The fin array in Figure $1$ is constructed from $5$ aluminum fins and has a wall height of $25$ mm $,$ width of $25$ mm $,$ thickness of $3$ mm and a length $L=30mm.$ Air surrounding the fin array is at a temperature $T_{}=30C$ and has a convective heat transfer coefficient of $h=40\frac{W}{m^2}K.$ The fins are at a base temperature of $T_b=105C.$ Given that the thermal conductivity of aluminum at the given conditions is $k=239\frac{W}{m}K$ and assuming steady state conditions, no heat generation and negligible radiation, find $($a$)$the heat transfer rate for one of the fins and $(25$ points$),($b$)$ the fin efficiency for one of the fins $(10$ points$).$ You may use any of the following values if applicable: $h\frac{P}{k}{A}_c=124\mathrm{.}9651m^{-2},hPk{A}_c=0\mathrm{.}040152\frac{W^2}{K^2}$ and $w{t}^2=2\mathrm{.}25{10}^{-7}{m}^3.$

Figure $1$