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

Shivakumara, I. S.; Malashetty, M. S.; Chavaraddi, Krishna B.

doi:10.1139/p06-085

Cited by 31 publications

(18 citation statements)

References 17 publications

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“…Yoon et al (2004) have followed the formulation of Akhatov and Chembarisova (1993) and sought analytically the onset of thermal convection in an isothermally heated porous layer saturated with viscoelastic fluid. Shivakumara et al (2006) and Malashetty et al (2006a,b) have discussed, respectively, the effect of local thermal nonequilibrium on the onset of convection in a sparsely and densely packed Oldroyd-B viscoelastic fluid-saturated porous medium. Shivakumara and Sureshkumar (2007) have used linear stability theory to investigate convective instability in a horizontal porous layer saturated with viscoelastic fluid of Oldroyd-B type in the presence of vertical throughflow, and these authors have also extended their previous work to include the effect of quadratic drag in the presence of an additional diffusing component (Shivakumara and Sureshkumar 2008).…”

Section: Introductionmentioning

confidence: 99%

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

et al. 2010

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The linear stability of Walters B viscoelastic fluid-saturated horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and the corresponding wave number. The shift in critical Rayleigh number is calculated as a function of modulation frequency, viscoelastic parameter, and Prandtl number. The effect of all three types of modulations is found to be destabilizing as compared to the unmodulated system. This result is in contrast to the system with other types of fluids. Besides, the influence of physical parameters on the control of convective instability of the system is discussed.

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Section: Introductionmentioning

confidence: 99%

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

et al. 2010

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“…Straughan (2006) has considered a problem of thermal convection in a fluid-saturated porous layer using a global nonlinear stability analysis with a LTNE model. Malashetty et al (2006) and Shivakumara et al (2006) have analyzed the onset of convection in a porous layer saturated with an (2008) has studied the onset of Darcy-Brinkman convection using a thermal non-equilibrium model for rigid isothermal boundaries. Recently, Shivakumara et al (2010a,b)have analyzed the effects of temperature dependent viscosity and quadratic density as well as boundary effect on the onset of free convection in a porous layer using a thermal non-equilibrium model.…”

Section: Introductionmentioning

confidence: 99%

Effect of Thermal Non-Equilibrium on Convective Instability in a Ferromagnetic Fluid-Saturated Porous Medium

Lee

Shivakumara

Ravisha³

2010

Transp Porous Med

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The effect of local thermal non-equilibrium (LTNE) on the onset of thermomagnetic convection in a ferromagnetic fluid-saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated. A modified Forchheimer-extended Darcy equation is employed to describe the flow in the porous medium, and a two-field model is used for temperature representing the solid and fluid phases separately. It is found that both the critical Darcy-Rayleigh number and the corresponding wave number are modified by the LTNE effects. Asymptotic solutions for both small and large values of scaled interphase heat transfer coefficient H t are presented and compared with those computed numerically. An excellent agreement is obtained between the asymptotic and the numerical results. Besides, the influence of magnetic parameters on the instability of the system is also discussed. The available results in the literature are recovered as particular cases from the present study.

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“…Straughan [19] has considered a problem of thermal convection in a fluidsaturated porous layer using a global nonlinear stability analysis with a LTNE model. Malashetty et al [20] and Shivakumara et al [21] have analyzed the onset of convection in a porous layer saturated with an Oldroyd-B fluid by considering a LTNE model. Nouri-Borujerdi et al [22] have discussed the effect of internal heat generation and thermal non-equilibrium effects on the onset of convection in a porous channel.…”

Section: Introductionmentioning

confidence: 99%

Boundary and thermal non-equilibrium effects on the onset of Darcy–Brinkman convection in a porous layer

Shivakumara

Mamatha²,

Ravisha³

2010

J Eng Math

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A local thermal non-equilibrium model for the temperature representing the solid and fluid phases separately is used to study the onset of free convection in a sparsely packed porous layer using the Brinkman-extended Darcy model. The lower boundary of the porous layer is considered to be rigid and isothermal, while the upper isothermal boundary is assumed to be either rigid or free. The Galerkin method is used to obtain the eigenvalue equation, which is then solved numerically. The effects of thermal non-equilibrium and other physical parameters on the onset of convection are analyzed and compared for two types velocity boundary conditions considered. Besides, some known results available in the literature are compared with those obtained from the present study and good agreement is found.

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

Cited by 31 publications

References 17 publications

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

Effect of Thermal Non-Equilibrium on Convective Instability in a Ferromagnetic Fluid-Saturated Porous Medium

Boundary and thermal non-equilibrium effects on the onset of Darcy–Brinkman convection in a porous layer

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