Unsteady Stagnation Point Heat Transfer

Abstract

An analysis is presented for the unsteady laminar, forced-convection heat transfer at a two-dimensional and axisymmetrical front stagnation due to an arbitrarily prescribed wall temperature or heat flux variation. The flow is incompressible and steady. The procedure begins with a consideration of the thermal boundary-layer response caused by either a step change in surface temperature or heat flux. Two appropriate asymptotic solutions, valid for small and large times, respectively, are found and satisfactorily joined for Prandtl numbers ranging from 0.01 to 100. The key to the small time solution is the transformation of the energy equation in the Laplace transform plane to an ordinary differential equation with a large parameter. An essential feature of the large time solution is the use of Meksyn’s transformation variable and the method of steepest descent in the evaluation of integrals. It is found that, for both two-dimensional and axisymmetrical stagnation, the time required for the thermal boundary layer to attain steady condition, for either a step change in surface temperature or heat flux, varies inversely with the free stream velocity and directly with 1/4 power of the Prandtl number of the fluid.