Chapter 3, Problem 3.143P

The fin array of Problem 3.142 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, $T_o=T_L,$ thereby establishing symmetry about the midplane 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 airflow and the fin surfaces. The length of the fin passages between adjoining parallel plates is $L=8\text{mm,}$ whereas the fin thermal conductivity and convection coefficient are $k=200\text{W/m}\cdot \text{K}$ (aluminum) and $h=150{\text{W/m}}^{\text{2}}\cdot \text{K,}$ respectively.

1. If the fin thickness and pitch are $t=1\text{mm}$ and $S=4\text{mm,}$ respectively, what is the value of the thermal resistance for a one-half section of the tin array?
2. 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.