The onset of Magneto–Darcy–Rayleigh–Bénard convection under local thermal non-equilibrium with two-layer system

The investigation focuses on the consequences of various thermal distributions examined in the context of Magneto–Darcy–Rayleigh–Bénard (MDRB) convection onset under local thermal non-equilibrium (LTNE). The system under consideration consists of a two-layer configuration, with an incompressible fluid and horizontally positioned adiabatic peripheries. An analytical solution to the resultant problem is accomplished using the regular perturbation method. Concerning the six thermal distributions, we examine variables such as the ratio of heat expansion in the solid phase, the ratio of heat diffusivities in the solid phase, and the inter-phase heat diffusivity ratio, which exhibits a propensity towards LTNE. Furthermore, we investigate the consequences of modifying the values of constraints, namely, the ratio of heat expansion in the fluid phase, the ratio of heat diffusivities in the fluid phase, the porous parameter, the heat ratio, and the Chandrasekhar number. The empirical observations indicate that the model (iii) exhibits a significantly higher degree of instability when compared to other distributions. Conversely, model (v) demonstrates a notable level of stability. Moreover, it is intriguing that the system governed by the model (vi) exhibits higher stability than the model (iv) thermal distribution within the context of a composite system.