A two-dimensional model for heat transfer in reacting channel flow is developed along with an analytical solution that relates the temperature field in the channel to the flow Pe number. The solution is derived from first principles by modeling the flame as a volumetric heat source and by applying “jump conditions” across the flame. The model explores the role of heat recirculation via the channel’s walls by accounting for the thermal coupling between the wall and the gas. The uniqueness of the model lies in that it is developed by simultaneously solving the two dimensional temperature fields in both the wall and structure analytically. The solution is obtained using separation of variables in the streamwise (x) and the transverse (y) direction. Thermal coupling between the wall and gas is achieved by requiring that the temperature and heat flux match at the interface. The outer wall boundary can be either adiabatic or have a convective heat loss based on Newton’s law of cooling. The resulting solution is a Fourier series (for both wall and gas temperature fields) which depends on the flow Pe and the outer wall boundary condition. This simple model and the resulting analytical solution provide an extremely computationally efficient tool for exploring the effects of varying channel height and gas velocity on the temperature distribution associated with reacting (combusting) flow a channel. Understanding these tradeoffs is important for developing miniaturized, combustion-based power sources.

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