Chapter 15 Steady Heat Conduction3-117 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. Assumptions1Steady operating conditions exist. 2The temperature along the fins varies in one direction only (normal to the plate). 3Heat transfer from the fin tips is negligible. 4 The heat transfer coefficient is constant and uniform over the entire fin surface. 5The thermal properties of the fins are constant. 6 The heat transfer coefficient accounts for the effect of radiation from the fins. PropertiesThe 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 ahpkAhDkDhkDc====°°=π2444353860 002512 04/()(.).W/m . CW/m. Cmm2-1ηfin-1-1m mm××=tanhtanh(..)...aLaL12 040 0312 040 030 959 The number of fins, finned and unfinned surface areas, and heat transfer rates from those areas are n10 0060 00627777mm)m)2(.
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