$(10$ points$)$ Consider an ammonia parallel flowing past an isothermal flat plate with length $L=30mm.$ The plate maintains at a temperature of $T_S=50C.$ The flow is at a velocity of $v_{}=150\frac{m}{s}$ and a temperature of $T_{}=300C.$ Ammonia has the kinematic viscosity $v=50{10}^{-6}\frac{m^2}{s}$ and Prandtl number $Pr=1.$ Obtain the temperature $T$ at the point with $x=15mm$ and $y=0\mathrm{.}2mm$ within the thermal boundary layer $($Figure $3).$

Figure $3$