Abstract <p>A model of thermal dispersion in spiral combustion on a porous plane surface is proposed. The effect of thermal dispersion on the spiral combustion process in a system for which the thermal conductivity of the solid phase is significantly higher than the thermal conductivity of gas is studied using the combustion synthesis of titanium carbide from a titanium and carbon mixture in air as an example. It is found that thermal dispersion leads to the formation of a heated circular core resulting from combustion spreading to the region of a large area located near the initiation of combustion. The effect of the ignition duration on the inhomogeneity and expansion of the heated core and the structure of alternating wave zones with local temperature maxima and regions of comparatively low temperature is considered. The study is based on the heat balance equations in the approximation of thermal equilibrium between the solid and gas phases that contain dispersion coefficients depending on the local gas velocity, as well as the Darcy–Brinkman equations for gas flow through a porous medium. The structures of the thermal field are compared with the previously obtained results.</p>