Non-Linear Two Dimensional Double Diffusive Convection in a Rotating Porous Layer Saturated by a Viscoelastic Fluid

Abstract

Double diffusive convection in a rotating anisotropic porous layer, saturated by a viscoelastic fluid, heated from below and cooled from above has been studied making linear and non-linear stability analyses. The fluid and solid phases are considered to be in equilibrium. In momentum equation, we have employed the Darcy equation which includes both time derivative and Coriolis terms. The linear theory based on normal mode method is considered to find the criteria for the onset of stationary and oscillatory convection. A weak non-linear analysis based on minimal representation of truncated Fourier series analysis containing only two terms has been used to find the Nusselt number and Sherwood number as functions of time. We have solved the finite amplitude equations using a numerical scheme. The results obtained, during the above analyses, have been presented graphically and the effects of various parameters on heat and mass transfer have been discussed. Finally, we have drawn the steady and unsteady streamlines, isotherms, and isohalines for various parameters.

Nonlinear thermal convection in a viscoelastic nanofluid saturated porous medium under gravity modulation

“…It is found that with increasing the value of the strain retardation parameter, both Nu and Sh increase, indicating that it delays the onset of convection in viscoelastic nanofluid-saturated porous media and decrease heat and mass transport. The present results are comparable with the results obtained by Malashetty et al [39][40][41][42][43][44], Kumar and Bhadauria [45,46] for ordinary viscoelastic fluids.…”

“…This singularity can be removed when the nanofluid effects due to thermophoresis and Brownian motion become independent of the power-law index. The concept of thermal convection in a viscoelastic fluid-saturated porous medium was investigated by many authors given in [37][38][39][40][41][42][43][44][45][46][47].…”

Double-Diffusive Convection in a Saturated Anisotropic Porous Layer with Internal Heat Source

“…An excellent review of most of the findings related to the above subject has been given by Nield and Bejan (2006). Some of the researchers who have worked on double-diffusive convection without heat source are Nield (1968), Griffith (1981), Rudraiah and Malashetty (1986), Rudraiah and Siddheshwar (1998), Malashetty and Gaikwad (2002), Bahloul et al (2003), Malashetty and Swamy (2005), Malashetty et al (2006), Bhadauria (2007), Kuznetsov (2007a,b,c, 2008), Nield (2008, 2010), Malashetty and Heera (2008), Gaikwad et al (2007Gaikwad et al ( , 2009a, Kuznetsov and Nield (2010) and Kumar and Bhadauria (2011). Although sufficient literature on double-diffusive convection in porous medium saturated by ordinary fluid is available, very little attention has been devoted to the study of double-diffusive convection in a porous medium with internal heat source.…”

Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source

“…Since linear stability analysis cannot provide the information about the values of convection amplitudes nor about the aperiodic or chaotic motions, nonlinear analysis has to be performed. Kumar and Bhadauria [21][22][23] studied nonlinear double diffusive convection in a rotating porous layer saturated with viscoelastic fluid. Recently Bhadauria and Kiran [24,25] studied oscillatory nonlinear thermal instability in viscoelastic fluids under the effect of temperature and gravity modulations.…”