Question

Air enters a 23-cm-diameter 13-m-long underwater duct at 53°C and 1 atm at a mean velocity of 7 m/s, and is cooled by the water outside. If the average heat transfer coefficient is 85 W/m2 °C and the tube temperature is nearly equal to the water temperature of 5°C, determine the exit temperature of air and the rate of heat transfer. Use Table A-15 for the properties of air at the anticipated average temperature of 30°C. Answer in Watts.

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Answer 1

7g. m = SA, Varg Solution - From table A-15 , properties of air at the anticipated average $ = 1.164 kg/m Cp = 1007 mass flow rate of the water 8 I Do Vang 5 1164 YEx(0.239% + m = 0.3385 kg/s The Surface area of Heat' transfer. As = TDL • Tx 0.23x13 The temperature at the end of the tube is found from the number of transfer units, NTU = has 85% 9.393 = 2.342 mcp 0.3385 x 1007 9.393 m2 Temperature at the end of the tube Tout - T: -(Ts - Tin) e-NTU -5-(5-53) -2.342 Tout= 9.614 °C So exit temperature. Tout = 9.61°C

log mean Temperature difference LMAT Tout -Tin ln (Tout-Tis Tin-Ts 9.614-53 In 19.6145 53-5 LMAT = 18.524 °C So. heat transfer Q = ħA (LMAT)= 85 x 9.393 x18.524 14789-65 W u 8 = 14.8 KW