$2-(30$ pts $)$ A straight fin fabricated from aluminum alloy $(k=185\frac{W}{m}K)$ has a base thickness of $t=3mm$ and a length of $L=15mm.$ Its base temperature is $T_b=100C,$ and it is exposed to a fluid for which $T_{}=20C$ and $h=50\frac{W}{m^2}K.$ For the foregoing conditions and a fin of unit $(1$ m $)$ width, compare the fin heat transfer rates and efficiencies for rectangular and triangular profiles. Steady state conditions are valid, there is one$-$dimensional heat transfer, radiation is negligible, and convection coefficient is uniform.