In this study, the non-Darcy Three-Component Marangoni (NDTCM) convection issue is investigated in closed form using a non-Darcy model for the porous layer with constant heat source/sink (HSS) and uniform vertical magnetic field in a two-layer system with a porous layer under a fluid layer. This two-layer construction has a rigid and adiabatic lower enclosure for the porous layer and a free adiabatic/isothermal upper enclosure for the liquid layer. The thermal Marangoni numbers (TMNs) for lower rigid and upper free boundaries with surface tension, depending on both temperature and concentrations, are determined in closed form for two cases of temperature boundary conditions (TBCs), Case (i) Adiabatic–Adiabatic and Case (ii) Adiabatic–Isothermal. The ordinary differential equations are solved by an exact method of solution to attain an analytical expression for the Marangoni number. The impacts of applicable factors are discussed elaborately versus thermal ratio and shown graphically using MATHEMATICA. It is noticed that case (i) TBC is stable as the eigenvalue obtained is higher than that for case (ii) TBC for the fluid layer dominant (FLD) two-layer systems.
In the presence of a constant heat source/sink in both layers of the porous–fluid system, the Darcy–Bènard Triple-Diffusive Convection (DBTDC) problem is investigated for two types of Thermal Boundary Combinations (TBCs). For type (i) adiabatic–adiabatic and type (ii) adiabatic–isothermal TBCs, the system of ordinary differential equations derived from normal mode analysis is solved in closed form for the eigenvalue, Thermal Marangoni Number (TMN). The depth ratio thoroughly explains the influence of several parameters on the eigenvalue, hence on DBTDMC. It is noticed that the parameters in the study have a larger influence on the porous layer dominant composite layer systems than that on the fluid layer dominant composite systems.
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