Local thermal non-equilibrium effects on thermal convection in a rotating anisotropic porous layer

Effects of local thermal non-equilibrium (LTNE) on thermal convection in a rotating fluid-saturated anisotropic porous layer are investigated. The analysis has been carried out by constructing a simplified model consisting of six coupled nonlinear ordinary differential equations. The study reveals the equivalence of linear and nonlinear stability boundaries indicating the linearized instability theory captures completely the physics of the onset of convection. Results show that the presence of rotation is to introduce oscillatory convection once the Taylor number exceeds a threshold value. The preferred mode of instability is found to be influenced significantly by the mechanical anisotropy parameter as well and it is demonstrated that it has both stabilizing and destabilizing effects on the steady onset in the presence of rotation. Besides, asymptotic analyses for small and large values of the interphase heat transfer coefficient are presented. Heat transport is calculated in terms of Nusselt number. Also, the coupled nonlinear ordinary differential equations are solved numerically using Runge-Kutta method and the transient behavior of Nusselt number is demonstrated for various values of physical parameters. © 2015 Elsevier Inc

Linear and weakly nonlinear magnetoconvection in a porous medium with a thermal nonequilibrium model

Two-dimensional magnetoconvection in a layer of Brinkman porous medium with local thermal nonequilibrium (LTNE) model is investigated by performing both linear and weakly nonlinear stability analyses. Condition for the occurrence of stationary and oscillatory convection is obtained in the case of linear stability analysis. It is observed that the presence of magnetic field is to introduce oscillatory convection once the Chandrasekhar number exceeds a threshold value if the ratio of the magnetic diffusivity to the thermal diffusivity is sufficiently small. Besides, asymptotic solutions for both small and large values of the inter-phase heat transfer coefficient are presented for the steady case. A weakly nonlinear stability analysis is performed by constructing a system of nonlinear autonomous ordinary differential equations. It is observed that subcritical steady convection is possible for certain choices of physical parameters. Heat transport is calculated in terms of Nusselt number. Increasing the value of Chandrasekhar number, inter-phase heat transfer coefficient and the inverse Darcy number is to decrease the heat transport, while increasing the ratio of the magnetic diffusivity to the thermal diffusivity and the porosity modified conductivity ratio shows an opposite kind of behavior on the heat transfer

Effects of thermal nonequilibrium and non-uniform temperature gradients on the onset of convection in a heterogeneous porous medium

The simultaneous effect of local thermal nonequilibrium (LTNE), vertical heterogeneity of permeability, and non-uniform basic temperature gradient on the criterion for the onset of Darcy-Benard convection is studied. The eigenvalue problem is solved numerically using the Galerkin method. The interaction of various types of permeability heterogeneity and non-uniform basic temperature gradient functions on the stability characteristics of the system is analyzed. It is observed that the linear variation (about the mean) of the permeability and the basic temperature gradient with depth has no added effect on the criterion for the onset of convection. However, the concurrent variation in heterogeneous permeability and non-uniform basic temperature gradient functions has more stabilizing effect on the system, while opposite is the trend when the effect of non-uniform basic temperature gradient alone is present. (C) 2011 Elsevier Ltd. All rights reserved

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

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. © 2010 Springer Science+Business Media B.V

Thermomagnetic convection in porous media: Effect of anisotropy and local thermal nonequilibrium

The onset of thermomagnetic convection in an anisotropic layer of Darcy porous medium in the presence of a uniform vertical magnetic field is investigated using a local thermal nonequilibrium (LTNE) model for energy equation representing the solid and fluid phases separately. Anisotropies in permeability as well as in fluid and solid thermal conductivities are considered. The principle of exchange of stability is shown to be valid. Asymptotic solutions for the Rayleigh number for both small and large values of scaled interphase heat transfer coefficient t H are presented and the comparison of results with those computed numerically shows good agreement. The mechanical and thermal anisotropy parameters have opposing influence on the stability characteristics of the system. Besides, the influence of magnetic parameters on the instability of the system is also reported. © 2017 Trans Tech Publications, Switzerland

Effects of variable viscosity and density maximumon the onsetofdarcy-benard convection usinga thermal nonequilibrium model

The effects of the temperature-dependent viscosity and density maximum on the criterion for the onset of convection in a horizontal porous layer are investigated when the solid and fluid phases are not in local thermal equilibrium. A two-field model that represents the fluid-and solid-phase temperature fields separately is used for the energy equation. The Galerkin method is used to obtain the eigenvalue equation, which is then solved numerically. It is noted that higher values of the viscosity number and the parameter representing the maximum-density property have the effect of delaying the onset of convection and reducing the size of convection cells. In addition, the influence of parameters representing the thermal nonequilibrium effects on convective instability is discussed in detail. © 2010 by Begell House, Inc

Effect of nonuniform temperature gradientson thermogravitational convectionin aporouslayer using a thermal nonequilibrium model

The effect of various forms of nonuniform basic temperature gradients on the onset of convection in a Newtonian fluidsaturated isotropic porous layer is investigated when the fluid and solid phases are not in local thermal equilibrium. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation and the Forchheimer-extended Darcy model is used to describe the flow. The eigenvalue problem is solved numerically using the Galerkin technique. Comparisons are also made of the critical stability parameters between the present results and published ones for the linear basic temperature profile case, and the agreement is found to be good. The possibility of delaying or hastening the onset of convection by the basic state temperature gradients along with the influence of parameters representing the local thermal non-equilibrium effect is analyzed in detail. When compared with the nonuniform temperature gradients, it is found that the linear temperature profile indicates a reinforcement of stability. In addition, the role of thermal depth on the critical conditions is assessed in the case of piecewise linear temperature profiles. © 2011 by Begell House, Inc

Boundary and thermal non-equilibrium effects on convective instability in an anisotropic porous layer

The effects of boundary and local thermal non-equilibrium on the criterion for the onset of convection in a sparsely packed horizontal anisotropic porous layer are investigated. A two-field temperature model each representing the solid and fluid phases separately is used and the flow in the porous medium is described by the Brinkman extended-Darcy model. The lower boundary is rigid, while the upper boundary is considered to be either rigid or free with fixed temperature conditions at the boundaries. The stability equations are solved numerically using the Galerkin method to extract the critical stability parameters. The influence of local thermal non-equilibrium, mechanical and thermal anisotropy parameters representing the fluid and solid phases is assessed on the stability characteristics of the system. The existing results are obtained as limiting cases from the present study. © 2011 The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg

Effects of alternating current electric field and thermal non-equilibrium on the Brinkman-Bénard instability

The onset of thermal convection in a layer of dielectric fluid-saturated Brinkman porous medium is investigated under the influence of a uniform vertical alternating current (AC) electric field using a local thermal non-equilibrium (LTNE) model considering the boundaries to be either free-free or rigid-rigid or lower rigid and upper free. It has been shown that the principle of exchange of stability is valid irrespective of the nature of boundaries. The eigenvalue problem is solved exactly for free-free boundaries and numerically using shooting method for rigid-rigid and lower rigid-upper free boundaries. The results for different velocity boundary conditions are found to be qualitatively similar but differ only quantitatively. It is observed that an increase in the AC electric Rayleigh number Rea is to augment heat transfer and to hasten the onset of convection, while an increase in the inter-phase heat transfer coefficient H, inverse Darcy number Da-1, and the ratio of viscosities � as well as a decrease in the porosity modified conductivity ratio γ is to delay the onset of electrothermal convection. Besides, increase in Rea and Da-1 as well as decrease in γ, H, and � is to reduce the size of convection cells. Asymptotic solutions for both small and large values of H for free-free boundaries compare well with those obtained from the exact formula. © 2017 by Begell House, Inc