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

The linear instability and a weakly nonlinear stability of a rotating double‐diffusive convection in a viscoelastic fluid layer are investigated. An Oldroyd‐B constitutive equation is used to describe the rheological behavior of the viscoelastic fluid. Several remarkable departures from those of single‐diffusive and double‐diffusive viscoelastic fluid systems are explored by performing the linear instability analysis. Under certain conditions, it is observed that (i) a non‐rotating double diffusive viscoelastic fluid layer becomes destabilized by rotation, (ii) a rotating viscoelastic fluid layer gets destabilized by the addition of heavy solute to the bottom of the layer, (iii) disconnected closed convex oscillatory neutral curve from the stationary neutral curve exists, and (iv) three critical thermal Rayleigh numbers are required to specify the linear instability criteria, as opposed to a single critical value. The nature of linear instability characteristics for Oldroyd‐B, Maxwell and Newtonian fluids is found to be contradictory for the identical values of governing parameters. By performing a weakly nonlinear stability analysis, a cubic Landau equation for the amplitude corresponding to stationary convection is derived and the stability of bifurcating equilibrium solution is discussed. The viscoelastic parameters influence the stability of stationary bifurcation despite their effect is not felt on the stationary onset. The influence of various parameters on heat and mass transfer is also elucidated.

show abstract

“…A small perturbation parameter χ that indicates the deviation from the critical state is introduced. Consequently, the unknown variables

Φ = [\begin{matrix} ψ & V & T & S & τ_{x x} & τ_{z z} & τ_{x z} & τ_{x y} & τ_{y z} \end{matrix}]

are expanded in terms of χ, following [23–26], in the form

R_{T} = R_{T c} + χ^{2} R_{T 2} + \cdot \cdot \cdot and Φ = \sum_{n = 1}^{\infty} χ^{n} Φ_{n} .

…”

Section: A Weakly Nonlinear Stationary Stability Analysismentioning

confidence: 99%

Double‐diffusive convection in a rotating viscoelastic fluid layer

Raghunatha

Shivakumara

2021

Z Angew Math Mech

View full text Add to dashboard Cite

show abstract

“…The linear instability theory gives us the critical Darcy‐Rayleigh number, but it does not predict the amplitude of the convective motion, stability of steady/oscillatory bifurcations, and heat and mass transfer. Thus, the weak nonlinear stability analysis is carried out by using the well‐known perturbation method 28,29 . In the analysis, a small bifurcation parameter

χ

that indicates deviation from the critical state is introduced and the variables are expanded in powers of

χ

in the form

false(ψ, T, S_{m} false) = false(ψ_{1}, T_{1}, S_{m 1} false) χ + false(ψ_{2}, T_{2}, S_{m 2} false) χ^{2} + ⋯ (m = 1, 2), R_{T} = R_{T c} + χ^{2} R_{T 2} + ⋯ .

…”

Section: Weak Nonlinear Stability Analysismentioning

confidence: 99%

“…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%

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

Raghunatha

Shivakumara

Pallavi³

2020

Heat Trans

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…The triple diffusion flow appears in diverse engineering and scientific fields like geology, astrophysics, disposals of nuclear waste, deoxyribonucleic acid (DNA), chemical engineering, etc. [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Triple Diffusive Unsteady Flow of Eyring–Powell Nanofluid Over a Periodically Accelerated Surface With Variable Thermal Features

Khan¹,

Vaidya²,

Chammam³

et al. 2020

Front. Phys.

View full text Add to dashboard Cite

This research communicates the triple diffusion perspective of Eyring-Powell nano-materials configured by a periodically moving configuration. The thermal consequences of variable natures are utilized as a novelty. Combined magnetic and porous medium effects are also involved, which result in a magneto-porosity parameter. The thermophoretic and Brownian motion aspects are reported by using Buongiorno's nanofluid theory. The formulated flow equations in non-dimensional forms are tackled with the implementation of a homotopy analysis algorithm. A detailed physical investigation against derived parameters is presented graphically. Due to periodically accelerated surface, the oscillations in velocity and wall shear stress have been examined.

show abstract

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

Cited by 21 publications

References 39 publications

Double‐diffusive convection in a rotating viscoelastic fluid layer

Double‐diffusive convection in a rotating viscoelastic fluid layer

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

Triple Diffusive Unsteady Flow of Eyring–Powell Nanofluid Over a Periodically Accelerated Surface With Variable Thermal Features

Contact Info

Product

Resources

About