Begell House Inc.
Journal of Porous Media
JPM
1091-028X
10
5
2007
Effect of Combined Brinkman-Electric Boundary Layer on the Onset of Marangoni Electroconvection in a Poorly Conducting Fluid-Saturated Porous Layer Cooled from Below in the Presence of an Electric Field
421-434
10.1615/JPorMedia.v10.i5.10
N.
Rudraiah
National Research Institute for Applied Mathematics, 492/G, 7th Cross, 7th Block (West), Jayanagar, Bangalore 560 082, and UGC-DSA Centre in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore 560 001, India
Takashi
Masuoka
The University of Kitakyushu, and Department of Mechanical Engineering, Kyushu University, Kyushu, Japan
Premini
Nair
Department of Mathematics, Mount Carmel College, Bangalore 560 052, India
The effect of Brinkman-electric boundary layer on the onset of electroconvection driven by the electric force and surface tension gradient, in a thin horizontal Poorly electrically conducting, fluid-saturated, sparsely packed porous layer bounded by adiabatic free boundaries is studied. The energy method combined with single term Galerkin expansion technique is shown to be convenient and useful to determine eigenvalues. The convergence of the result obtained by Galerkin technique is checked by comparing the result with those obtained using a regular perturbation technique. We found that the single-term Galerkin expansion is accurate only for small values of the combined porous and electric parameter d1. The effect of large values of d1 on the onset of Marangonielectroconvection is determined using the method of matched asymptotic expansion. The effect of boundary layer that exists for large values of d1 is shown to increase the critical Marangoni number by an amount of 2d1 compared to that for small values of d1. The results obtained are useful in the manufacture of smart materials of nanonstructure free from impurities.
Instability of Slip Flow in a Channel Occupied by a Hyperporous Medium
435-442
10.1615/JPorMedia.v10.i5.20
Andrey V
Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA
A. A.
Avramenko
Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine
D A
Nield
University of Auckland
Auckland, New Zealand
Stability of a slip flow in a channel occupied by a hyperporous medium saturated by a rarefied gas is investigated. The evolution equation for analyzing the effect of three-dimensional disturbances on this flow is obtained. Numerical analyses for two-dimensional and three-dimensional disturbances are carried out using the collocation method. The dependence of the critical Reynolds number on porosity and parameter σ (dependent on the Knudsen number) is investigated. Squire's theorem for the case of two-dimensional shear flows in a Navier-Stokes fluid, which states that two-dimensional disturbances are more critical for instability than three-dimensional disturbances, is extended to the case of this flow.
Hydromagnetic Instability of Fluid-Particle Kelvin-Helmholtz Flow in Oldroydian Viscoelastic Porous Media
443-458
10.1615/JPorMedia.v10.i5.30
Mohamed F.
El-Sayed
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis (Roxy), Cairo, Egypt; Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraidah 51452, Saudi Arabia
The Kelvin-Helmholtz instability of two viscoelastic Oldroydian superposed conducting fluids permeated with suspended particles in a porous medium is studied when the whole system is immersed in a uniform magnetic field. The dispersion equation for the considered system is obtained, which also yields the dispersion relation for Maxwellian fluids as a limiting case in the presence of suspended particles through a porous medium in hydromagnetics. It is found that both the magnetic field and surface tension have stabilizing effects and completely suppress the Kelvin-Helmholtz instability for small wavelengths. The medium porosity reduces the stability range given in terms of the fluids and Alfven velocities. The stability conditions are discussed analytically in detail. The numerical results show that the stress relaxation time, number density of the suspended particles, porosity of the porous medium, Stokes's drag coefficient, and the strain retardation time have destabilizing as well as stabilizing effects for small and large wave numbers. The medium permeability is found to have an opposite effect. The magnetic field has a stabilizing effect only for small wave numbers; otherwise, it has no effect on the stability of the system. Both the kinematic viscosity and fluid velocity are found to have destabilizing effects. The corresponding results in the limiting case of Maxwellian fluids have been compared with the previous results of Oldroydian fluids.
Effect of an Aligned Magnetic Field on the Instability of Two Superposed Conducting Fluids in a Porous Medium
459-472
10.1615/JPorMedia.v10.i5.40
The effect of aligned magnetic field on the instability of two superposed conducting fluids in porous medium has been investigated. The unstable and stable cases of the resulting dispersion relation have been separately dealt with. In the unstable case, it is shown, for non-porous media, and for horizontal to vertical magnetic field values λ ≤ 1, that no mode of maximum instability exists. However, when λ > 1, there is a mode of maximum instability which would assert itself during the initial period of motion. The stability effect holds in the presence of porous medium or when λ > 1 is found to be faster than its effect in the corresponding case of non-porous medium or when λ < 1, respectively. If the vertical magnetic field dominates, we found that the kinematic viscosity has a stabilizing effect, and both the porosity of porous medium and the medium permeability have destabilizing effects on the considered system. If the horizontal magnetic field dominates, we found that the kinematic viscosity and the medium permeability has a stabilizing and a destabilizing effects, respectively; while the porosity of porous medium has a destabilizing effect (for small wavenumbers) as well as stabilizing effect (for large wavenumbers). In the stable case, it is found that no normal mode solution exists, and that whether the medium is porous or not, the potentially stable configuration remains stable in the presence of an oblique magnetic field.
Partial Slip Effects on the Oscillatory Flows of a Fractional Jeffrey Fluid in a Porous Medium
473-488
10.1615/JPorMedia.v10.i5.50
Masood
Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
The exact analytical solutions are obtained for three basic fluid flow problems in a porous medium when the no-slip condition is no longer valid. The fractional calculus approach is used to describe the constitutive model of a magnetohydrodynamic fractional Jeffrey fluid. The porous medium is taken into account using modified Darcy 's law for fractional viscoelastic fluid. The effects of Hall current are also taken into account. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the velocity profiles. In each case, the analytical solutions are obtained using Fourier transform for fractional calculus. The solutions for the no-slip condition are special cases of the presented analysis. The critical assessment is made for the cases of partial slip and no-slip conditions. Moreover, the well-known solutions for a Newtonian fluid in nonporous and porous media are limiting cases of our solutions.
Effects of Chemical Reactions, Heat, and Mass Transfer on Nonlinear Magnetohydrodynamic Boundary Layer Flow over a Wedge with a Porous Medium in the Presence of Ohmic Heating and Viscous Dissipation
489-502
10.1615/JPorMedia.v10.i5.60
P. G.
Palanimani
Department of Mathematics, Erode Sengunthar Engineering College, Erode 638057, India
An analysis is carried out to study the effects of chemical reactions, heat, and mass transfer on nonlinear magnetohydrodynamic (MHD) boundary layer flow over a wedge with a porous medium in the presence of Ohmic heating and viscous dissipation. The fluid is assumed to be incompressible, viscous, electrically conducting, and Boussinesq. A magnetic field is applied transversely to the direction of the flow. A numerical solution for the steady MHD laminar boundary layer flow over a wall of the wedge with suction in the presence of species concentration and mass diffusion has been obtained by transforming the governing equations to nonlinear ordinary differential equations through similarity transformations and further utilizing the R. K. Gill method. Numerical calculations up to the third level of truncation are carried out for different values of dimensionless parameters of the problem under consideration. An analysis of the results obtained shows that the flow field is influenced appreciably by the strength of the magnetic field, chemical reactions, and suction at the wall of the wedge.
Magnetohydrodynamics and Radiative Effects on Free Convection Flow of Fluid with Variable Viscosity from a Vertical Plate through a Porous Medium
503-514
10.1615/JPorMedia.v10.i5.70
M. Modather M.
Abdou
Department of Mathematics, Faculty of Science Aswan, South Valley University, Aswan, Egypt; Department of Mathematics, College of Science and Humanity Studies, Salman Bin AbdulAziz University, Al-Kharj, KSA
S.M.M.
EL-Kabeir
Department of Mathematics, Salman bin Abdulaziz University, College of Science and Humanity Studies, Al-Kharj, 11942, Saudi Arabia; Department of Mathematics, Aswan University, Faculty of Science, 81528, Egypt
The effect of thermal radiation on free convection flow with variable viscosity and uniform suction velocity along a uniformly heated vertical porous plate embedded in a porous medium in the presence of a uniform transverse magnetic field is analyzed. The viscosity of the fluid is taken as a function of temperature. The effect of internal heat generation/absorption is also considered. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing equations are solved using the local nonsimilarity method. Numerical results for the transient velocity, the temperature, the local and average skin friction, and the rate of heat are shown in graphic and tabulated forms.
Effect of Inertia on the Onset of Mixed Convection in a Porous Layer Using a Thermal Nonequilibrium Model
515-524
10.1615/JPorMedia.v10.i5.80
Adrian
Postelnicu
Department of Thermal Engineering and Fluid Mechanics, Transilvania University of Brasov, Brasov, Romania
The article deals with the onset of mixed convection in a porous layer heated from below by considering the effect of inertia when the fluid and solid phases are not in local thermal equilibrium in the frame of a linear stability analysis. The mixed convection is considered in the sense of a mean horizontal pressure gradient. Critical Rayleigh number and wave number are analytically determined in both two-dimensional (2-D) and 3-D cases. In the 2-D case the parameters of the problem are the inertia-modified parameter G*, porosity-scaled conductivity ratio γ, and scaled interphase heat transfer coefficient H. In the 3-D case an additional parameter occurs, namely, the angle of roll inclination α. The inertia effect acts as a stabilizing factor in the convection onset, and this factor dominates the effect produced by the local thermal nonequilibrium conditions.