Regimes of combustion of a premixed mixture of gases in a heated microchannel with the wall temperature smoothly increasing in the downstream direction

Specific features of the unsteady flame in a microchannel with a controlled wall temperature are theoretically studied within the framework of a one-dimensional diffusion-thermal model. The case with the channel wall temperature increasing in the gas flow direction and the channel size being smaller than the critical value determined on the basis of the ambient temperature is considered. Depending on the flow rate of the combustible mixture of gases through the channel, either flame stabilization or alternation of flame repetitive extinction/ignition is possible. The influence of the characteristic length of channel wall heating on the domains of existence of various combustion modes is studied for the first time. The theoretical study shows that there exists a critical value of the temperature gradient in the channel walls, below which the regime of flame repetitive extinction/ignition is no longer observed. At small values of the temperature gradient, a hysteresis phenomenon is found, which is associated with different changes in the flame position in the cases with increasing and decreasing flow rates of the gas.