Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer

The linear stability of a viscoelastic fluid-saturated sparsely packed porous layer heated from below is studied analytically using the Darcy–Brinkman–Jeffreys model with different boundary combinations. The Galerkin technique is employed to determine the criterion for the onset of oscillatory convection. The effects of the viscoelastic parameters, the Prandtl number, and the porous parameter on the critical Rayleigh number, the wave number, and the frequency are analyzed. The results are compared with those obtained for both a Darcy–Jeffrey fluid and a Maxwell fluid. It is shown that under certain conditions for the viscoelastic parameters, the flow is overstable. The possibility of the occurrence of bifurcation is also discussed.

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Fluid convection in a rotating porous layer under modulated temperature on the boundaries

Transport in Porous Media ◽

10.1007/s11242-006-9027-x ◽

2006 ◽

Vol 67 (2) ◽

pp. 297-315 ◽

Cited By ~ 20

Author(s):

B. S. Bhadauria

Keyword(s):

Porous Layer ◽

Modulated Temperature ◽

Fluid Convection

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Onset of convection in a viscoelastic-fluid-saturated sparselypacked porous layer using a thermal nonequilibrium model

Canadian Journal of Physics ◽

10.1139/p06-085 ◽

2006 ◽

Vol 84 (11) ◽

pp. 973-990 ◽

Cited By ~ 21

Author(s):

I S Shivakumara ◽

M S Malashetty ◽

K B Chavaraddi

Keyword(s):

Porous Layer ◽

Viscoelastic Fluid ◽

Convective Instability ◽

Field Model ◽

Hopf Bifurcations ◽

Fluid Viscosity ◽

Onset Of Convection ◽

Thermal Nonequilibrium ◽

Viscoelastic Parameters ◽

Fluid Convection

A linear stability analysis is carried out to study viscoelastic fluid convection in a sparsely packed horizontal porous layer heated from below. The viscoelastic fluid flow in the porous medium is modeled by using a modified Brinkman–Lapwood-extended Darcy model with the fluid viscosity different from the effective viscosity, which accounts for the viscoelastic properties and frictiondue to macroscopic shear. Besides, a two-field model for temperature each representing the solid and fluid phases separately is employed. The conditions for the occurrence of direct and Hopf bifurcations of the thermal convective instability are obtained analytically. It is shown that Hopf bifurcation occurs only if the retardation to relaxation-time ratio, Λ, is less than unity and the elasticity parameter, Γ, exceeds a threshold. Further, the effects of the viscoelastic parameters and the thermal nonequilibrium on the onset of convection are analyzed in detail.PACS No.: 47.55.–pb

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The Horton–Rogers–Lapwood problem in a Jeffrey fluid influenced by a vertical magnetic field

Proceedings of the Institution of Mechanical Engineers Part E Journal of Process Mechanical Engineering ◽

10.1177/09544089211031108 ◽

2021 ◽

pp. 095440892110311

Author(s):

Dhananjay Yadav ◽

Abdul A Mohamad ◽

Mukesh K Awasthi

Keyword(s):

Magnetic Field ◽

Darcy Number ◽

Critical Conditions ◽

Jeffrey Fluid ◽

Vertical Magnetic Field ◽

Magnetic Prandtl Number ◽

Fluid Convection ◽

The Stability ◽

Convective Cells ◽

The Impact

In this work, the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium is investigated theoretically. The layer of Jeffrey fluid is heated from below and is operated by a consistent upright magnetic field. Using the normal mode procedure, a dispersion equation is obtained analytically and this dispersion relation is utilized to derive the critical conditions for the onset of stationary and oscillatory patterns of convection. The results reveal that the stability of the system diminished with the augmentation of the Jeffrey parameter, while an opposite result is obtained with magnetic field parameters (magnetic Chandrasekhar–Darcy number and magnetic Prandtl number). The size of convective cells decreases with Jeffrey and magnetic field parameters. It is also found that the existence of a magnetic field indicates the possibility of the survival of the oscillatory mode of convection.

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