Stability of fluid flow in a Brinkman porous medium—A numerical study

Shankar, B. M.; Kumar, Jai; Shivakumara, I. S.; Ng, Chiu‐On

doi:10.1016/s1001-6058(14)60076-7

Cited by 17 publications

(2 citation statements)

References 13 publications

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“…The results are mainly concentrated on the flow pattern in the absence of a magnetic field and surface drove convection. Shankar et al 13 have discussed numerically the stability of the fluid flow for the Brinkman model for a uniform viscous fluid. Dhiman and Sharma 14 have investigated the influence of viscosity, which varies with respect to temperature for micropolar fluid in the case of thermal convection, and reported that viscosity influences the stability of the system on the onset of convection.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh–Bénard and Bénard–Marangoni magnetoconvection in variable viscosity finitely conducting liquids

2021

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The thermorheological effect on magneto‐Bénard‐convection is studied numerically in fluids with finite electrical conductivity. A nonlinear thermorheological equation is considered in the problem. The results are compared with the classical approach of constant viscosity, which depicts the fact that the effect of increasing the strength of the magnetic field is to delay the onset of convection. The magnetic field is shown to have a rheostatic influence on convective instabilities. The results obtained by the study have possible applications in the field of astrophysics, sunspots, and in space applications under microgravity.

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Section: Introductionmentioning

confidence: 99%

Rayleigh–Bénard and Bénard–Marangoni magnetoconvection in variable viscosity finitely conducting liquids

2021

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“…Shankar et al. [14] examined numerically the stability of porous Poiseuille flow by considering the Brinkman model with the ratio of viscosities as an independent parameter. The stability of fluid flow in a horizontal porous channel saturated by couple‐stress fluid was analyzed by Shankar et al.…”

Section: Introductionmentioning

confidence: 99%

Stability of Poiseuille flow in an anisotropic porous layer with oblique principal axes: More accurate solution

Shankar

Shivakumara

2020

Z Angew Math Mech

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The stability of fluid flow in an anisotropic porous medium of Brinkman type is investigated. Anisotropy in the permeability is considered such that its longitudinal principal axis is oriented arbitrarily with the horizontal, while transversely it is isotropic. A fourth‐order eigenvalue problem obtained by performing a linear stability analysis is solved numerically using the Chebyshev collocation and the compound matrix methods. The critical Reynolds number and the critical wave number are computed for different values of porous parameter, orientation angle of the principal axis and the mechanical anisotropy parameter. The porous and the mechanical anisotropy parameters disclose contrasting contributions to the stability of fluid flow. The orientation angle instills either stabilizing or destabilizing effects on the fluid flow depending on the value of anisotropy parameter. Besides, the streamlines of the perturbation modes are presented for various values of orientation angle and anisotropy parameter. For the Darcy case, a simple analytical method is employed and established that the flow is stable for all infinitesimal perturbations.

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