Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
10
1
2007
The Stability of a Developing Thermal Front in a Porous Medium. I Linear Theory
In this paper, we analyze the stability of the developing thermal boundary layer that is induced by suddenly raising the temperature of the lower horizontal boundary of a uniformly cold semi-infinite porous domain. A full linear stability analysis is developed, and it is shown that disturbances are governed by a parabolic system of equations. Numerical solutions of this system are compared with the neutral stability curve obtained by approximating the system as an ordinary differential eigenvalue problem. Different criteria are used to mark the onset of convection of an evolving disturbance, namely, the maximum disturbance temperature, the surface rate of heat transfer, and the disturbance energy. It is found that these different measures yield different neutral curves. We also show that the disturbances have a favoured evolutionary path in the sense that disturbances introduced at different times or with different initial profiles eventually tend toward that common path.
Asma
Selim
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
D. Andrew S.
Rees
Department of Mechanical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
1-16
The Stability of a Developing Thermal Front in a Porous Medium. II Nonlinear Evolution
We consider the instability of the unsteady thermal boundary that is caused by suddenly raising the temperature of the lower boundary of an otherwise cold saturated porous medium. In particular, we focus attention on strongly nonlinear two-dimensional convection. A comprehensive set of results is presented which shows the effects of varying the amplitude of the disturbance, its wave number, and the time at which the disturbance is introduced into the developing thermal boundary layer. We indicate, in detail, how the evolution of the instabilities with time is affected by nonlinearity and how the characteristics of that evolution are changed from those that arise in linearized theory. We also determine when linearized theory is inadequate to describe the global features of the evolution, such as the re stabilisation of convection.
Asma
Selim
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
D. Andrew S.
Rees
Department of Mechanical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
17-34
Effects of Hall Current and Heat Transfer on the Flow in a Porous Medium with Slip Condition
Based on modified Darcy's law, the fluctuating rotating flow of a second-grade fluid past a porous heated plate with variable suction is investigated. The flow is analyzed in the presence of a transversely applied uniform magnetic field, and the Hall current is taken into account. The induced magnetic field due to the motion of an electrically conducting fluid is negligible. The analytical solutions are determined for the velocity, shear stress, and temperature. Graphs are plotted for velocity and temperature profiles for various values of magnetic parameter, Hall parameter, permeability parameter, and slip parameter. The results are compared to those known from the literature.
Zaheer
Abbas
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
Saleem
Ashgar
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Islamabad, Pakistan
35-50
Flow Laws in Metallic Foams: Experimental Determination of Inertial and Viscous Contributions
We present here experiments dealing with the hydrodynamic characterization of high-porosity metallic foam, performed on copper foam. The experimental setup and the procedure used to obtain the hydrodynamic data are described. Analysis of these measurements is conducted using the parameter estimation method. Brazing foam on the channel wall is found to have no effects on pressure drop. This study demonstrates that for this category of porous material, the inertial factor is evaluated accurately, whereas the permeability cannot be determined with reasonable uncertainties. A general trend for metallic foam hydraulic parameters is deduced using the present results and those given in the open literature. Macroscopic characteristics are not sufficient to establish the flow laws. Pore scale topology of the metallic foam should be taken into account in the flow law model.
Brahim
Madani
Laboratory of Multiphase Transport and Porous Media (LTPMP), Faculty of Mechanical and Process
Engineering (FGMGP)/USTHB, BP. 32, El Alia, Algiers, Algeria
Frederic
Topin
Polytech Marseille, Laboratoire IUSTI, UMR CNRS 7343, Technopole de Chateau Gombert, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
Fabrice
Rigollet
Aix Marseille Univ, CNRS, IUSTI
Lounes
Tadrist
Laboratoire IUSTI CNRS UMR 6595, Aix-Marseille Universite, Technopole de Chateau-Gombert, 5, rue Enrico Fermi, 13453 Marseille Cedex 13, France
51-70
Identification of the Hydraulic Properties of Heterogeneous Rocks from Laboratory Flow-Pump Experiments
Transient flow analysis has numerous geophysical and geotechnical applications and it is necessary for the understanding and development of laboratory measurement techniques in rock and soil mechanics, particularly in the determination of their permeabilities. In this paper, we model a laboratory flow-pump permeability test and formulate an inversion technique in order to retrieve homogeneous/spacewise dependent/discontinuous properties of materials. The direct problem is solved using boundary element or finite difference methods, while the recovery of the hydraulic properties of rocks is sought through a genetic algorithm (GA) optimization approach. Well-known constrained optimization routines are often trapped in a local optimum due to a poor initial guess, and further require the calculation of the gradient of a least-squares type functional that is assumed to be differentiable. However, GAs find the global optimum and require neither the calculation of the gradient nor the assumption that the functional be differentiable. Both exact and simulated noisy data are incorporated at optimally selected instants in time through the test, the data measurements used being consistent with the sensitivity analysis that is performed prior to inversion.
Daniel
Lesnic
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Simon D.
Harris
Rock Deformation Research, School of Earth Sciences, University of Leeds, Leeds, LS2 9JT, UK
Lionel
Elliott
Department of Applied Mathematical Studies, The University of Leeds, Leeds LS2 9JT, West Yorkshire, England.
Radu
Mustata
Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK
M. Ben
Clennell
Rock Deformation Research, School of Earth Sciences, University of Leeds, Leeds, LS2 9JT, UK
Derek B.
Ingham
Centre for CFD, Department of Applied Mathematical Studies, The University of Leeds, Leeds, LS2 9JT, UK; Energy-2050, Faculty of Engineering, University of Sheffield, Sheffield, S10 2TN, UK
71-92
A Note on Symmetry Analysis of Second-grade Flow and Heat Transfer Through a Porous Medium
This paper look at steady two-dimensional flow with heat transfer analysis in a porous medium. Lie point symmetries are obtained using the Lie group method and hence the exact solutions are obtained by using these symmetries.
Ahmer
Mehmood
Department of Mathematics, International Islamic University, Islamabad, Pakistan
93-98
Chebyshev Finite Difference Method for Hydro magnetic Free Convection from a Cone and a Wedge Through Porous Media with Radiation
In this paper, we study the effects of non-Darcy parameters on hydro-magnetic free convection from a cone and a wedge, taking into account the effects of radiation, free convection, magnetic field, and external heat generation. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. A new Chebyshev finite difference method is proposed for solving the governing equations of the boundary-layer flow. The Falkner-Skan equation has been solved as a model problem. Numerical computations are carried out for the nondimensional physical parameters. Comparisons with previously published work are performed and excellent agreement between the results is obtained. The effects of various parameters on the velocity and temperature profiles as well as the heat transfer coefficient and the skin friction are presented graphically and in tabulated form.
M. A.
Seddeek
Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, P.O. Box 11795 Cairo, Egypt; Current address: Kingdom of Saudi Arabia, Qassim University, College of Science, Mathematics Department, P. O. Box 237, Buriedah, 81999, KSA
99-108