Two-dimensional analytical model of heat transfer for flames in channels

A two-dimensional model for heat transfer in reacting channel flow with a constant wall temperature is developed along with an analytical solution that relates the temperature field in the channel to the flow Peclet 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 for plug and Hagen-Poiseuille velocity profiles and is validated via comparison with more detailed computational fluid dynamics solutions. The analytical solution provides a computationally efficient tool for exploring the effects of varying channel height and gas velocity on the temperature distribution in a channel in which a flame is stabilized. The results show that the Peclet number is the principal parameter controlling the temperature distribution in the channel. It is also found that although the Nusselt number is independent of the Peclet number (or velocity) in the postflame region, it can change by nearly 3 ord ers o f magnitude in the preflame region over the range of Peclet numbers (or velocities) expected in microcombustors. This has important implications for quasi-onedimensional numerical modeling of micro/mesoscale combustion, in which it is usual to select a single Nusselt value from the heat transfer literature.Acorrelation to facilitate incorporation of the streamwise Nusselt number variation is provided.

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