Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
14
3
2011
OPTIMUM POROUS INSERT CONFIGURATIONS FOR ENHANCED HEAT TRANSFER IN CHANNELS
Studies to establish the optimum arrangement and thickness of porous inserts in parallel plate channels subjected to uniform heat flux for enhancement of forced convective heat transfer are reported here. The flow and thermal fields have been considered as fully developed. The different arrangements considered are: (1) a given amount of porous material is attached to one of the walls of the channel (arrangement 1), (2) distributed equally at the two walls (arrangement 2), and (3) placed as one insert in the middle of the channel (arrangement 3). It has been found that the configuration described in arrangement 3 above yields the maximum enhancement in heat transfer per unit pressure gradient followed by arrangements 1 and 2. The optimum porous fraction for the configuration (arrangement 3) varies from 0.675 to 0.450 as the Darcy number increases from 0.0005 to 0.05.
D.
Bhargavi
Department of Mathematics, National Institute of Technology, Warangal, India-506004
V. V.
Satyamurty
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302 , India
187-203
A NEW CONSTRAINED CONSTITUTIVE EQUATION FOR UNSATURATED FLOWS OF INCOMPRESSIBLE LIQUIDS THROUGH RIGID POROUS MEDIA
This article proposes a new constitutive model for the partial pressure in unsaturated flows of incompressible liquids through rigid porous media. This constitutive equation for the pressure gives rise to a mathematical description in which the geometrical bound, representing the rigid porous medium assumption, is naturally taken into account—so that only physically meaningful solutions are allowed. A mixture theory approach describes the flow by considering three overlapping continuous constituents, representing the porous matrix (solid constituent), the fluid (liquid constituent), and an inert gas included to account for the compressibility of the mixture as a whole. Examples of Riemann problem solutions showing connections by rarefactions and shocks for both the classical model and the proposed constitutive approach for the partial pressure support the latter.
Maria Laura
Martins-Costa
Laboratory of Theoretical and Applied Mechanics (LMTA) Mechanical Engineering Graduate
Program (TEM-PGMEC), Universidade Federal Fluminense, Rua Passo da Pátria, 156,
24210-240, Niterói, RJ, Brazil
Rogerio M. Saldanha
da Gama
Mechanical Engineering Department, Universidade do Estado do Rio de Janeiro, Brazil
205-217
NUMERICAL MODELING OF CONTAMINANT TRANSPORT IN FRACTURED POROUS MEDIA USING MIXED FINITE-ELEMENT AND FINITEVOLUME METHODS
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods; i.e., the mixed finite-element (MFE) method and the finite-volume method. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocity fields for both the fractures and matrix, which are crucial to the convection part of the transport equation. The finite-volume method and the standard MFE method are used to approximate the convection and dispersion terms, respectively. The temporary evolution for the pressure distributions, streamline fields, and concentration profiles are obtained for six different arrangements of fractures. The results clearly show the distorted concentration effects caused by the ordered and disordered (random) patterns of the fractures and illustrate the robustness and efficiency of the proposed numerical model.
Shuyu
Sun
Department of Mathematical Sciences, Clemson University, USA; Computational Transport Phenomena Laboratory (CTPL), Division of Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Saudi Arabia
Chen
Dong
Department of Mathematical Sciences, Clemson University, USA
Glenn A.
Taylor
Savannah River National Laboratory, Aiken, South Carolina 29808, USA
219-242
PERMEABILITY PREDICTION OF POROUS MEDIA WITH VARIABLE POROSITY BY INVESTIGATION OF STOKES FLOWOVER MULTI-PARTICLES
Investigation of fluid flow through porous media necessitates a comprehensive recognition of medium characteristics. Porous media represent an extremely complicated network of channels with obstructions. This paper introduces a new conceptual approach for fluid flow in porous media. A variable porosity bed including a few Liapanov arbitrary shape particles has been considered. The Reynolds number is assumed to be less than 1. The creep flow on one sphere is modeled by the Stokes equation, while there is no solution available for multi-particle flow in the literature. Also, numerical solution of such a problem is very lengthy and tedious. Conversion of the governing equations from domain to boundaries using Green’s theorem is considered. The equation is solved by the boundary element method. One- and two-layer potentials and Fredholm’s integral forms are introduced over all particles with Liapanov arbitrary shape. Therefore, it is possible to model the variable porosity bed with nonuniform solid particles. Equations are solved for a sample bed with an air gap between the wall and edge of the particles and the results are presented in the form of the Darcy equation. In addition, this method is described to predict the permeability of variable porosity porous media. Also, comparison of the motion equation numerical solution based on this evaluated permeability with the experimental results is presented. The experimental results are achieved from the tests with special apparatus that has been designed by the authors.
A.
Vahabikashi
Mechanical Engineering Department, K. N. Toosi University of Technology, Tehran 19697, Iran
M. R.
Shahnazari
Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
243-250
EFFECT OF COUPLE STRESSES ON A PULSATILE MHD BIVISCOSITY FLUID FLOWWITH HEAT AND MASS TRANSFER THROUGH A NON-DARCY POROUS MEDIUM BETWEEN TWO PERMEABLE PARALLEL PLATES
The Runge-Kutta-Merson method and Newton iteration in the shooting and matching technique were used to obtain the solution of the system of the nonlinear ordinary differential equations. These equations describe the two-dimensional magneto-hydrodynamic pulsatile flow of a non-Newtonian fluid obeying the biviscosity model type with heat and mass transfer through a non-Darcy porous medium between two permeable parallel plates. Accordingly, the solutions of momentum, magnetic field, energy, and concentration equations were obtained. The numerical formula of the velocity, the magnetic field, the temperature, and the concentration distributions of the problem were illustrated graphically. The effects of some parameters of the problem, such as couple stress parameter a, Reynolds number Re, upper limit of apparent viscosity coefficient β, permeability parameter K, Forchheimer number Fs, magnetic-field parameter M, Prandtle number Pr, Eckert number Ec, Schmidt number Sc, Soret number Sr, and magnetic Prandtle number Rm on the flow phenomena are numerically discussed.
Abeer A. E.
Mohammed
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis Cairo, Egypt
Ahmed A. A.
Hassan
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis Cairo, Egypt
253-264
HEAT TRANSFER IN BOUNDARY LAYER FLOWPAST A CURVED SURFACE IN A SATURATED POROUS MEDIUM WITH VARIABLE PERMEABILITY
This paper is focused on the steady heat transfer in boundary layer flow past a curved surface in a saturated porous medium with variable permeability. The nonlinear coupled differential equations governing the boundary layer flow, heat transfer, and mass transfer are solved by using the two-term perturbation method with Eckert and Prandtl numbers. The similarity solutions obtained for both the zeroth-order and the first-order thermal boundary layer equations have been presented for two cases; namely, uniform permeability and variable permeability. Numerical results for the velocity and temperature profiles as well as for the skin fraction coefficient and wall heat transfer rate are obtained and reported graphically for various conditions to show the interesting aspects of the solution.
Ahmed A.
Mohammadein
Mathematics Department, Faculty of Science, South Valley University, Aswan 81528, Egypt
N. A.
Al Shear
Mathematics Department, Faculty of Science, South Valley University, Aswan 81528, Egypt
265-271
MAGNETOHYDRODYNAMIC FLOWOF A BI-VISCOSITY FLUID THROUGH POROUS MEDIUM IN A LAYER OF DEFORMABLE MATERIAL
This paper investigates the hydromagnetic flow of a non-Newtonian fluid of biviscosity type through porous medium under a uniform magnetic field in a layer of deformable material. The porous material is assumed to be isotropic, homogeneous, linear elastic solid. Governing equations are deduced for the solid displacement and the fluid velocity and have been solved analytically using the Fourier series. The effects of interaction between the solid and the fluid phases in the porous layer, magnetic field, and non-Newtonian parameters on the fluid flow are investigated and illustrated graphically for both steady and unsteady flow cases when the solid phase is rigid.
Nabil T. M.
Eldabe
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt
Gamal
Saddeek
Ain Shams University - Faculty of Education
Khaled
Elagamy
Ain Shams University, Faculty of Education, Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt
273-283