Abstract
The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field. The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects. The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); these are type (i) Adiabatic-Adiabatic and type (ii) Adiabatic-Isothermal. The corresponding two TMNs are obtained and the impacts of the porous parameter, solute Marangoni number, modified internal Rayleigh numbers, viscosity ratio, and the diffusivity ratios on the non-Darcian-Bènard double diffusive magneto - Marangoni convection are studied in detail.
Highlights
Double diffusive convection (DDC) is a type of convection, which consists of double density gradients diffusing at varied rates
The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid–saturated porous medium was theoretically investigated by Shivakumara et al [2]
A numerical study of double-diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with a porous medium was conducted by Al-Farhany and Turan [3]
Summary
Double diffusive convection (DDC) is a type of convection, which consists of double density gradients diffusing at varied rates. A numerical study of double-diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with a porous medium was conducted by Al-Farhany and Turan [3]. Sumithra et al [12, 13] and Manjunatha and Sumithra [14] studied the effects of constant heat source / sink and temperature gradients on composite layer with and without magnetic field. They obtained the closed form of solution to thermal Marangoni number for three different temperature gradients.
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