Analyzing the effects of internal heating and chemical reactions in a porous layer due to a vertical oblique magnetic field and gravity modulation

The stability of a vertical oblique magnetic field is investigated both theoretically and numerically, considering the effects of internal heat and chemical reaction under gravity modulation. The experimental setup comprises two opposite plates held at different uniform temperatures and solute concentrations, with the other two plates being permeable. A meticulous stability analysis of a porous medium under the influence of a uniform vertical oblique magnetic field is executed using the Darcy-Lapwood-Brinkman model. For linear stability analysis, normal mode techniques are employed to solve the resulting eigenvalue problem. Subsequently, the critical thermal Rayleigh number, without gravity modulation, is determined for the steady flow regime. The finding results indicate that increasing the magnetic field inclination increases the critical thermal Rayleigh number, signifying increased stability. A nonlinear Ginzburg-Landau equation is derived in the weakly nonlinear analysis using the regular asymptotic perturbation method, based on the assumption of a small modulation amplitude. The effects of gravity modulation on heat and mass transfer are examined through the Nusselt and Sherwood numbers. Additionally, the impact of various parameters on heat and mass transfer is analyzed and presented graphically. The findings show that increasing the Chandrasekhar number decreases the stability of system, thus stabilizing the flow.