Rayleigh−Bénard ferroconvection with Langevin magnetization: Effects of internal heat source and mixed boundary conditions

This investigation explores how internal heat sources or sinks influence the onset of Rayleigh–Bénard ferroconvection under generalized boundary conditions for velocity, temperature, and magnetic potential. Using the Langevin formulation together with a Chebyshev pseudospectral method, the analysis captures nonlinear magnetization effects that fundamentally alter classical convection thresholds. Additional findings include (i) a non-monotonic variation of the critical internal Rayleigh number with the Langevin parameter—destabilizing near unity but restabilizing at larger values, (ii) internal heating (ξ>0) reducing the convection threshold, while heat absorption (ξ<0) delays instability, and (iii) stronger magnetic parameters (M1,M3) consistently destabilizing the system. The unified formulation naturally recovers free, rigid, adiabatic, and isothermal limits, thereby generalizing earlier ferroconvection models. A key outcome of this work is the demonstration that the well-established stability ordering of Newtonian fluids is significantly modified in ferrofluids due to magnetothermal coupling: boundary conditions that are most stabilizing in Newtonian convection may become less effective once magnetic forces are introduced. In particular, rigid–Robin/isothermal combinations yield the greatest stability, while free–adiabatic combinations are the least stable.