Theoretical study of conjugate heat transfer effects on temperature profiles in parallel flow with embedded heat sources

A two-dimensional model for heat transfer in a "simulated flame" modeled as an embedded heat source 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 heat release zone. The model explores the role of heat recirculation via the structure of the device by accounting for the thermal coupling between the structure and the gas. The unique aspect of the model is that it solves for the two-dimensional temperature fields in both the structure and the gas simultaneously. The solution is obtained using separation of variables in the streamwise (x) and the transverse (y) directions. Thermal coupling between the structure and gas is achieved by requiring that the temperatures and heat fluxes match at the interface. The outer structure 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 structure and gas temperature fields) which depends on the flow Pe and the outer structure 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 in a channel. Understanding these tradeoffs is important for developing miniaturized, combustion-based power sources