A linear stability analysis is performed for mono-diffusive convection in an anisotropic rotating porous medium with temperature-dependent viscosity. The Galerkin variant of the weighted residual technique is used to obtain the eigen value of the problem. The effect of Taylor-Vadasz number and the other parameters of the problem are considered for stationary convection in the absence or presence of rotation. Oscillatory convection seems highly improbable. Some new results on the parameters' influence on convection in the presence of rotation, for both high and low rotation rates, are presented.

The effects of temperature-dependent viscosity, gravity modulation and thermomechanical anisotropies on heat transport in a low-porosity medium are studied using the Ginzburg-Landau model. The effect of gravity modulation is to decrease the Nusselt number, N u and variable viscosity leads to increase in N u. The thermo-mechanical anisotropies have opposite effect on N u with thermal anisotropy decreasing the heat transport.

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The investigation of Non-Darcian Benard Marangoni Convection (NDBMC) is carried out in a Superposed Fluid-Porous (SFP) layer, which consists of an incompressible, sparsely packed single component fluid saturated porous layer above which lies a layer of the same fluid, with temperature dependent heat sources in both the layers. The upper surface of the SFP layer is free with Marangoni effects depending on Temperature, where the lower surface of the SFP layer is rigid. The thermal Marangoni numbers are obtained in closed form for two sets of thermal boundaries set (i) Adiabatic-Adiabatic and set (ii) Adiabatic-Isothermal. Influence of temperature dependent heat source in terms of internal Rayleigh numbers, viscosity ratio, Darcy Number, thermal diffusivity ratio on NDBMC, is investigated in detail.

The problem of Benard double diffusive Marangoni convection is investigated in a horizontally infinite composite layer system enclosed by adiabatic boundaries for Darcy model. This composite layer is subjected to three temperature gradients with constant heat sources in both the layers. The lower boundary of the porous region is rigid and upper boundary of the fluid region is free with Marangoni effects. The Eigenvalue problem of a system of ordinary differential equations is solved in closed form for the Thermal Marangoni number, which happens to be the Eigen value. The three different temperature profiles considered are linear, parabolic and inverted parabolic profiles with the corresponding thermal Marangoni numbers are obtained. The impact of the porous parameter, modified internal Rayleigh number, solute Marangoni number, solute diffusivity ratio and the diffusivity ratio on Darcy-Benard double diffusive Marangoni convection are investigated in detail.