Similarity solutions of energy and momentum boundary layer equations for a power-law shear driven flow over a semi-infinite flat plate

The problem of a steady forced convection thermal boundary-layer driven by a power-law shear is investigated. The search for similarity solutions reduces the problem to a couple of ordinary differential equations containing three parameters: the exponent of the decaying exterior velocity profile, the exponent of the power-law prescribing the thermal condition on the wall and Prandtl number. The effects of these parameters on the existence and form of similarity solution are investigated and the functional dependence of the local Nusselt number on these parameters is reported and discussed. An analysis of the assumptions usually accepted to derive similarity solutions is also reported in order to show the range of values of the exterior velocity power-law exponent for which such solutions may exist.