Analysis of the heat transfer of an impinging laminar flame jet

Flame jet impingement is used in many industrial processes. In this paper an analytical expression is derived for the heat flux of a laminar flame impinging on a flat plate, where the flame jet is approximated by a hot inert jet with the position of the tip of the flame taken equal to the nozzle position. The heal flux in this expression is dependent on the nozzle-to-plate spacing, in contradiction to existing (semi-analytical) relations. The geometry is divided in a region far from the plate and a region dose to the plate. For both regions the velocity profiles are calculated using only the dominant terms of the balance equations. Subsequently these profiles are linked to each other at the boundary between the two zones. Implementing the resulting velocity profile for the complete geometry in the energy equation and integrating over the whole domain results in an expression for the heat flux from the flame to the plate at the hot spot. Numerical calculations show very good agreement with the results of the analytical derivation.