Onset of Triply Diffusive Convection in a Maxwell Fluid Saturated Porous Layer

Appl. Math. Mech.-Engl. Ed.

Shankar

2017

The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves are found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt numbers.

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear stability analysis of triple diffusive convection in a Maxwell fluid saturated porous layer

Appl. Math. Mech.-Engl. Ed.

Shankar

2017

“…A condition of local thermal equilibrium between the solid phase and the fluid phase of the porous medium is assumed. A modified Darcy-Oldroyd model relevant to the case of a Darcy porous medium has been considered to describe the flow in a porous medium in the form [34][35][36][37][38]…”

Section: Governing Equationsmentioning

confidence: 99%

“…Whereas Tracey [31] followed the analysis of Pearlstein et al [24] to study the triple diffusive convection in porous media, and Rionero [32][33] extended the study to obtain some additional results. The linear instability of the triple diffusive Maxwell fluidsaturated porous layer was considered by Zhao et al [34] while a weakly nonlinear stability analysis of the problem has been investigated recently by Raghunatha et al [35] .…”

Section: Introductionmentioning

confidence: 99%

Stability of triple diffusive convection in a viscoelastic fluid-saturated porous layer

Appl. Math. Mech.-Engl. Ed.

2018

The triple diffusive convection in an Oldroyd-B fluid-saturated porous layer is investigated by performing linear and weakly nonlinear stability analyses. The condition for the onset of stationary and oscillatory is derived analytically. Contrary to the observed phenomenon in Newtonian fluids, the presence of viscoelasticity of the fluid is to degenerate the quasiperiodic bifurcation from the steady quiescent state. Under certain conditions, it is found that disconnected closed convex oscillatory neutral curves occur, indicating the requirement of three critical values of the thermal Darcy-Rayleigh number to identify the linear instability criteria instead of the usual single value, which is a novel result enunciated from the present study for an Oldroyd-B fluid saturating a porous medium. The similarities and differences of linear instability characteristics of Oldroyd-B, Maxwell, and Newtonian fluids are also highlighted. The stability of oscillatory finite amplitude convection is discussed by deriving a cubic Landau equation, and the convective heat and mass transfer are analyzed for different values of physical parameters.

“…Rionero 24 considered a triple convective‐diffusive fluid mixture saturating a porous layer in the Darcy‐Oberbeck‐Boussinesq scheme, whereas Rionero 25 studied triple‐diffusive convection in porous media and obtained the conditions for inhibiting the onset of convection, guaranteeing the global nonlinear stability of the thermal conduction solution and the absence of subcritical instabilities. Recent contributions include the study of instability and stability of triple‐diffusive convection in a viscoelastic fluid‐saturated porous and nonporous layers 26‐31 …”

Section: Introductionmentioning

confidence: 99%

“…Recent contributions include the study of instability and stability of triple-diffusive convection in a viscoelastic fluid-saturated porous and nonporous layers. [26][27][28][29][30][31] The objective of this article is to study the linear instability and a weak nonlinear stability of triple-diffusive convection in a couple stress fluid-saturated porous layer and to unveil the effect of couple stresses on some of the intriguing features the system is capable of supporting. Finding the nature of instability and weak nonlinear stability thresholds (subcritical/supercritical) for the problem is imperative to assess the suitability of linear theory to predict the instability of the problem.…”

Section: Introductionmentioning

confidence: 99%

Couple stress effects on the stability of three‐component convection‐diffusion in a porous layer

Pallavi³

2020

Heat Trans

In this study, the stability (linear and weak nonlinear) of triple‐diffusive convection in a couple stress fluid‐saturated porous layer has been studied. A normal mode analysis yields an exact dispersion equation of fourth degree, and the criterion for the onset of stationary and oscillatory convection is obtained accordingly. The numerical computations are carried out for diffusivity elements experimentally determined for an aqueous NaCl‐KCl‐Sucrose system. Contrary to the double‐diffusive couple stress fluid system, it is found that (i) oscillatory convection occurs even if the diffusivity ratios are greater than unity and (ii) a disconnected heart‐shaped oscillatory neutral curve exists for certain choices of physical parameters, demonstrating the requirement of three critical values of Darcy‐Rayleigh number to specify the linear instability criteria. The impact of a couple stress parameter on some of these unusual behaviors is emphasized. The cubic Landau equations are derived by performing a weak nonlinear stability analysis and the stability of stationary and oscillatory bifurcating solutions is discussed. The heat and mass transfer for stationary and oscillatory convection modes is presented, and the influence of the couple stress parameter on the same is analyzed.