Problem $3.$ Read the section titled, "Heat transfer in a pin fin", pages $109-110$ of P$.$A$.$ Ramachandran. Derive equation $2\mathrm{.}69$ and render this ODE dimensionless using the dimensionless variables below $($you will inevitably end up with a dimensionless fin parameter, $M=h\frac{L^2}{k}A).$ Solve the ODE using Maple and plot the solution across the range of fin parameters varying between $M=0$ to $1.$

$=\frac{(\text{:}T\text{:})-T_a}{T_o-T_a},$ and $,=\frac{x}{L}$