Theoretical analysis of unsteady convective heat transfer from a flat plate with time-varying and spatially-varying temperature distribution

Abstract

Convective heat transfer due to laminar, incompressible flow past a flat plate has been extensively researched due to applications in a variety of engineering systems. In several cases, such as thermal management of Li-ion cells and phase change based energy storage, the flat plate temperature may vary as a function of both time and space, and the resulting plate heat flux is of interest. This paper presents an integral method based analytical model for predicting the heat flux distribution from a flat plate with a time-varying and spatially-varying temperature. Third-order Karman-Pohlhausen polynomial forms of velocity and temperature distributions are used in the integral energy equation to derive an ordinary differential equation that predicts the plate heat flux distribution in response to an arbitrary time- and space-dependent plate temperature distribution. The generalized results derived here are shown to reduce to previously reported results for special cases of only time-dependent or only spatially varying or constant plate temperature. Results are also shown to be in good agreement with finite-element simulations. The analytical model developed here is used to predict the plate heat flux in response to realistic plate temperature distributions that may be encountered in practical applications. These results improve the fundamental understanding of an important convective heat transfer process, and may help in the design and optimization of a broad variety of engineering systems involving convective heat transfer.