Linear stability analysis of buoyancy-affected non-equidiffusive premixed flame in an inclined Hele–Shaw cell in the presence of wall heat loss

This study presents a quasi-two-dimensional theoretical framework for the linear stability analysis of buoyancy-affected premixed flame propagating in inclined Hele–Shaw cells with wall heat loss. The model incorporates finite-rate Arrhenius chemistry, non-equidiffusive transport, buoyancy, and non-adiabatic wall heat losses while fully resolving the internal flame structure. The stationary flame solutions and the associated eigenvalue problem are solved numerically to determine the dispersion relation and stability boundaries. Wall heat loss reduces the burning velocity and flame temperature, giving rise to multi-branch stationary solutions and significant changes in the dispersion relation. Buoyancy exhibits a strong directional effect: positive gravity destabilizes downward-propagating flames, whereas negative gravity stabilizes upward-propagating flames and can completely suppress perturbation growth. Furthermore, wall heat loss significantly modifies the critical gravitational acceleration required for complete stabilization. The present framework provides physical insight into the coupled effects of buoyancy, heat loss, and differential diffusion on flame stability in confined combustion systems.