Exact Solution for Heat Transfer across the Boundary Layer Induced by an Isothermal moving Surface

We consider the problem of convective heat transfer across the laminar boundary layer induced by an isothermal moving surface in a Newtonian fluid. In a previous work, an exact power series solution was derived for the hydrodynamic flow. Here, we utilize this expression to develop an exact solution for the associated thermal boundary layer as characterized by the Prandtl number (Pr) and local Reynolds number along the surface. To extract the dimensionless form of the location-dependent heat transfer coefficient, the dimensionless temperature gradient at the wall is required; this gradient is solely a function of Pr and is expressed as an integral of the hydrodynamic boundary layer solution. The exact solution for the temperature gradient is computationally unstable at large Pr, and a large Pr expansion for the temperature gradient is obtained using Laplace's method. A composite solution is obtained, which is easy to implement and accurate to (10 −10 )⁠. Although divergent, the classical power series solution for the Sakiadis boundary layer—expanded about the wall—may be used to obtain all higher-order corrections in the asymptotic expansion. We show that this result is connected to the physics of large Prandtl number flows.