Linear and nonlinear stability of double diffusive convection in a couple stress fluid–saturated porous layer

Abstract

The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluidsaturated porous medium is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides, heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge-Kutta-Gill method. Streamlines, isotherms, and isohalines are also displayed.

Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

“…In the case when medium is isotropic i.e. This is the result for stationary mode for the onset of double-diffusive convection with couple stress fluid saturated isotropic porous media given by Malashetty et al [25] (27) The above expression of thermal Rayleigh number for double-diffusive convection in porous media is the result for stationary mode given by Nield [7]. For single component couple stress fluid saturated porous medium i.e.…”

“…Malashetty and Kollur [26] studied the onset of double diffusive convection in a couple stress fluid saturated anisotropic porous layer. Shivkumara et al [27] carried out linear and nonlinear stability analysis of double diffusive convection in a couple stress fluid saturated porous layer.…”

Double Diffusive Convection in a Couple Stress Fluid Saturated Rotating Anisotropic Porous Layer with Internal Heating and Soret Effect.

“…Malashetty and Kollur [25] investigated the onset of double diffusive convection in a couple stress fluids saturated anisot ropic porous layer. Shivkumara [26] carried out linear and non linear stability analysis of double diffusive convection in a couple stress fluid saturated porous layers.…”

Effect of Horizontal Magnetic Field and Horizontal Rotation on Thermosolutal Stability of a Dusty Couple-Stress Fluid through a Porous Medium: a Brinkman Model

“…Shivakumara et al (2011) illustrated the linear and nonlinear stability problem of double diffusive convective phenomena for couple-stress fluid through a porous layer. Kumar et al (2015aKumar et al ( , b, 2016 considered, theoretically, thermal convection problems for both couple-stress fluid and ferrofluid to include the effects due to magnetic field, rotation, compressibility, variable gravity and heat source strength through Darcy as well as Brinkman porous medium.…”