Backward boundary layer heat transfer in a converging channel

The backward boundary layer flow in a converging channel described by the classical Pohlhausen solution is considered. The associated forced convection temperature boundary layer corresponding to the power-law wall temperature distribution Tw(x)=T∞+T0·(x/L)γ is investigated analytically. While in general, self-similar forced convection thermal boundary layers do exist for all (real) values of the power-law exponent γ, in the present case it is found that, surprisingly, they only can exist for negative values of γ, but not for γ⩾0. The corresponding solutions of the energy equation are given in terms of Gauss' hypergeometric function. The heat transfer characteristics of the flow as functions of the exponent γ and the Prandtl number are investigated in detail.