The fin array of Problem 3.130 is commonly found in compact heat exchangers, whose function is to provide a large surface area per unit volume in transferring heat from one fluid to another. Consider conditions for which the second fluid maintains equivalent temperatures at the parallel plates, To = TL, thereby establishing symmetry about the mid plane of the fin array. The heat exchanger is 1 m long in the direction of the flow of air (first fluid) and 1 m wide in a direction normal to both the air flow and the fin surfaces. The length of the fin passages between adjoining parallel plates is L = 8 mm, while the fin thermal conductivity and convection coefficient are k = 200 W/m ∙ K (aluminum) and h = 150 W/m2 ∙ K, respectively.

(a) If the fin thickness and pitch are t = 1 mm and S = 4 mm, respectively, what is the value of the thermal resistance Rt,o for a one-half section of the fin array?

(b) Subject to the constraints that the fin thickness and pitch may not be less than 0.5 and 3 mm. respectively, assess the effect of changes in t and S.