In a reference frame attached to the flame front, the flame spreading rate becomes an eigenvalue for the flame spreading over a rod fuel. A numerical model is presented for the problem which is consisted of the conservation equations in gas phase and massand energy balance equations in solid phase. SIMPLE algorithms are used for gas-phase equations.Newton and Continuaton-Newton algorithms are used for solid-phase equations.Iterations are made between gas phase and solid phase until convergence is reached. It is shown that the combination of Continuation-Newton and SIMPLE algorithms is good enough for the eigenvalue problem which is consisted of non-linear differential equations coupled each other between solid phase and gas phase.
