Oscillatory convection in a viscoelastic fluid through a porous layer heated from below

Rudraiah, N.; Kaloni, P. N.; Radhadevi, P. V.

doi:10.1007/bf01354768

Cited by 57 publications

(31 citation statements)

References 17 publications

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“…Herbert (1963) and Green (1968) were first to analyze the problem of oscillatory convection in an ordinary viscoelastic fluid of the Oldroyd type under the condition of infinitesimal disturbances. Later on, Rudraiah et al (1989Rudraiah et al ( , 1990 had studied the onset of stationary and oscillatory convection in a viscoelastic fluid of porous medium. Laroze et al (2007) have analyzed the effect of viscoelastic fluid on bifurcations of convective instability, he analyzed that the nature of the convective solution depends largely on the viscoelastic parameters.…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Two Dimensional Double Diffusive Convection in a Rotating Porous Layer Saturated by a Viscoelastic Fluid

Kumar

Bhadauria

2010

Transp Porous Med

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Double diffusive convection in a rotating anisotropic porous layer, saturated by a viscoelastic fluid, heated from below and cooled from above has been studied making linear and non-linear stability analyses. The fluid and solid phases are considered to be in equilibrium. In momentum equation, we have employed the Darcy equation which includes both time derivative and Coriolis terms. The linear theory based on normal mode method is considered to find the criteria for the onset of stationary and oscillatory convection. A weak non-linear analysis based on minimal representation of truncated Fourier series analysis containing only two terms has been used to find the Nusselt number and Sherwood number as functions of time. We have solved the finite amplitude equations using a numerical scheme. The results obtained, during the above analyses, have been presented graphically and the effects of various parameters on heat and mass transfer have been discussed. Finally, we have drawn the steady and unsteady streamlines, isotherms, and isohalines for various parameters.

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Section: Introductionmentioning

confidence: 99%

Non-Linear Two Dimensional Double Diffusive Convection in a Rotating Porous Layer Saturated by a Viscoelastic Fluid

Kumar

Bhadauria

2010

Transp Porous Med

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“…Convection of non-Newtonian fluids in a porous medium is of considerable importance in several fields of application such as oil recovery, food processing, and the spread of contaminants in the environment, and in various processes in the chemical and materials industries. The onset of thermal convection of a viscoelastic fluid-saturated porous medium was studied by many authors (Rudraiah et al 1989;Kim et al 2003;Yoon et al 2004;Malashetty et al 2006). Since elastic behavior is inherent in non-Newtonian fluids, oscillatory instabilities can set in before stationary modes.…”

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confidence: 99%

Thermal Instability in a Porous Medium Layer Saturated with a Viscoelastic Nanofluid

Sheu

2011

Transp Porous Med

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The onset of convection in a horizontal layer of a porous medium saturated with a viscoelastic nanofluid was studied in this article. The modified Darcy model was applied to simulate the momentum equation in porous media. An Oldroyd-B type constitutive equation was used to describe the rheological behavior of viscoelastic nanofluids. The model used for the viscoelastic nanofluid incorporates the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection was analytically derived. The effects of the concentration Rayleigh number, Prandtl number, Lewis number, capacity ratio, relaxation, and retardation parameters on the stability of the system were investigated. Oscillatory instability is possible in both bottom-and top-heavy nanoparticle distributions. Results indicated that there is competition among the processes of thermophoresis, Brownian diffusion, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary modes. Regimes of stationary and oscillatory convection for various parameters were derived and are discussed in detail.

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“…The corresponding problem in the case of a porous medium has also not received much attention. Rudraiah et al (1989) have studied the linear stability of a viscoelastic fluid in a densely packed porous layer using an Oldroyd model. It is found that the effect of elasticity of the fluid is to destabilize the system and that of porosity is to stabilise the same.…”

Section: Introductionmentioning

confidence: 99%

Convective Instability of Oldroyd-B Fluid Saturated Porous Layer Heated from Below using a Thermal Non-equilibrium Model

et al. 2006

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The linear stability of a viscoelastic fluid saturated densely packed horizontal porous layer heated from below and cooled from above is investigated by considering the Oldroyd-B type fluid. A generalized Darcy model, which takes into account the viscoelastic properties, is employed as momentum equation and a two-field model is used for energy equation each representing solid and fluid phases separately. Linear stability analysis suggests that, there is a competition between the processes of viscous relaxation and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Analytical expression for the occurrence of oscillatory onset is obtained, and it is found that the necessary condition for the existence of the same is < 1. Besides, the effect of viscoelastic parameters and the thermal non-equilibrium on the stability of the system is analyzed.

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Oscillatory convection in a viscoelastic fluid through a porous layer heated from below

Cited by 57 publications

References 17 publications

Non-Linear Two Dimensional Double Diffusive Convection in a Rotating Porous Layer Saturated by a Viscoelastic Fluid

Non-Linear Two Dimensional Double Diffusive Convection in a Rotating Porous Layer Saturated by a Viscoelastic Fluid

Thermal Instability in a Porous Medium Layer Saturated with a Viscoelastic Nanofluid

Convective Instability of Oldroyd-B Fluid Saturated Porous Layer Heated from Below using a Thermal Non-equilibrium Model

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