Conjugate heat transfer is one of the most important aspects of energy conversion and plays an important role in the thermal efficiency and fuel consumption of chambers. In the present work, a two-dimensional model for reacting flow is presented to calculate transport equations of mass, momentum, energy and species. A new solver is developed for the open-source OpenFOAM software. This new solver is able to predict the conjugate heat transfer effects of reactions and transport processes in fluid and heat conduction in solid as well as radiation in surrounding surface. The coupled method is used and the continuity of temperature and heat flux on the fluid and solid interface is applied in order to analyze conjugate heat transfer through boundary conditions. Experimental data of honeycomb burner is used to validate the new solver. Numerical results are in a good agreement with experimental data. The results show that change of fluid inlet condition and geometry dimensions affect the interaction of conjugate heat transfer and location of released heat of combustion. The location of flame is moved toward outlet as the inlet velocity is increased and toward inlet as the equilibrium ratio is increased. Increasing the length and thickness of solid reduces the preheat area as well.