Finned passages are frequently formed between parallel plates to enhance convection heat transfer in compact heat exchanger cores. An important application is in electronic equipment cooling, where one or more air-cooled stacks are placed between heat-dissipating electrical components. Consider a single stack of rectangular fins of length L and thickness t, with convection conditions corresponding to hand T∞.

(a) Obtain expressions for the fin heat transfer rates, qf,o and qf,L, in terms of the base temperatures, To and T1.

(b) In a specific application, a stack that is 200 mm wide and 100 mm deep contains 50 fins, each of length L = 12 mm. The entire stack is made from aluminum, which is everywhere 1.0 mm thick. If temperature limitations associated with electrical components joined to opposite plates dictate maximum allowable plate temperatures of To = 400 K and TL = 350 K, what are the corresponding maximum power dissipations if h = 150 W/m2 ∙ K and T'∞ = 300 K?

-200 mm- 100 mm T. L. 14 mm Air T h