Consider the chip cooling scheme of .146,but with an

Chapter 7, Problem 7.97

(choose chapter or problem)

Consider the chip cooling scheme of 3.146,but with an insulated top wall placed at the pin tips toforce airflow across the pin array. Air enters the array at20?C and with a velocity Vthat may be varied but can-not exceed 10 m/s due to pressure drop considerations.The pin fin geometry, which includes the number ofpins in the NNsquare array, as well as the pin diam-eter Dpand length Lp, may also be varied, subject to theconstraint that the product NDpnot exceed 9 mm.Neglecting heat transfer through the board, assess theeffect of changes in air velocity, and hence ho, as wellas pin fin geometry, on the air outlet temperature andthe chip heat rate, if the remaining conditions of Prob-lems 3.146 and 3.27, including a maximum allowablechip temperature of 75?C, remain in effect. Recom- mend design and operating conditions for which chipcooling is enhanced. Hint:The air outlet temperatureis governed by a relation of the form [(Ts?To)/(Ts?Ti)]?exp[?(At?o)/cp], where is the massflow rate of air passing through the array, Atis the totalheat transfer surface area (chip and pins), and o? is theoverall surface efficiency defined by Equation 3.107.