Shown in the figure is the case of a fluid flowing parallel to a flat plate, where for a d...

Shown in the figure is the case of a fluid flowing parallel to a flat plate, where for a distance X from the leading edge, the plate and fluid are at the same temperature. For values of x > X, the plate is maintained at a constant temperature, Ts, where Ts > T∞. Assuming a cubic profile for both the hydrodynamic and the thermal boundary layers, show that the ratio of the thickness, x, is expressed as

Also show that the local Nusselt number can be expressed as