Reference no: EM13946763

Consider the chip cooling scheme of Problem 3.146, but with an insulated top wall placed at the pin tips to force airflow across the pin array. Air enters the array at 20°C and with a velocity V that may be varied but can- not exceed 10 m/s due to pressure drop considerations. The pin fin geometry, which includes the number of pins in the N X N square array, as well as the pin diam- eter Dp and length Lp, may also be varied, subject to the constraint that the product NDp not exceed 9 mm. Neglecting heat transfer through the board, assess the effect of changes in air velocity, and hence ho, as well as pin fin geometry, on the air outlet temperature and the chip heat rate, if the remaining conditions of Prob- lems 3.146 and 3.27, including a maximum allowable chip temperature of 75°C, remain in effect. Recom- mend design and operating conditions for which chip cooling is enhanced. Hint: The air outlet temperature is governed by a relation of the form [(Ts - To)/(Ts  - Ti)] = exp[-(h AtYo)/mcp],  where  m  is  the  mass flow rate of air passing through the array, At is the total heat transfer surface area (chip and pins), and Yo is the overall surface efficiency defined by Equation 3.107.