Abstract This paper examines the influence of mixing a fuel with an oxidizer-rich reactant on the existence and propagation of partially premixed flames formed in a porous-wall channel. The amount of the injected fuel has been taken as a parameter to generate different states of the combustion mixtures. The problem has been mathematically formulated in the framework of the thermodiffusive model under a single-step chemical reaction. Numerical simulations based on finite elements were then employed to solve the governing partial differential equations. The study has shown that the degree of fuel premixing in the combustion mixtures as well as the value of the Lewis number of fuel and oxidizer plays a great role on the existence and structure of triple flames. It is found also that flame extinguishes for larger values of the premixing parameter. Flame structures were also found to exhibit several changes such as the shift of the leading edge toward the fuel supply side and the formation of twin flames. It has been predicted that the premixing can substantially enhance the reactivity of the combustion mixture, but on the other hand it tends to shift the flame to the boundary which may destroy the underlying combustion chamber. For nonunit Lewis numbers, fuel premixing is found to shift triple flames from the stoichiometric surface and attach the flame to the channel walls. It is predicted also that the maximum reaction rate reduces with increasing the Lewis numbers.