Integrated circuit (IC) boards are stacked within a

Chapter 9, Problem 9.47

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Integrated circuit (IC) boards are stacked within a ductand dissipate a total of 500 W. The duct has a squarecross section with w?H?150 mm and a length of0.5 m. Air flows into the duct at 25?C and 1.2 m3/min,and the convection coefficient between the air andthe inner surfaces of the duct is . Theentire outer surface of the duct, which is anodized withan emissivity of 0.5, is exposed to ambient air and largesurroundings at 25?C.Your assignment is to develop a model to estimate theoutlet temperature of the air, Tm,o, and the average sur-face temperature of the duct, Ts.(a) Assuming a surface temperature of 37?C, estimatethe average free convection coefficient, , for theouter surface of the duct. (b) Assuming a surface temperature of 37?C, estimatethe average linearized radiation coefficient, , for the outer surface of the duct.(c) Perform an energy balance on the duct by consider-ing the dissipation of electrical power in theICs, the rate of change in the energy of air flowingthrough the duct, and the rate of heat transfer fromthe air in the duct to the surroundings. Express thelast process in terms of thermal resistances betweenthe mean temperature, , of the air in the ductand the temperature of the ambient air and thesurroundings.(d) Substitute numerical values into the expression ofpart (c) and calculate the air outlet temperature,Tm,o. Estimate the corresponding value of Ts. Com-ment on your results and the assumptions inherentin your model.