Explanation Given: the thermal conductivity of the steel tube is 40 W / m . K , The inner diameter of the tube is 50 mm , the wall thickness of the tube is 4 mm , the mass flow rate of the exhaust gase is 2 kg / s , the temperature of exhaust gas at the inlet of tube is 400 ° C , the temperature of exhaust gas at the outlet of tube is 215 ° C , the fouling resistance on the gas side of the tube is 0.0015 m 2 ⋅ K / W and the pressure of the saturated bar is 11.7 bar . The properties of air at 11.7 bar are given below, The density of the air is 0.6 kg / m 3 . The thermal conductivity of the air is 0.0457 W / m . K . The specific heat capacity of the oil is 1047 J / kg ⋅ K . The prandtl number for the air is 0.684 . The kinematic viscosity of the air is 4.991 × 10 − 5 m 2 / s . The temperature of the air is 187 ° C . The expression for Nusselt number is given by, N u = − ln ( 1 − ε ) ...... (1) Here, ε is the effectiveness of the heat exchanger. The expression for the effectiveness of the heat exchanger is, ε = T h i − T h o T h i − T c i Here, T h i is the temperature of the exhaust gas at inlet of the tube. T h o is the temperature of the exhaust gas at outlet of the tube. T c i is the temperature of the coolant. Substitute 400 °C for the T h i , 215 ° C for the T h o and 187 ° C for the T c i in the above equation. ε = 400 °C − 215 ° C 215 ° C − 187 ° C = 0.86 Substitute 0.86 for ε in equation (1). N u = − ln ( 1 − 0.86 ) = 2.21 The expression for Nusselt number is given by, N u = U A s C min ...... (2) Here, U is the overall heat transfer coefficient. A s is the area of the tube exposed to transfer of heat. c min is the minimum heat capacity. The expression for minimum heat capacity of the air is given by, C min = m ˙ c g Here, m ˙ is the mass flow rate of air. c g is the specific heat capacity of the air. Substitute 2 kg / s for m ˙ and 1047 W / K for c g in equation (1). C min = ( 2 kg / s ) ( 1047 ) = 2094 W / K Substitute 2094 W / K for C min and 2

7th Edition

ISBN: 9780470501979

Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

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Heat exchangers are the types of equipment that are primarily employed to transfer the thermal energy from one fluid to another, provided that one of the fluids should be at a higher thermal energy content than the other fluid.

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The heat exchanger is a combination of two words ''Heat'' and ''Exchanger''. It is a mechanical device that is used to exchange heat energy between two fluids.

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Chapter 11, Problem 11.62P

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The number of tubes in shell and tube heat exchanger and the total length of the tubes.

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Chapter 11, Problem 11.61P

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