Heat transfer characteristics of a boundary-layer flow driven by a power-law shear over a semi-infinite flat plate

The hydrodynamic and thermal boundary layer similarity flows driven past a semi-infinite impermeable flat plate by a power-law shear with asymptotic velocity profile U∞(y)=βy−1/2 (y→∞,β>0) is considered (y denotes the coordinate normal to the plate). Assuming that the buoyancy and viscous dissipation effects may be neglected, the special cases of an isothermal and of an adiabatic flat plate are examined both analytically and numerically.