Analysis of the heat transfer of an impinging laminar flame jet

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