Linear and non-linear thermosolutal convection in a fluid saturated anisotropic porous layer with internal heating and thermal non-equilibrium model

Abstract

Influence of internal heating and anisotropy parameters on thermal non-equilibrium double diffusive convection in a couple stress fluid saturated anisotropic porous layer heated and salted from below is investigated analytically using linear and nonlinear stability theory. Normal mode technique is considered for linear theory, while the nonlinear theory is conducted based on minimal representation of truncated double Fourier series. The critical thermal Rayleigh number and wave number for stationary mode are obtained analytically using linear theory. Energy equation is represented by a two-field model, where the fluid and solid phase temperature fields are processed separately. Consequently, the thermal anisotropy parameter is considered for both fluid and solid phases. The onset criterion for stationary convection has derived analytically. The effect of anisotropy parameters, couple stress parameter, solute Rayleigh number, Vadasz number, Lewis number, inter-phase heat transfer coefficient, and internal heat parameter on the stationary and oscillatory convection, as well as heat and mass transfer are discussed and presented graphically. It is observed that increasing mechanical anisotropy parameter, thermal anisotropy parameter for fluid phase, and internal heat parameter destabilizes the system. On the other hand, increasing the values of couple stress parameter, inter-phase heat transfer coefficient, and concentration Rayleigh number are to stabilize the system. Thermal anisotropy parameter for solid phase has a stabilizing effect for stationary mode, while an opposite is observed for oscillatory one.