Consider steady two$-$dimensional laminar boundary layer flow of a very low Prandtl number fluid, over a flat plate, with a free$-$stream velocity and temperature U$\backslash$infty and T$\backslash$infty respectively. Assuming constant properties and that the temperature profile inside the thermal boundary layer at any location x from the leading edge to be T $($x$,$ y$)=$ A$+$ B sin $($Cy$),$ where A$,$ B and C are constants; determine the following: a$.$ Expression for the thermal boundary layer thickness, b$.$ Expression for the local wall Nusselt number.