Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases

Effect of Cross-Diffusion on the Stability of a Triple-Diffusive Oldroyd-B Fluid Layer

The onset and stability of a triple cross-diffusive viscoelastic fluid layer is investigated. The rheology of viscoelastic fluid is approximated by the nonlinear Oldroyd-B constitutive equation which encompasses Maxwell and Newtonian fluid models as special cases. By performing the linear instability analysis, analytical expression for the occurrence of stationary and oscillatory convection is obtained. The numerical results show that the elasticity and cross-diffusion effects reinforce together in displaying complex dynamical behavior on the system. The presence of cross-diffusion is found to either stabilize or destabilize the system depending on the strength of species concentration as well as elasticity of the fluid and also alters the nature of convective instability. The disconnected closed oscillatory neutral curve lying well below the stationary neutral curve is observed to be convex in its shape in contrast to quasiperiodic bifurcation from the quiescent basic state noted in the case of Newtonian fluids. This striking feature is attributed to the viscoelasticity of the fluid. By performing a weakly nonlinear stability analysis, the stability of bifurcating solution is discussed. It is worth reporting that the viscoelastic parameters significantly influence the stability of stationary bifurcation though the stationary onset is unaffected by viscoelasticity. Besides, subcritical instability is occurs and the critical Rayleigh number at which such an instability is possible decreases in the presence of cross-diffusion terms. The results of Maxwell and Newtonian fluids are delineated as particular cases from the present study

Stability of Triple Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer

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

Weakly Nonlinear Stability Analysis of Triple Diffusive Convection in a Maxwell Fluid Saturated Porous Layer

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 number

Effect of Cross-Diffusion on the Stability of a Triple-Diffusive Oldroyd-B Fluid Layer

The onset and stability of a triple cross-diffusive viscoelastic fluid layer is investigated. The rheology of viscoelastic fluid is approximated by the nonlinear Oldroyd-B constitutive equation which encompasses Maxwell and Newtonian fluid models as special cases. By performing the linear instability analysis, analytical expression for the occurrence of stationary and oscillatory convection is obtained. The numerical results show that the elasticity and cross-diffusion effects reinforce together in displaying complex dynamical behavior on the system. The presence of cross-diffusion is found to either stabilize or destabilize the system depending on the strength of species concentration as well as elasticity of the fluid and also alters the nature of convective instability. The disconnected closed oscillatory neutral curve lying well below the stationary neutral curve is observed to be convex in its shape in contrast to quasiperiodic bifurcation from the quiescent basic state noted in the case of Newtonian fluids. This striking feature is attributed to the viscoelasticity of the fluid. By performing a weakly nonlinear stability analysis, the stability of bifurcating solution is discussed. It is worth reporting that the viscoelastic parameters significantly influence the stability of stationary bifurcation though the stationary onset is unaffected by viscoelasticity. Besides, subcritical instability is occurs and the critical Rayleigh number at which such an instability is possible decreases in the presence of cross-diffusion terms. The results of Maxwell and Newtonian fluids are delineated as particular cases from the present study

Implication of Cross-Diffusion on the Stability of Double Diffusive Convection in an Imposed Magnetic Field

The effects of cross-diffusion on linear and weak nonlinear stability of double diffusive convection in an electrically conducting horizontal fluid layer with an imposed vertical magnetic field are investigated. The criterion for the onset of stationary and oscillatory convection is obtained analytically by performing the linear instability analysis. Several noteworthy departures from those of doubly diffusive fluid systems are unveiled under certain parametric conditions. It is shown that (i) disconnected closed convex oscillatory neutral curve separated from the stationary neutral curve exists requiring three critical thermal Rayleigh numbers to completely specify the linear instability criteria instead of a usual single critical value, (ii) an electrically conducting fluid layer in the presence of magnetic field can be destabilized by stable solute concentration gradient, and (iii) a doubly diffusive conducting fluid layer can be destabilized in the presence of magnetic field. It is demonstrated that small variations in the off-diagonal elements enforce discrepancies in the instability criteria. A weak nonlinear stationary stability analysis has been performed using a perturbation method and a cubic Landau equation is derived and the stability of bifurcating equilibrium solution is discussed. It is found that subcritical bifurcation occurs depending on the choices of governing parameters

A Novel Approach on Micropolar Fluid Flow in a Porous Channel with High Mass Transfer via Wavelet Frames

In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed

Nonlinear Convection in an Elasticoviscous Fluid-Saturated Anisotropic Porous Layer Using a Local Thermal Nonequilibrium Model

By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy-Oldroyd-B model, and the fluid and solid phase temperatures are represented using a two-field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimension-two points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study

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