a$)$ In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as$,$

$\frac{T-T_{}}{T_{}-T_{}}=1-$exp$(-Pr(\frac{u_{}y}{v}))$

Where $y$ is the distance normal to the surface and $Pr=0\mathrm{.}7.$ If $\frac{u_{-}}{v}=\frac{5000}{m}$ and the air and surface temperatures are respectively $400$ K and $300$ K $,$ determine the surface heat flux.

$(18$ marks$)$