A gas at $u_{}=20\frac{m}{s}$ and $T_{}=27C$ flows over half of a wedge, with an angle of $18.$ The base is perfectly insulated, and its top surface is maintained at a uniform temperature of $T_w=300C$ by heating inside. Solve the steady state heat transfer and fluid flow boundary layers, assuming the similarity velocity and temperature profiles. The gas properties are $v=5\mathrm{.}21{10}^{-4}\frac{m^2}{s},k=36\mathrm{.}4$ x ${10}^{-3}\frac{W}{m}*K,$ and $Pr=0\mathrm{.}7.$

$($a$)$ Plot $\frac{u}{u_{}}$ versus $\frac{y}{\sqrt[\phantom{2}]{v\frac{x}{u_{}}}}.$

$($b$)$ Plot $\frac{(T-T_{})}{(T_w-T_{})}$ versus $\frac{y}{\sqrt[\phantom{2}]{v\frac{x}{u_{}}}}.$

$($c$)$ Plot $u(y),$ at $x=0\mathrm{.}5m.$

$($d$)$ Plot $T(y),$ at $x=0\mathrm{.}5m.$