Thermodynamics HW Solutions 237

Thermodynamics HW Solutions 237 - Chapter 15 Steady Heat...

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Chapter 15 Steady Heat Conduction 3-117 A hot plate is to be cooled by attaching aluminum pin fins on one side. The rate of heat transfer from the 1 m by 1 m section of the plate and the effectiveness of the fins are to be determined. Assumptions 1 Steady operating conditions exist. 2 The temperature along the fins varies in one direction only (normal to the plate). 3 Heat transfer from the fin tips is negligible. 4 The heat transfer coefficient is constant and uniform over the entire fin surface. 5 The thermal properties of the fins are constant. 6 The heat transfer coefficient accounts for the effect of radiation from the fins. Properties The thermal conductivity of the aluminum plate and fins is given to be k = 237 W/m °C. Analysis Noting that the cross-sectional areas of the fins are constant, the efficiency of the circular fins can be determined to be a hp kA hD kD h kD c == = = ° ° = π 2 4 44 3 5 386 0 0025 12 04 / () ( . ) . W/m . C W/m. C m m 2 -1 η fin -1 -1 m m m × × = tanh tanh( . . ) .. . aL aL 12 04 0 03 12 04 0 03 0 959 The number of fins, finned and unfinned surface areas, and heat transfer rates from those areas are n 1 0 006 0 006 27777 m m) m) 2 (.
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