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Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium

Nanofluid Saturated Porous Layer Using Darcy Model With Cross Diffusion. Meccanica, 49 (2014), No. 5 , 1159–1175. [31] R ana , G. C., R. C. T hakur , S. K. K ango . On the Onset of Double-Diffusive Convection in a Layer of Nanofluid under Rotation Saturating a Porous Medium. Journal of Porous Media, 17 (2014), No. 8 , 657-667. [32] Nield, D. A., A. V. Kuznetsov. Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model. Int. J. of Heat and Mass Transfer , 68 (2014), No. 4 , 211-214. [33] C hand , R., G. C. R ana

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Linear Stability Effect of Densely Distributed Porous Medium and Coriolis Force on Soret Driven Ferrothermohaline Convection

Abstract

The effect of Coriolis force on the Soret driven ferrothermohaline convection in a densely packed porous medium has been studied. A linear stability analysis is carried out using normal mode technique. It is found that stationary convection is favorable for the Darcy model, therefore oscillatory instability is studied. A small thermal perturbation is applied to the basic state and linear stability analysis is used for which the normal mode technique is applied. It is found that the presence of a porous medium favours the onset of convection. The porous medium is assumed to be variable and the effect of the permeable parameter is to destabilize the system. The present work has been carried out both for oscillatory as well as stationary instabilities. The results are depicted graphically.

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Brinkman – Forchheimer – Darcy Flow Past an Impermeable Sphere Embedded in a Porous Medium

). [12] I. Pop, D.B. Ingham, Flow past a sphere embedded in a porous medium based on the Brinkman model, Int. Commun. Heat Mass Transf. 23, 865-874 (1996). [13] L.A. Romero, Low or high Peclet number ow past a sphere in a saturated porous medium, SIAM J. Appl. Math. 54, 42{71 (1994). [14] N. Rudraiah, I.S. Shivakumaran, D. Palaniappan, D.V. Chandrashekar, Flow past an impervious sphere embedded in a porous medium based on non-Darcy model, Adv. Fluid Mech. 2, 253-256 (2004). [15] C.Y. Wang, Darcy Brinkman ow with solid

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Transient Free Convective Radiative Flow Between Vertical Parallel Plates Heated/Cooled Asymmetrically with Heat Generation and Slip Condition

] Kuznetsov A.V. and Austria V. (1998): Analytical investigation of heat transfer in Coutte flow through a Porous medium utilizing the Brinkman-Forchheimer-extended Darcy model . – Acta Mechanica, vol.129, pp.13-24. [20] Nakayama A. (1998): A unified treatment of Darcy-Forchheimer boundary layer flows . – Transport Phenomena in Porous Media, vol.1, pp.179-204. [21] Leong K.C. and Jin L.W. (2004): Heat transfer of oscillating and steady flows in a channel filled with porousmedium . – Int. Commun. Heat Mass Transfer, vol.31, pp.63-72. [22] Singh A.K. and

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Penetrative convection due to absorption of radiation in a magnetic nanofluid saturated porous layer

Abstract

The present study investigates the onset of penetrative convection in- duced by selective absorption of radiation in a magnetic nanofluid saturated porous medium. The influence of Brownian motion, thermophoresis, and magnetophoresis on magnetic nanofluid treatment is taken into consideration. The Darcy’s model is selected for the porous medium. We conduct a linear stability analysis to examine the onset of instability and evaluate the results for two different configurations, namely, when the layer is heated from below and when the layer is heated from above. The numerical investigations are carried out by applying the Chebyshev pseudospectral method. The effect of the porosity parameter E, parameter Y (represents the ratio of internal heating to boundary heating), Lewis number Le, concentration Rayleigh number Rn, Langevin parameter αL, width of nanofluid layer d, diffusivity ratio η, and modified diffusivity ratio NA is examined at the onset of convection. The results indicate that the convection commences easily with an increase in the value of Y, Le, and NA but opposite in the case with a decrease in the value of E, αL, η and d for both the two configurations. The parameter Rn advances the onset of convection when the layer is heated from below, while delays the onset of convection when the layer is heated from above.

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On the Onset of Thermal Convection in a Layer of Oldroydian Visco-Elastic Fluid Saturated by Brinkman–Darcy Porous Medium

Abstract

Thermal instability in a horizontal layer of Oldroydian visco-elastic fluid in a porous medium is investigated. For porous medium the Brinkman–Darcy model is considered. A linear stability analysis based upon perturbation method and normal mode technique is used to find solution of the fluid layer confined between two free-free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically. The influence of the Brinkman–Darcy, Prandtl–Darcy number, stress relaxation parameter on the stationary and oscillatory convection is studied both analytically and graphically. The sufficient condition for the validity of PES has also been derived.

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Variable Gravity Effects on Thermal Instability of Nanofluid in Anisotropic Porous Medium

Abstract

In this paper, we study the effects of variable gravity on thermal instability in a horizontal layer of a nanofluid in an anisotropic porous medium. Darcy model been used for the porous medium. Also, it incorporates the effect of Brownian motion along with thermophoresis. The normal mode technique is used to find the confinement between two free boundaries. The expression of the Rayleigh number has been derived, and the effects of variable gravity and anisotropic parameters on the Rayleigh number have been presented graphically

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Numerical model of heat transfer in three phases of the poroelastic medium

Abstract

In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot–Darcy model.

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Effect of chemical reaction and radiation on double diffusive flow of a viscous, dissipative fluid through porous medium in a rectangular cavity with heat sources

Abstract

In this paper, an attempt is made to discuss the combined influence of radiation and dissipation on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular cavity using the Darcy model. Making use of the incompressibility, the governing non-linear coupled equations for the momentum, energy and diffusion are derived in terms of the non-dimensional stream function, temperature and concentration. The Galerkin finite element analysis with linear triangular elements is used to obtain the global stiffness matrices for the values of stream function, temperature and concentration. These coupled matrices are solved using an iterative procedure and expressions for the stream function, temperature and concentration are obtained as linear combinations of the shape functions. The behavior of temperature, concentration, the Nusselt number and Sherwood number is discussed computationally for different values of the governing parameters, such as the Rayleigh Number (Ra), heat source parameter (α), Eckert number (Ec), Schmidt Number (Sc), Soret parameter (S0), buoyancy ratio (N).

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A Discrete Duality Finite Volume Method for Coupling Darcy and Stokes Equations

References [1] B. Andreianov, F. Boyer, and F. Hubert. Discrete duality finite volume schemes for leray-lions-type elliptic problems on general 2d meshes. 23(1):145–195. [2] Y. Boubendir and S. Tlupova. Stokesdarcy boundary integral solutions using preconditioners. 228(23):8627–8641. [3] F. Boyer, F. Hubert, and S. Krell. Non-overlapping schwarz algorithm for solving 2d m-DDFV schemes. 30(4):Pp 1062–1100. [4] M. Cai, M. Mu, and J. Xu. Preconditioning techniques for a mixed stokes/darcy model in porous media applications. 233

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