Influence of chemical reaction on convective flow in porous medium with varying viscosity generated by internal heat source in thermal non-equilibrium temperature conditions

Abstract

This study investigates the onset of natural convection in a horizontal fluid-saturated porous medium subject to uniform internal heat generation and chemical reactions under local thermal non-equilibrium (LTNE) temperature conditions. The fluid viscosity is assumed to vary nonlinearly with temperature, capturing realistic thermophysical behavior often encountered in high-temperature and chemically reactive porous systems. Such configurations are frequently encountered in engineering applications, including geothermal energy extraction, thermal insulation in buildings, chemical catalytic reactors, nuclear waste disposal, and porous heat exchangers. In these systems, internal heat generation, chemical reactions, and non-equilibrium heat exchange between fluid and solid phases play a critical role in determining thermal stability and efficiency. The present analysis employs linear stability theory using the normal mode technique, and the resulting eigenvalue problem is solved via the Galerkin-weighted residual method. A comparative study is conducted for three thermal boundary conditions: rigid-rigid $(R/R)$, rigid-free $(R/F)$, and free-free $(F/F)$ for the stationary case, while oscillatory instabilities are analyzed for the F/F case. Graphical representations are used to illustrate how the main controlling parameters affect the stationary and oscillatory onset. It is reported that the system is more stable with increasing values of $H$ (inter-phase heat transfer coefficient) and $\text{Da}$ (Darcy number), while it is less stable with increasing values of $\chi$ (Damköhler number), $M_1$ (linear viscosity variation parameters), $M_2$ (nonlinear viscosity variation parameters), and $Q_f$ (the fluid heat generation parameter). It is also established that the system is more stable for $R/R$ boundary combinations and least stable for $F/F$ boundaries.