Effect of cross-diffusion on the stability of a triple-diffusive Oldroyd-B fluid layer

Raghunatha, K. R.; Shivakumara, I. S.; Swamy, Mahantesh

doi:10.1007/s00033-019-1143-x

Cited by 18 publications

(17 citation statements)

References 30 publications

(36 reference statements)

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“…Gentile and Straughan [22] studied tridispersive thermal convection in a porous medium of which one of the diffusive components is temperature. Raghunath et al [23] investigated the problem of triple diffusive convection in an Oldroyd-B fluid with cross-diffusion. They found that viscoelastic parameters influence the stability of the stationary bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Convection in a horizontal layer of water with three diffusing components

et al. 2020

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Triple diffusive convection in water is modelled with properties like density, specific heat, thermal conductivity, thermal diffusivity and thermal expansion, modified in the presence of salts. The Ginzburg-Landau equation is derived to study heat and mass transports of different combinations of salts in water. A table is prepared documenting the actual values of thermophysical properties of water with different salts and the critical Rayleigh number is calculated. This information is used in the estimation of Nusselt and Sherwood numbers and their relative magnitudes are commented upon. A detailed study on different single, double and triple diffusive systems is done and comparison is made of the results. The local nonlinear stability analysis made via a Ginzburg-Landau model mimics many properties of the original governing equations, namely, Hamiltonian character and a bounded solution.

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Section: Introductionmentioning

confidence: 99%

Convection in a horizontal layer of water with three diffusing components

et al. 2020

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“…The critical value of

R_{T}^{o}

with respect to the wave number, denoted by

R_{T c}^{o}

, is calculated using the procedure explained by Raghunatha et al. [21].…”

Section: Linear Instability Analysismentioning

confidence: 99%

“…Recently, Raghunatha et al. [21] explored the ramifications of cross diffusion terms on the onset of triple‐diffusive convection in an Oldroyd‐B fluid layer and uncovered some of the unfamiliar results not noticed in double diffusive viscoelastic fluid systems.…”

Section: Introductionmentioning

confidence: 99%

Double‐diffusive convection in a rotating viscoelastic fluid layer

Raghunatha

Shivakumara

2021

Z Angew Math Mech

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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.

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“…It is intriguing to note that the existence of cross‐diffusion in the diffusivity matrix contributes significantly to the instability of the system and even alters the character of the instability mechanism. The intricacies of cross‐diffusion on convective instability in a triply diffusive Newtonian fluid layer have been deliberated by Terrones 44 and in an Oldroyd‐B fluid layer by Raghunatha et al 45 Nonetheless, off‐diagonal contributions on the onset of triple‐diffusive convection in a porous layer have not been explored despite recognizing the ramifications of cross‐diffusion terms on the instability characteristics. We have examined the effect of all nine elements in the diffusivity matrix on the instability of the viscoelastic triply diffusive fluid‐saturated porous layer for the first time in this article.…”

Section: Introductionmentioning

confidence: 99%

Cross‐diffusion and viscoelastic effects on multidiffusive porous convection

Shivakumara

Rangadhamappa

2020

Heat Trans

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The onset of triply cross-diffusive convection in a viscoelastic fluid-saturated porous layer is investigated as the study is found very relevant for describing natural phenomena (contaminant transport, underground water flow, improved oil recovery, polymer processing).A modified Darcy-Oldroyd-B model is used to describe the viscoelastic fluid flow in a porous medium with full cross-diffusion terms in the diffusivity matrix. A normal mode analysis yields an exact dispersion equation of fifth degree and accordingly the criterion for the onset of stationary and oscillatory convection is obtained. The numerical computations are carried out for diffusivity elements experimentally determined for lysozymesodium chloride-bovine serum albumin (BSA)-water system. Instability is found to occur via oscillatory mode for a certain choice of governing parameters. The relaxation and retardation viscoelastic parameters portray opposing contributions on the oscillatory onset and an increase in the relaxation parameter is to increase the range of retardation parameter up to which the oscillatory convection is preferred. The cross-diffusion is to either delay/hasten the onset of instability based on the magnitude of the stratifying agents. Even minute variations in the cross-diffusion elements indict complete change in the linear instability criteria. The topology of neutral curves disclosed the occurrence of disconnected closed convex oscillatory neutral curve revealing the requirement of three critical solute Darcy-Rayleigh numbers to state fully the instability criteria instead of the usual single value; a novel result ensured from the study. Moreover, the nature of instability for Oldroyd-B, Maxwell and Newtonian fluids turns out to be dissimilar for the same governing parameters. K E Y W O R D Scross-diffusion, disconnected neutral curve, Oldroyd-B fluid, porous media, triple-diffusive convection

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Effect of cross-diffusion on the stability of a triple-diffusive Oldroyd-B fluid layer

Cited by 18 publications

References 30 publications

Convection in a horizontal layer of water with three diffusing components

Convection in a horizontal layer of water with three diffusing components

Double‐diffusive convection in a rotating viscoelastic fluid layer

Cross‐diffusion and viscoelastic effects on multidiffusive porous convection

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