Heat transfer on a plate beneath an external uniform shear flow

The thermal characteristics of the flow over a semi-infinite flat plate driven by a uniform shear in the far field are investigated and compared to those of the corresponding classical Blasius flow problem. Similarity solutions are given in an exact analytic form in terms of the incomplete gamma function and the confluent hypergeometric function. Substantial differences are found concerning the scaling behavior of the wall heat flux for prescribed constant wall temperature Tw, as well as for the wall temperature distribution for prescribed constant heat flux qw, both with respect to the wall coordinate x and the Prandtl number Pr. While for the Blasius flow different scaling laws hold for small and large values of Pr, in the uniform shear flow problem a universal scaling law is found for all Pr.