Gas flows of varying temperature occur in heat exchangers, nuclear reactors, non-steady flow devices, and combustion engines, among other applications with heat transfer processes that influence energy conversion efficiency. A general numerical method is developed for predicting the transient laminar thermal boundary layer response to arbitrarily prescribed changes in the bulk far-field fluid temperature. The method is tested for the step change of the far-field flow temperature of a two-dimensional semi-infinite flat plate with steady hydrodynamic boundary layer and constant wall temperature assumptions. Changes of the fluid-wall temperature difference in magnitude and sign are considered, including flow with no initial temperature difference and built-up thermal boundary layer. The governing differential equations for momentum and energy are solved based on the Keller-Box finite difference method. The accuracy of the solutions is verified through comparing with the steady state solution. Transient heat transfer coefficients are presented, which indicate that both magnitude and direction of heat transfer can be significantly different from quasi-steady models commonly used.

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