Explanation Given: The prescribed heat transfer coefficient is h o = 1000 W / m 2 ⋅ K . The upper limit for heat transfer coefficient is h o = 250 W / m 2 ⋅ K . The maximum temperature limit is T = 75 ° C . The pin diameter is D p . The pin length is L p . The product limit is N 1 2 D p ≥ 9 mm . Formula used: The expression for total power dissipation is given as, q c = A c ( T c − T ∞ i ) 1 h i + R ″ t c + L b k b Here, R ″ t c is resistance on chip. The expression for resistance of pin array is given as, R t o = ( η o h o A t ) − 1 η o = 1 − N A t A t ( 1 − η t ) A t = N A f + A b A f = π D p ( L p + D p 4 ) Calculation: The assumptions made in the analysis are as follow, Steady state condition. One dimension heat transfer in chip-board assembly. Negligible pin-chip contact resistance. Constant properties. Negligible chip thermal resistance. Uniform chip temperature. The subject to the constraint is N 1 2 D p ≤ 9 mm , the above expression of q t used as a function of D p for value of 36 , L p = 15 mm and N = 16 , 25 , using performance calculation, extended surface model for the pin fin array we get,

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ISBN: 9780470501962

Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

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Introduction to Heat Transfer

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The effect of changes in pin fin geometry.

Solution Summary: The author explains the effect of changes in pin fin geometry. The prescribed heat transfer coefficient is 1000, the upper limit is 250, and the maximum temperature is 75°.

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