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.
