Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
17
10
2014
VISCOUS DISSIPATION EFFECTS ON HEAT TRANSFER, ENERGY STORAGE, AND ENTROPY GENERATION FOR FLUID FLOW IN A POROUS CHANNEL SUBMITTED TO A UNIFORM MAGNETIC FIELD
A numerical study of viscous dissipation effects on heat transfer, thermal energy storage by sensible heat and entropy generation within a porous channel with insulated walls was carried out in a laminar flow regime. The channel is subjected to the effect of a transverse magnetic field. In the flow modeling, the Brinkman-Forchheimer extended Darcy model (DBLF) is incorporated in the momentum equation. The mathematical model for the energy equation is based on the local thermal equilibrium assumption and takes into account the viscous dissipation effects. The obtained governing equations are solved with the lattice Boltzmann Method (LBM). Efforts are focused on identifying the influence of the Darcy number, Eckert number, Hartmann number, the thermal conductivity ratio and the heat capacity ratio on fluid flow, heat transfer, energy storage, and entropy generation throughout this paper.
Bayssain
Amami
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Université de Monastir, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisia
Hacen
Dhahri
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Université de Monastir, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisia
Abdallah
Mhimid
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Université de Monastir, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisia
841-859
MHD FLOW OF AN INCOMPRESSIBLE FLUID THROUGH POROUS MEDIUM BETWEEN DILATING AND SQUEEZING PERMEABLE WALLS
In this article laminar flow of an incompressible electrically conducting viscous fluid is considered through a porous medium confined in a rectangular domain with infinite length and bounded by two moving preamble walls which enable the fluid to enter or exit during successive deformations. The solution to the problem is approximated by using a variation iteration method (VIM). To investigate the effect of nondimensional wall deformation α, permeation Reynolds number R, reciprocal of porosity coefficient K, and magnetic parameter M on the flow field, graphical results are presented. The analytical solution obtained by VIM is supported by numerical results and both show excellent agreement. The study of flow between dilating or squeezing porous walls is a drastic simplification of the transport of biological fluids through dilating or squeezing vessels.
Naveed
Ahmed
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt Pakistan
Umar
Khan
COMSATS Institute of Information Technology Abbottabad
Zulfiqar Ali
Zaidi
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt Pakistan; COMSATS Institute of Information Technology, University Road, Abbottabad, Pakistan
Saeed Ullah
Jan
COMSATS Institute of Information Technology, University Road, Abbottabad, Pakistan
Asif
Waheed
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt Pakistan
Syed Tauseef
Mohyud-Din
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt Pakistan
861-867
EFFECTS OF THE IRROTATIONAL VISCOUS PRESSURE ON MAGNETOHYDRODYNAMIC KELVIN−HELMHOLTZ INSTABILITY WITH MASS TRANSFER THROUGH POROUS MEDIA
In this paper, we investigate the effects of irrotational, viscous pressure on the Kelvin−Helmholtz instability of the interface between two viscous and magnetic fluids in a fully saturated porous medium and, when there is heat and mass transfer across the interface. The analysis extends our earlier work in which the Kelvin−Helmholtz instability of two viscous and electrically conducting fluids in a fully saturated porous medium was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. The whole system is acted by a horizontal magnetic field to the interface. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by selecting viscous contributions to the irrotational pressure. We use the Darcy−Brinkman model and a dispersion relation has been derived. Stability criterion is given in terms of a critical value of relative velocity as well as critical value of applied magnetic field. It has been observed that heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.
Mukesh Kumar
Awasthi
Department of Mathematics, University of Petroleum and Energy Studies, Dehradun-248007, (Uttarakhand), India
869-881
LINEAR STABILITY ANALYSIS OF DOUBLE-DIFFUSIVE CONVECTION IN MAGNETIC NANOFLUIDS IN POROUS MEDIA
The double-diffusive convective instability in a thin layer of a magnetic nanofluid, heated and salted from below and saturating a porous medium, is examined within the framework of linear stability theory. The model used incorporates the effect of Brownian diffusion, thermophoresis, and magnetophoresis. The eigenvalue problem is solved by employing the Chebyshev Pseudospectral method and the results are discussed for water and ester based magnetic nanofluids. The effects of the important parameters of problem are examined at the onset of convection.
M. K.
Sharma
Department of Mathematics, Central University of Himachal Pradesh, TAB, Shahpur, District Kangra (H.P.), India
Ravinder
Singh
Department of Mathematics, Central University of Himachal Pradesh, TAB, Shahpur, District Kangra (H.P.), India
883-900
EFFECTS OF MAGNETO-MARANGONI CONVECTION WITH VARIABLE PROPERTIES ON NON-NEWTONIAN BIVISCOSITY FLUID OVER STRETCHING SHEET IN POROUS MEDIUM
The magneto-Marangoni convection effect on non-Newtonian biviscosity fluid flow in a thin film over an unsteady horizontal stretching sheet through a porous medium with variable viscosity and variable thermal diffusivity has been investigated. The governing partial differential equations are nondimensionalized using suitable transformation variables and the resulting equations have been solved numerically using the Chebyshev pseudospectral method for some representative values of the parameters. Numerical results are obtained and displayed graphically for pertinent physical parameters to show interesting aspects of the solutions. The velocity and temperature distributions, free-surface temperature, wall shear stress, and surface heat flux in the film are found to be affected significantly by the thermally induced Marangoni convection adjacent to the free surface. It is also shown that a non-Newtonian biviscosity fluid is less sensitive to the Marangoni effect.
N. S.
Elgazery
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
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
901-912
SINGLE-PHASE FLOWS IN SWELLING, LIQUID-ABSORBING POROUS MEDIA: A DERIVATION OF FLOW GOVERNING EQUATIONS USING THE VOLUME AVERAGING METHOD WITH A NONDETERMINISTIC, HEURISTIC APPROACH TO ASSESSING THE EFFECT OF SOLID-PHASE CHANGES
A novel theoretical derivation of governing equations for single-phase flow of Newtonian fluids in swelling, liquid-absorbing porous media is performed. Some unique forms of mass balance (continuity) and momentum balance (Darcy's law) are developed using the volume averaging method. Solid-phase distribution is not predicted and is expected to be determined from in situ microscopic studies of the concerned porous media. The intake of flowing liquid into constituent particles or fibers leads to suspension of the no-slip boundary condition on their surfaces, resulting in new equation forms. The volume averaging of the continuity equation leads to the generation of sink and source terms; the equation is simplified further by defining an absorption coefficient b. The case of b being unity, which corresponds to the liquid absorption rate being equal to the particle expansion rate, results in the classic form of the continuity equation. In the proposed macroscopic equations as well as in the corresponding closure formulation, inertial terms are shown to be insignificant through order-of-magnitude analyses. The final formulation, which can be solved in a periodic unit cell in the absence of a significant porosity gradient, reveals a method to estimate macroscopic permeability using pore-scale topology, thus establishing an effective micro−macro coupling for the posed problem. The continuity equation, in conjunction with Darcy's law, explains quite well the experimental results observed during wicking of liquids into absorbent paper as well as observed during pressurized injection of liquids into swelling porous media made from natural fibers.
Krishna M.
Pillai
Laboratory for Flow and Transport Studies in Porous Media, Mechanical Engineering, University of Wisconsin-Milwaukee, 3200, N. Cramer Street, Milwaukee, Wisconsin 53211, USA
915-935