Because of the large number of devices in today's PC chips, finned heat sinks are often used to maintain the chip at an acceptable operating temperature. Several fin designs are to be evaluated, all of which have base (unfinned) area dimensions of 53 mm × 57 mm. The fins are fabricated from an extruded aluminum alloy with a thermal conductivity of 175 W/m · K. Cooling air may be supplied at 25 °C, and the maximum allowable chip temperature is 75 °C. Other features of the design and operating conditions are tabulated. Finn dimension
Design Cross Section Length L(mm) Number of fins in array Convection Coefficient (Wm^2.K)
w x w (mm)
A 3 x 3 30 6 x 9 125
B 1 x 1 7 14 x 17 375

Required:
Determine which fin arrangement is superior. In your analysis, calculate the heat rate, efficiency, and effectiveness of a single fin, as well as the total heat rate and overall efficiency of the array. Since real estate inside the computer enclosure is important, compare the total heat rate per unit volume for the two designs.