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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When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a bur…

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Chapter 3, Problem 3.148P

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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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