An analysis is developed for mixed, forced, and free convective combustion on a flat fuel surface of arbitrary inclination that makes use of the laminar boundary layer approximation to describe the gas flow and of the flame-sheet approximation to describe the gas-phase reactions. A mixed-convection parameter (Rexn + Grxm)1/2n that properly scales the dependent and independent variable fields and a mixed convection ratio (Grxm/Rexn)1/2 that plays the role of the downstream local similarity coordinate are introduced in the nondimensionalization of the equations. It is shown that these two parameters, rather than the standard Reynolds, Rex, and Grashof, Grx, numbers are the optimum choice of governing nondimensional groups for this problem. The values of m and n are selected to obtain a similarity solution of the governing equations in the pure free convection limit for a vertical (m = 2, n = 4) and a horizontal (m = 2, n = 5) surface, which are the cases solved in this work. With this formulation, the solution of the problem provides for both cases smooth transition of all physical variables from one convective limit to the other. Results are obtained from numerical integration of the governing equations and from application of the local similarity approximation. It is shown that the range of validity of local similarity is extended beyond that obtained with alternate formulations and that the proper limits are approached. For use in practical applications, the results suggest that explicit expressions for the mass burning rate and for the fraction of unburnt pyrolyzate can be found that will suffice over the whole range of mixed-flow intensity.

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