Theoretical modeling of heat transfer in a multilayer rectangular body with spatially-varying convective heat transfer boundary condition

Abstract

Theoretical analysis of heat transfer in a multilayer body is relevant for several engineering applications where heat transfer occurs through a stack of thermally dis-similar materials. In most of such literature, a constant convective heat transfer coefficient is assumed as a boundary condition at one end of the body. In contrast, there is a lack of work to model a problem with spatial variation in the convective heat transfer coefficient. This paper presents an analytical solution for thermal conduction in a multilayer rectangular body with spatially varying convective heat transfer coefficient at one end. In addition, this solution also accounts for internal heat generation and inter-layer thermal contact resistance and spatially varying heat flux on the other end of the body. The solution is derived in a series form, and it is shown that the coefficients of the series can be determined by solving a well-defined set of linear algebraic equations. The analytical solution is verified by comparison with numerical simulations, as well as with standard solution for a simplified special case. The impact of spatially varying cooling provided by jet impingement is analyzed using the analytical solution. A resource optimization problem pertaining to the optimal use of jet cooling is solved. Results presented here may benefit thermal management analysis of a broad variety of engineering applications involving heat transfer in multi-layer bodies.