Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
15
3
2012
UNSTEADY FLUID DYNAMICS FLOW AND HEAT TRANSFER IN CROSS FLOW OVER A HEATED CYLINDER EMBEDDED IN A POROUS MEDIUM
In the present work, a numerical analysis is performed to study fluid dynamics and heat transfer for flow over a cylinder embedded in a porous medium. The objective of the work is twofold: first, to address the effect of porous medium on von Karman vortex formation at the cylinder wake, where it is found that porous media may suppress the formation of the vortex for a certain range of controlling parameters; and, second, adding porous medium to the domain of interest (air) modifies the effective thermal conductivity by many fold, depending on the material of the porous medium. Hence, an increase in the rate of heat transfer is expected. The work tries to quantify the rate of heat transfer. In this work the effect of the Reynolds number, Darcy number, and thermal conductivity ratio on the flow separation and rate of heat transfer are introduced and discussed. The Prandtl number is fixed at 0.71 (air). It is found that the porous medium enhances the rate of heat transfer and the rate of enhancement is a strong function of the thermal conductivity ratio. A correlation is suggested for the rate of heat transfer (Nusselt number) as a function of the Reynolds number and effective thermal conductivity ratio for the range of the investigated Darcy numbers.
L. B.
Younis
SNC-Lavalin Inc, Calgary, Alberta, T2P 3H5, Canada
A. A.
Mohamad
College of Engineering, Alfaisal University, P.O. Box 50927, Riyadh 11533, Saudi Arabia
203-210
NUMERICAL SIMULATION OF FREE FALL AND CONTROLLED GRAVITY DRAINAGE PROCESSES IN POROUS MEDIA
Multiphase flow simulation in porous media requires understanding of the physics of transport, tools for managing complicated scale-dependent structures, and effective solution methods. Complex two-phase flow in porous media under gravity drainage is addressed in this paper; mathematical simulation of the process in homogeneous and fractured porous media was carried out using COMSOL. A new approach is proposed to simulate time-dependent drainage in vertical porous physical models to investigate aspects of gravity drainage (free fall or controlled gravity drainage) on oil saturation distribution and oil production history. The effect of permeability heterogeneity in the form of fractures on the drainage process, as well as the evolution of relative permeability of the wetting and non-wetting phases, capillary pressure, and some other significant parameters, was mathematically investigated. The results obtained are compared with experimental data from laboratory tests were reported in the literature, showing a good agreement.
Sohrab
Zendehboudi
Memorial University
Ali
Shafiei
Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario, Canada
Ioannis
Chatzis
Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2l 3G1, Canada
Maurice B.
Dusseault
Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
211-232
NANOFLUID BIOCONVECTION IN POROUS MEDIA: OXYTACTIC MICROORGANISMS
This paper investigates a new type of a nanofluid that contains, in addition to nanoparticles, oxytactic motile microorganisms. One of the paradigmic problems, the Horton−Rogers−Lapwood problem (i.e., the stability of a horizontal fluid-saturated porous layer of finite depth), is solved for this new nanofluid. The stability of this nanofluid is controlled by three agencies: the nanoparticle distribution, the density stratification induced by the vertical temperature gradient, and the density stratification induced by upswimming of oxytactic microorganisms. Both non-oscillatory and oscillatory instability situations are investigated. Oscillatory instability is shown to be possible when the nanoparticle distribution is stabilizing (bottom heavy) and the vertical temperature variation is destabilizing (heating from the bottom). It is also shown that the presence of oxytactic microorganisms makes the suspension less stable but tends to destroy the oscillatory instability in favor of non-oscillatory instability.
Andrey V
Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA
233-248
SMALL NIELD NUMBER CONVECTION IN A POROUS LAYER HEATED FROM BELOW VIA A CONSTANT HEAT FLUX AND SUBJECT TO LACK OF LOCAL THERMAL EQUILIBRIUM
The lack of local thermal equilibrium leads to distinct basic temperature profiles for the fluid and solid phases when a constant heat flux instead of a constant temperature is imposed on the lower boundary. Despite these distinct basic temperature profiles, the equations governing their linear stability for small Nield numbers eventually degenerate to the same form as for the case of local thermal equilibrium subject to constant heat flux on the lower boundary. A complete linear stability analysis is performed presenting an accurate solution to the latter; the corresponding neutral curves; accurate eigenvalues; and, in particular, the distinct type of eigenfunctions producing the shape of the convection patterns.
Peter
Vadasz
Department of Mechanical Engineering, Northern Arizona University, PO Box 15600, Flagstaff, Arizona 86001, USA ; Faculty of Engineering, University of KZ Natal, Durban 4041, South Africa
249-258
THERMAL RADIATION EFFECTS ON MAGNETOHYDRODYNAMIC HEAT AND MASS TRANSFER FROM A HORIZONTAL CYLINDER IN A VARIABLE POROSITY REGIME
A mathematical model is presented for multiphysical transport of an optically dense, electrically conducting fluid along an isothermal horizontal circular cylinder embedded in a variable-porosity medium. A constant, static, magnetic field is applied transverse to the cylinder surface. The non-Darcy effects are simulated via the second-order Forchheimer drag force term in the momentum boundary layer equation. The cylinder surface is maintained at a constant temperature and concentration. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite-difference scheme. The increasing magnetohydrodynamic body force parameter (Μ) is found to decelerate the flow. Increasing porosity (ε) is found to elevate velocities (i.e., accelerate the flow but decrease temperatures; cool the boundary layer regime). Increasing the Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing the Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. The local Nusselt number is also found to be enhanced with increasing both porosity and radiation parameters.
V. Ramachandra
Prasad
Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle-517325, Andrapradesh, India
B.
Vasu
Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle 517325, India
O. Anwar
Beg
Fluid Mechanics, Bio-Propulsion and Nanosystems, Aeronautical and Mechanical Engineering Division, Room UG17, Newton Building, University of Salford, M54WT, United Kingdom
D. Rana
Parshad
Division of Mathematics and Computer Science, Clarkson University, Potsdam, New York 13676, USA
261-281
QUASI-STATIC DEFORMATION CAUSED BY A LONG TENSILE DISLOCATION IN AN ELASTIC HALF-SPACE IN WELDED CONTACT WITH A POROELASTIC HALF-SPACE
An analytical solution of the plane strain problem of a long tensile fault embedded in an elastic half-space in welded contact with a poroelastic half-space is obtained. The tensile fault is horizontal with dislocation in the vertical direction. The solution obtained is in the Laplace−Fourier transform domain. Stehfest’s formula is used for the Laplace inversion and the extended Simpson’s formula for the Fourier inversion. Diffusion of the pore pressure and the consolidation rate are studied numerically. It is found that an increase in the rigidity ratio of the poroelastic/elastic half-spaces results in an increase in the pore pressure at the interface. The compressibility of the fluid constituents of the poroelastic half-space diminishes the amplitude of vertical displacement. However, it has no effect on the consolidation rate. Similarly, a change in the rigidity ratio of the poroelastic/elastic half-spaces has no effect on the consolidation rate.
Raman
Kumar
Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar-125001, India
Sunita
Rani
Department of Mathematics,Guru Jambheshwar University of Science & Technology,Hisar-125001, India
Sarva Jit
Singh
Indian National Science Academy, New Delhi-110002, India
283-291
SUCTION AND BLOWING EFFECTS ON UNSTEADY FLOW AND HEAT TRANSFER THROUGH POROUS MEDIA WITH VARIABLE VISCOSITY
Unsteady boundary layer flow and heat transfer characteristics of a viscous fluid through porous media have been studied in the case of variable viscosity and variable Prandtl number. The plate surface is embedded in a uniform Darcian porous medium. In order to allow for possible fluid wall suction or blowing the plate is assumed to be uniformly porous. The similarity transformation is used to transform the system of partial differential equations, describing the problem under consideration, into a system of coupled ordinary differential equations. Analytic and numerical solutions of these equations are obtained using the homotopy analysis method and Runge−Kutta shooting technique, respectively. The results are presented graphically and it is concluded that the flow field and other quantities of physical interest are significantly influenced by the involved parameters.
Saira
Husnain
Department of Mathematics, Quaid-i-Azam University, 45320 Islamabad 44000, Pakistan
Ahmer
Mehmood
Department of Mathematics, International Islamic University, Islamabad, Pakistan
O. Anwar
Beg
Fluid Mechanics, Bio-Propulsion and Nanosystems, Aeronautical and Mechanical Engineering Division, Room UG17, Newton Building, University of Salford, M54WT, United Kingdom
Asif
Ali
Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan
293-302