Homework_4_Solution

Homework_4_Solution - 3-114 Circular cooling fins of a...

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Unformatted text preview: 3-114 Circular cooling fins of a specified dimension are used to enhance heat transfer from a surface. Given that the ends of the fins are connected to another surface, determine (a) -=TxTx)()(along a fin, and calculate the temperature at 2/Lx=; (b) the rate of heat transferred from the hot surface through each fin and the fin effectiveness, as well as whether the use of fins is justified; (c) the total rate of heat transfer given the surface area and number of fins being used.Assumptions Steady operating conditions exist. The thermal conductivity and convection coefficients are constant. The radiation of the fins is taken into account through the conduction and convection coefficients. The temperature along the fins varies axially but not radially. Known ================-1-27222221m623.31m10854.74m00314.m0.009541.1.fins625KW/m100K15.273K15.273K15.405KW/m400m0254.m001.ccSsskAhPmDADPD-nAnhTTTkLDUnknown totfinfinQQLTx..,,),2/(),(Property Relations and Laws mLmLmLmLmLmLmLmLssmxmxeeCeCCeCeCeCeCeCTTLCCCCTTeCeCx222212212121212211211)(1)(:(3)and(2)From(3))((2))(K132)((1))(-=-=-=-==+-=-==+-=+=---Plugging into (1) and rearranging yields ][)]([)()()()()()()()(1)()()()(222mLSinhLxmSinheeeexeeeeeeeexLxmLxmmLmLmLmxmxmLmLmLmLmxmxmL--=--=--=--=----+--+-(a) ( )C61Sinh[mL]x)]Sinh[m(LTTos1=+=--=TLLT(x))2/()2/((b) W1.97==--=-=-=89.34.1K)132()m623.31)(m10854.7(K)W/m400(][)()(1-27.mLSinhmLCoshmkAdxdTkAQcxcfinTherefore, the fins are justified since 190 is sufficiently larger than 1 (c)W1357=+=-+=-+-=-=K))(132mK)(0.0095W/m100(89....
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This note was uploaded on 03/24/2008 for the course MCEN 3022 taught by Professor Gustavojoseph during the Spring '08 term at Colorado.

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Homework_4_Solution - 3-114 Circular cooling fins of a...

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