overall heat transfer coefficient based on the inner side of the tube is given to be 20 Btu/h · ft2 · °F. Determine the length of the tube required for a tube internal diameter of 0.5 in
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13–115 By taking the limit as T2 → T1, show that when T1 T2 for a heat exchanger, the Tlm relation reduces to Tlm T1 T2
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13–116 The condenser of a room air conditioner is designed to reject heat at a rate of 15,000 kJ/h from Refrigerant-134a as the refrigerant is condensed at a temperature of 40°C. Air (Cp 1005 J/kg · °C) flows across the finned condenser coils, entering at 25°C and leaving at 35°C. If the overall heat transfer coefficient based on the refrigerant side is 150 W/m2 · °C, determine the heat transfer area on the refrigerant side.
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13–117 Air (Cp 1005 J/kg · °C) is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at 95 kPa and 20°C at a rate of 0.8 m3/s. The combustion gases (Cp 1100 J/kg · °C) enter at 180°C at a rate of 1.1 kg/s and leave at 95°C. The product of the overall heat transfer coefficient and the heat transfer surface area is UAs 1620 W/°C. Assuming both fluids to be unmixed, determine the rate of heat transfer
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13–118 In a chemical plant, a certain chemical is heated by hot water supplied by a natural gas furnace. The hot water (Cp 4180 J/kg · °C) is then discharged at 60°C at a rate of 8 kg/min. The plant operates 8 h a day, 5 days a week, 52 weeks a year. The furnace has an efficiency of 78 percent, and the cost of the natural gas is $0.54 per therm (1 therm 100,000 Btu 105,500 kJ). The average temperature of the cold water entering the furnace throughout the year is 14°C. In order to save energy, it is proposed to install a water-to-water heat exchanger to preheat the incoming cold water by the drained hot water. Assuming that the heat exchanger will recover 72 percent of the available heat in the hot water, determine the heat transfer rating of the heat exchanger that needs to be purchased and suggest a suitable type. Also, determine the amount of money this heat exchanger will save the company per year from natural gas savings
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13–119 A shell-and-tube heat exchanger with 1-shell pass and 14-tube passes is used to heat water in the tubes with geothermal steam condensing at 120ºC (hfg 2203 kJ/kg) on the shell side. The tubes are thin-walled and have a diameter of 2.4 cm and length of 3.2 m per pass. Water (Cp 4180 J/kg · ºC) enters the tubes at 22ºC at a rate of 3.9 kg/s. If the temperature difference between the two fluids at the exit is 46ºC, determine (a) the rate of heat transfer, (b) the rate of condensation of steam, and (c) the overall heat transfer coefficient.
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13–120 Geothermal water (Cp 4250 J/kg · ºC) at 95ºC is to be used to heat fresh water (Cp 4180 J/kg · ºC) at 12ºC at a rate of 1.2 kg/s in a double-pipe counter-flow heat exchanger. The heat transfer surface area is 25 m2, the overall heat transfer coefficient is 480 W/m2 · ºC, and the mass flow rate of geothermal water is larger than that of fresh water. If the effectiveness of the heat exchanger is desired to be 0.823, determine the mass flow rate of geothermal water and the outlet temperatures of both fluids
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13–121 Air at 18ºC (Cp 1006 J/kg · ºC) is to be heated to 70ºC by hot oil at 80ºC (Cp 2150 J/kg · ºC) in a cross-flow heat exchanger with air mixed and oil unmixed. The product of heat transfer surface area and the overall heat transfer coefficient is 750 W/m2 · ºC and the mass flow rate of air is twice that of oil. Determine (a) the effectiveness of the heat exchanger, (b) the mass flow rate of air, and (c) the rate of heat transfer
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13–122 Consider a water-to-water counter-flow heat exchanger with these specifications. Hot water enters at 95ºC while cold water enters at 20ºC. The exit temperature of hot water is 15ºC greater than that of cold water, and the mass flow rate of hot water is 50 percent greater than that of cold water. The product of heat transfer surface area and the overall heat transfer coefficient is 1400 W/m2 · ºC. Taking the specific heat of both cold and hot water to be Cp 4180 J/kg · ºC, determine (a) the outlet temperature of the cold water, (b) the effectiveness of the heat exchanger, (c) the mass flow rate of the cold water, and (d) the heat transfer rate.
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