Chapter 4, Problem 4.66P

Consider a two-dimensional. straight triangular fin of length $L=50\text{mm}$ and base thickness $t=20\text{mm}.$ The thermal conductivity of the tin is $k=25\text{W/m}\cdot \text{K}\text{.}$ The base temperature is $T_b=50°\text{C,}$ and the tin is exposed to convection conditions characterized by $h=50{\text{W/m}}^{\text{2}}\cdot \text{K,}{T}_{\infty }=20°\text{C}\text{.}$ Using a finite difference mesh with $\Delta x=10\text{mm}$ and $\Delta y=2\text{mm,}$ and taking advantage of symmetry, determine the tin efficiency, ${\eta }_f.$ Compare your value of the tin efficiency with that reported in Figure 3.19.