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In the current work, in the presence of a heat source and temperature gradients, the onset of triple-diffusive convective stability is studied for a fluid, and a fluid-saturated porous layer confined vertically by adiabatic limits for the Darcy model is thoroughly analyzed. With consistent heat sources in both layers, this composite layer is subjected to three temperature profiles with Marangoni effects. The fluid-saturated porous region's lower boundary is a rigid surface, while the fluid region's upper boundary is a free surface. For the system of ordinary differential equations, the thermal surface-tension-driven (Marangoni) number, which also happens to be the Eigenvalue, is solved in closed form. The three different temperature profiles are investigated, the thermal surface-tension-driven (Marangoni) numbers are calculated analytically, and the effects of the heat source/sink are studied in terms of corrected internal Rayleigh numbers. Graphs are used to show how different parameters have an impact on the onset of triple-diffusive convection. The study's parameters have a greater influence on porous layer dominant composite layer systems than on fluid layer dominant composite layer systems. Finally, porous parameters and corrected internal Rayleigh numbers are stabilize the system, and solute1 Marangoni number and ratio of solute2 diffusivity to thermal diffusivity of fluid are destabilize the system.

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.

In the presence of a constant heat source and sink in each layer, the Non-Darcian Triple Diffusive Convection (NDTDC) problem in a combined layer that is horizontally infinite is examined. This composite layer is rigid and adiabatic in the lower enclosure of the porous layer and free as well as isothermal in the higher enclosure of the fluid layer. The thermal Marangoni number (tMn) for two cases of thermal boundary combinations (TBCs), case (i) adiabatic–adiabatic and case (ii) adiabatic–isothermal, is determined by solving the system of ordinary differential equations obtained following normal mode analysis in closed form. The effect of important parameters on NDTDC is studied in detail and illustrated visually versus the thermal ratio. It is noticed that case (i) is observed to be stable because the Eigenvalue obtained is higher than that for case (ii) and NDTDC can be postponed by making the upper boundary of the combined layer adiabatic and the same is augmented by converting the upper boundary of the combined layer to isothermal, as isothermal boundaries support early convections.

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.

The effect of a heat source and temperature gradient on Brinkman–Bènard Triple-Diffusive magneto-Marangoni (BBTDMM) convection in a two-layer system is investigated. The two-layer system is horizontally infinite and is surrounded on all sides by adiabatic boundaries. It is exposed to basic uniform and non-uniform temperature profiles and heat sources. The appropriate eigenvalues and thermal Marangoni numbers (TMNs), which depend on temperature and concentration, are obtained for the temperature profiles (TPs) for lower rigid and higher free boundaries with surface tension. The transformed system of ordinary differential equations is solved by using an exact technique. For all three TPs, the impact of significant relevant parameters on these eigenvalues, and hence on BBTDMM convection, are investigated versus the thermal ratio. It is observed that, by increasing the values of the modified internal Rayleigh number for the fluid layer and the solute Marangoni numbers, the Darcy number, and the viscosity ratio for the set of physical parameters chosen in the study, one can postpone BBTDMM convection. Higher values of the modified internal Rayleigh numbers for the porous layer augment BBTDMM convection.