Thermal-Boundary-Layer Response to Convected Far-Field Fluid Temperature Changes

Fluid flows of varying temperature occur in heat exchangers, nuclear reactors, nonsteady-flow devices, and combustion engines, among other applications with heat transfer processes that influence energy conversion efficiency. A general numerical method was developed with the capability to predict the transient laminar thermal-boundary-layer response for similar or nonsimilar flow and thermal behaviors. The method was tested for the step change in the far-field flow temperature of a two-dimensional semi-infinite flat plate with steady hydrodynamic boundary layer and constant wall temperature assumptions. Changes in the magnitude and sign of the fluid-wall temperature difference were considered, including flow with no initial temperature difference and built-up thermal boundary layer. The equations for momentum and energy were solved based on the Keller-box finite-difference method. The accuracy of the method was verified by comparing with related transient solutions, the steady-state solution, and by grid independence tests. The existence of a similarity solution is shown for a step change in the far-field temperature and is verified by the computed general solution. Transient heat transfer correlations are presented, which indicate that both magnitude and direction of heat transfer can be significantly different from predictions by quasisteady models commonly used. The deviation is greater and lasts longer for large Prandtl number fluids.