A
two dimensional model of a laminar flame near a solid surface in an infinite
domain is considered. It is supposed that the combustion product condenses on
the surface. It is assumed that there is a heat flow between the surface and
combustion mixture. High activation energy asymptotic assumptions have been
used, film surface geometry has been neglected and constant density of the
combustion mixture is supposed. Viscosity of the gaseous combusting mixture has
been neglected. High activation energy asymptotic assumption shrinks flame zone
to flame surface called flame front. Stationary solutions are found and
classified . Substitution of the boundary conditions to
stationary solutions of the differential equations gives nonlinear algebraic
equation for possible plane flame front distance from the reacting surface. A Newton method is applied for seeking the roots of this equation .
Simple calculus and asymptotic analysis have been used in order to determine
the number of solutions of the equation in all possible cases. For different
values of the governing parameters there are from 0 to 4 possible solutions.
The parameter space has been classified on the basis of the number of
stationary solutions . Stability analysis,
although incomplete (very fast oscillating perturbations are not considered),
has been done for stationary solutions. It has been shown that the method of
separation of variables cannot be applied in this model, so only a class of perturbations,
which do not depend on the coordinate parallel to the solid surface, is
considered. The results have been obtained by a combination of analytical and
numerical methods. The program pocket Mathematica has been extensively used.
