A rectangular fin heat sink is shown below. There is fluid flow on both sides of the $2024-$T$6$ aluminum alloy

$(k=186\frac{W}{m}K)$ exchanger. The convection coefficients at the straight and finned surfaces are $50\frac{W}{m^2}K$

and $20\frac{W}{m^2}K$ respectively. The flow air temperature at straight surface is $500$ K and finned surface is $300$

K$.$

The geometric parameters are given as;

Height : $15$ mm

Fin thickness : $2$ mm

Base thickness: $4$ mm

Width : $10$ mm

Length : $8$ mm

a$)$ Find the efficiency of a single fin.

b$)$ Find the efficiency of the fin array.

c$)$ Find the heat transfer rate.