Calor

Review Problems


3-152E Steam is produced in copper tubes by heat transferred from another fluid condensing outside the tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick layer of limestone is formed on the inner surface of the tube is to be determined.
Assumptions 1 Heat transfer is steady since there is no indication of any change withtime. 2 Heat transfer is one-dimensional since there is thermal symmetry about the centerline and no variation in the axial direction. 3 Thermal properties are constant. 4 Heat transfer coefficients are constant and uniform over the surfaces.
Properties The thermal conductivities are given to be k = 223 Btu/h(ft(°F for copper tubes and k = 1.7 Btu/h(ft(°F for limestone.
Analysis The totalthermal resistance of the new heat exchanger is
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After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate are determined to be
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Discussion Note that the limestone layer will change the inner surface area of the pipe and thus the internal convection resistance slightly, but this effect should be negligible.
3-153E Steam isproduced in copper tubes by heat transferred from another fluid condensing outside the tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick layer of limestone is formed on the inner and outer surfaces of the tube is to be determined.
Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer isone-dimensional since there is thermal symmetry about the centerline and no variation in the axial direction. 3 Thermal properties are constant. 4 Heat transfer coefficients are constant and uniform over the surfaces.
Properties The thermal conductivities are given to be k = 223 Btu/h(ft(°F for copper tubes and k = 1.7 Btu/h(ft(°F for limestone.
Analysis The total thermal resistance of the new heatexchanger is
[pic]
After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate are determined to be


[pic] [pic]
Discussion Note that the limestone layer will change the inner surface area of the pipe and thus the internal convection resistance slightly, but this effect should be negligible.
3-154 A cylindrical tank filled with liquidpropane at 1 atm is exposed to convection and radiation. The time it will take for the propane to evaporate completely as a result of the heat gain from the surroundings for the cases of no insulation and 7.5-cm thick glass wool insulation are to be determined.
Assumptions 1 Heat transfer is steady. 2 Heat transfer is one-dimensional. 3 The combined heat transfer coefficient is constant and uniformover the entire surface. 4 The temperature of the thin-shelled spherical tank is said to be nearly equal to the temperature of the propane inside, and thus thermal resistance of the tank and the internal convection resistance are negligible.
Properties The heat of vaporization and density of liquid propane at 1 atm are given to be 425 kJ/kg and 581 kg/m3, respectively. The thermal conductivity ofglass wool insulation is given to be k = 0.038 W/m(°C.
Analysis (a) If the tank is not insulated, the heat transfer rate is determined to be
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The volume of the tank and the mass of the propane are
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The rate of vaporization of propane is
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Then the time period for the propane tank to empty becomes
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(b) We now repeat calculations for the case of insulatedtank with 7.5-cm thick insulation.
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Noting that the insulation on the side surface and the end surfaces are in parallel, the equivalent resistance for the insulation is determined to be
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Then the total thermal resistance and the heat transfer rate become
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Then the time period for the propane tank to empty becomes
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3-155 Hot water is flowing through a...