Gravitational effects on chemically reacting laminar boundary layer flows over a horizontal flat plate

This is a theoretical study of the chemically reacting laminar boundary layer flow over a horizontal flat plate with gravitationally induced buoyant force. A diffusion flame sheet model was invoked to describe the combustion process. It was found that the effects of gravity on the purely force convection flow are characterized by a dimensionless coordinate quantity Grx/Rex5/2. The governing equations were obtained by expanding the dependent variables into series in terms of this coordinate quantity. The problem inherently is a coordinate perturbation and it is treated as such. A numerical solution of the zeroth and first order governing equations subject to the appropriate physical boundary conditions was obtained for various external flow conditions such as wall temperature, freestream oxygen concentration and aiding and opposing flows. It was shown that the cross stream buoyancy induced body force acts effectively to produce a streamwise pressure gradient in the fluid adjacent to the plate surface. The pressure gradient is favorable in aiding flows (plate facing upwards) and is adverse in opposing flows (plate facing downwards). Hence, the local boundary layer flow is accelerated or decelerated relative to the corresponding gravity-free forced convection flow. Correspondingly, there is an increase or decrease in the local skin friction and heat transfer rates, and consequently a decrease or increase in the flame “stand-off” distance, depending upon whether aiding or opposing flow occurs, respectively. Based on the present study we conclude that buoyancy plays an important role in boundary layer diffusion flames, and by retaining the buoyant force the current model is capable of explaining phenomena that have been observed experimentally but have not been predicted by classical boundary layer theory. Such previously unaccounted for effects include the acceleration of the boundary layer flow (sometimes a velocity overshoot is exhibited), and a decrease in the flame “stand-off” distance.