Stability analysis of marangoni magneto-convective flow with heat generation: effects of depth ratio and thermal boundaries

Abstract

The stability analysis of Marangoni magneto-convection (MMC) is investigated in a two-layer system consisting of an electrically conductive fluid-saturated porous layer overlain by an identical fluid layer, incorporating variable heat sources and a uniform magnetic field. The upper fluid surface is free, allowing surface-tension-driven convection, while the lower porous boundary is rigid. Two thermal boundary conditions are examined: (i) adiabatic–adiabatic (A–A) and (ii) adiabatic–isothermal (A–I). The governing equations are solved analytically using an exact method to obtain the thermal Marangoni number, an eigenvalue, as a function of depth ratio, Darcy number, Chandrasekhar number, internal Rayleigh numbers, wave number, and thermal diffusivity ratio. Graphical results show that the onset of MMC can be either advanced or delayed by appropriate choices of depth ratio and thermal boundary conditions. The novelty of the present work lies in deriving closed-form expressions for a composite fluid–porous system with simultaneous consideration of variable internal heat sources and magnetic effects under dual thermal boundary conditions, and demonstrating how depth ratio and thermal boundary conditions can be strategically tuned to either advance or delay the onset of instability.