Q$3.$ Pr$.5-35.$ One side of a $2-$m$-$high and $3-$m$-$wide vertical plate at $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is to be cooled by attaching aluminum fins $(\backslash ($ k$=237\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}\backslash$cdot$\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ))$ of rectangular profile in an environment at $\backslash (35^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The fins are $2$ cm long, $0\mathrm{.}3$ cm thick, and $0\mathrm{.}4$ cm apart. The heat transfer coefficient between the fins and the surrounding air for combined convection and radiation is estimated to be $\backslash (30\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{2.\}\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Assuming steady onedimensional heat transfer along the fin and taking the nodal spacing to be $0\mathrm{.}5$ cm $,$ determine $($a$)$ the finite difference formulation of this problem, $($b$)$ the nodal temperatures along the fin by solving these equations, $($c$)$ the rate of heat transfer from a single fin, and $($d$)$ the rate of heat transfer from the entire finned surface of the plate.