Onset of Darcy–Brinkman convection in a binary viscoelastic fluid saturated porous layer

Swamy, Mahantesh; Naduvinamani, N. B.; Sidram, W.

doi:10.1007/s11242-012-0008-y

Cited by 17 publications

(18 citation statements)

References 32 publications

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“…In the absence of the Soret parameter, i.e., S r = 0, Eq. (30) reduces to This is exactly the same as the one obtained by Swamy et al [31]. When Da → 0, Eq.…”

Section: Stationary Convectionsupporting

confidence: 85%

“…Kuznetsov and Nield analyzed the effect of local thermal nonequilibrium on the onset of convection in a porous layer saturated by a nanofluid using the Brinkman model. More recently, Swamy et al have studied the onset of Darcy–Brinkman convection in a binary viscoelastic fluid‐saturated porous layer. However, the studies on thermal convection in a binary viscoelastic fluid‐saturated porous layer based upon the non‐Darcian models are very sparse.…”

Section: Introductionmentioning

confidence: 99%

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Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

Gaikwad

Dhanraj

2013

Heat Trans. Asian Res.

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A linear and weakly nonlinear stability analyses is performed to study the onset of Darcy–Brinkman double diffusive convection in a binary viscoelastic fluid‐saturated porous layer in the presence of the Soret effect. The modified Darcy–Brinkman–Oldroyd model including the time derivative term is employed for the momentum equation. The expressions for stationary, oscillatory, and finite amplitude Rayleigh number are obtained as a function of the governing parameters. There is a competition between the processes of the Soret coefficient, viscoelasticity, thermal diffusion, and solute diffusion that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effects of the Soret parameter, Darcy number, relaxation and retardation parameters, and Darcy–Prandtl number on the stationary, oscillatory, and finite amplitude convection is shown graphically. The weakly nonlinear theory is based on truncated representation of the Fourier series method and is used to find the Nusselt and Sherwood numbers. Further, the transient behavior of the Nusselt and Sherwood numbers is investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta method. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 297–320, 2014; Published online 3 October 2013 in Wiley Online Library (http://wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21076

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“…In the absence of the Soret parameter, i.e., S r = 0, Eq. (30) reduces to This is exactly the same as the one obtained by Swamy et al [31]. When Da → 0, Eq.…”

Section: Stationary Convectionsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

Gaikwad

Dhanraj

2013

Heat Trans. Asian Res.

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“…This result exactly coincides with the one given by Swamy et al . When Da → 0, that is for densely packed porous medium Eq.…”

Section: Linear Stability Analysissupporting

confidence: 62%

Onset of Darcy‐Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer with Internal Heat Source

Gaikwad

Kouser

2013

Heat Trans. Asian Res.

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The onset of Darcy‐Brinkman convection in a binary viscoelastic fluid‐saturated sparsely packed porous layer with an internal heat source is studied using both linear and nonlinear stability analyses. The Oldroyd‐B model is employed to describe the rheological behavior of binary fluid. An extended form of the Darcy‐Oldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal diffusion, solute diffusion, and viscoelasticity that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effect of internal Rayleigh number, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy‐Prandtl number, and Lewis number on the stability of a system is investigated and is shown graphically. The nonlinear theory based on the truncated representation of the Fourier series method is used to find heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained using numerical methods. Some known results are recovered for the particular cases of the present study. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 676–703, 2013; Published online in Wiley Online Library (http://wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21056

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“…When the thermal convective instability in porous media is considered, a modified Darcy model which extended the Darcy model to include a time derivative term is usually adopted to study the oscillatory convection as well as stationary convection [22,40,59]. Besides, by analogy with the constitutive equation of Oldroyd-B fluid, some researchers proposed a Darcy-Oldroyd model for modeling flows of viscoelastic fluids in porous media, which introduces a relaxation parameter characterizing the elasticity of viscoelastic fluid and a retardation parameter characterizing the viscous damping of viscoelastic fluid [13,60,61]. In this work, the Darcy model is extended with the addition of the Coriolis term in rotating reference frame and is applied to characterize the flow in porous media [1].…”

Section: Mathematical Formulationmentioning

confidence: 99%

Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium

Kang

Xia

Liu

2015

Mathematical Problems in Engineering

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Thermal convection at the steady state for high Rayleigh number in a rotating porous half space is investigated. Taking into account the effect of rotation, Darcy equation is extended to incorporate the Coriolis force term in a rotating reference frame. The velocity and temperature fields of thermal convection are obtained by using the homotopy analysis method. The influences of Taylor number and Rayleigh number on the Nusselt number, velocity profile, and temperature distribution are discussed in detail. It is found that the Nusselt number decreases rapidly with the increase of Taylor number but tends to have an asymptotic value. Besides, the rotation can give rise to downward flow in contrast with the upward thermal convection.

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Onset of Darcy–Brinkman convection in a binary viscoelastic fluid saturated porous layer

Cited by 17 publications

References 32 publications

Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

Onset of Darcy‐Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer with Internal Heat Source

Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium

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