Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
12
9
2009
Roughness Effect on Squeeze Film Characteristics of Porous Circular Plates Lubricated with Couple Stress Fluid
This paper describes the combined effect of surface roughness and couple stress fluid on the performance characteristics of squeeze film lubrication between two circular plates. Using microcontinuum theory for the couple stress fluid and the Christensen stochastic model for the surface roughness, the modified Reynolds equation is derived by assuming the roughness asperity heights to be small compared to the film thickness. An eigenvalue problem involving Bessel functions enables analysis of the Reynolds equation. The expressions for mean pressure, load-carrying capacity, and squeeze film time are obtained for various probability distribution functions (pseudo normal, rectangular, and inverse square root distributions) that characterize the roughness of the lubricating surfaces. The influence of roughness and couple stress on bearing characteristics is presented in terms of the relative percentage in load for all these roughness patterns.
Nagendrappa
Bujurke
Karnatak University
D. P.
Basti
Department of Mathematics, SDM College of Engineering & Technology, Dharwad-580 002, India
Ramesh B.
Kudenatti
Department of Mathematics, Karnatak University, Dharwad-580 003, India
821-833
Crank-Nicolson Galerkin Model for nonlinearly Coupled Macrophase and Microphase Transport in the Subsurface
A subsurface can be considered to consist of two phases—the macrophase and the microphase in the context of contaminant transport. The inter-particle pore spaces constitute the macrophase with the intraparticle pore spaces constituting the microphase. The macrophase transport is oftentimes nonlinearly coupled with the microphase transport. The solution of nonlinearly coupled macrophase and microphase transport is particularly challenging. A Crank-Nicolson Galerkin finite element model has been developed to simulate the macrophase transport nonlinearly coupled with the microphase transport. The model is stable and provides oscillation-free results when the mesh Peclet number ≤ 2.5 and the Courant number ≈ 1. The model prediction was also found to be in excellent agreement with experimental data obtained from the literature.
Amena M.
Mayenna
Washington State University, Richland, WA 99354
Akram
Hossain
Civil and Environmental Engineering, Washington State University, Richland, WA 99354
835-845
Modeling, Optimization and Simulation for Chemical Vapor Deposition
Our studies are motivated by a desire to model chemical vapor deposition for metallic bipolar plates and optimization to deposit a homogeneous layer. We present a mesoscopic model, which reflects the transport and reaction of the gaseous species through a homogeneous media in the chamber. The models, which are discussed in the article, considered the conservation of mass and the underlying porous media is in accordance with the Darcy's law. The transport through the stationary and non-ionized plasma field is treated as a diffusion-dominated flow, (Gobbert and Ringhofer, SIAM J. Appl. Math., vol. 58, pp. 737-752, 1998) where the metallic deposit and the gas chamber, looking like a porous media, (Roach, Proc. of COMSOL Users Conference, Paris , 2006; Cao, Brinkman, Meijerink, DeVries, and Burggraaf J. Mater. Chem., vol. 3, pp. 1307-1311, 1993). We choose porous ceramic membranes and gas catalysts like Argon (Ar), (Cao et al., 1993) and apply our experience in simulating gaseous flow and modeling the penetration of such porous media (Jin and Wang, J. Comput. Phys., vol. 79, pp. 557-577, 2002). Numerical methods are developed to solve such multi-scale models. We combine discretization methods with respect to the various source terms to control the required gas mixture and the homogeneous layering. We present an expert system with various source and target controls to present the accuratest computational models. For such efficient choice of models, we apply our numerical methods and simulate an optimal homogeneous deposition at the target. The results are discussed by means of physical experiments to give a valid model for the assumed growth.
Juergen
Geiser
Department of Mathematics, Humboldt University of Berlin, Germany
M.
Arab
Humboldt-Universität zu Berlin,Department of Mathematics, Germany
847-867
Magnetohydrodynamic Peristaltic Pumping Through Uniform Channel with Porous Peripheral Layer and Hall Currents
The peristaltic pumping of a biofluid consisting of two immiscible fluids of different viscosity, one occupying the core and the other the peripheral layers on either side, in a two-dimensional channel partially filled with a layer of a porous material is investigated. The core region is described by the Eyring-Powell model and the peripheral region is taken to be electrically conducting Newtonian viscous fluid. The fluid in peripheral region is permeated by an external uniform magnetic field imposed perpendicularly to xy plane on the assumption of a small magnetic Reynolds number in the presence of the effect of Hall currents. The flow is examined in the wave frame of reference moving with the velocity of the wave. The Brinkman extended Darcy equation is utilized to model the flow in a porous layer. A shear stress jump boundary condition is used at the interface. The analytic solutions have been obtained in the form of a stream function from which the velocity fields and axial pressure gradient have been derived. The present analysis has been performed under long wavelength and low Reynolds number assumptions. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs and the phenomenon of trapping is also discussed.
Nabil T. M.
Eldabe
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt
A. Y.
Ghaly
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
H. M.
Sayed
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
869-886
Numerical Modeling of Coil Compaction in the Treatment of Cerebral Aneurysms Using Porous Media Theory
A numerical model was developed to quantify the reduction in blood velocity and pressure resulting from the placement of endovascular coils within a cerebral aneurysm using physiological velocity waveforms. The flow characteristics within the aneurysm sac were modeled using the volume-averaged porous media equations. We studied the effects of narrow and wide aneurysmal necks on the velocity fields and pressure within the aneurysmal sac in the absence of the coils. Within the sac at peak systole, wide-neck aneurysms experience higher velocity and pressure than narrow-neck aneurysms. Our study shows that velocity fields are significantly affected by the presence of an endovascular coil within the aneurysm sac. Moreover, we estimated that a volume density of a 20% platinum coil in the aneurysmal sac was sufficient to cause sufficient blood flow arrest in the aneurysm to allow for thrombus formation. A new model based on the porous media theory is proposed for the study of the effects of coiling in brain aneurysms. Porous media theory permits the study of fluid motion across small spaces of variable and complex geometry. A simple formula to calculate the length of platinum wire required to achieve flow arrest within an aneurismal sac of known diameter is presented.
khalil
Khanafer
University of Michigan Ann Arbor
Ramon
Berguer
Vascular Mechanics Laboratory, Department of Biomedical Engineering, and Section of Vascular Surgery, University of Michigan, Ann Arbor, MI 48109, USA
Marty
Schlicht
Vascular Mechanics Laboratory, Department of Biomedical Engineering, and Section of Vascular Surgery, University of Michigan, Ann Arbor, MI 48109, USA
Joseph L.
Bull
Vascular Mechanics Laboratory, Department of Biomedical Engineering, and Section of Vascular Surgery, University of Michigan, Ann Arbor, MI 48109, USA
887-897
Flow and Heat Transfer of an Unsteady MHD Axisymmetric Flow in a Porous Medium Due to a Stretching Sheet
This paper looks at the unsteady magnetohydrodynamic (MHD) flow and heat transfer characteristics of a viscous fluid filling a porous medium. The flow is induced by a radially stretching sheet. The basic equations governing the flow are reduced into a nonlinear partial differential equation using similarity transformations. The resulting partial differential equations are solved analytically by employing the homotopy analysis method. The heat transfer analysis has been carried out for the prescribed surface temperature and prescribed surface heat flux cases. Convergence of the obtained series solutions are shown. Furthermore, the influence of the various interesting parameters are discussed by plotting graphs. It is found that the obtained solution expressions are valid for all the times.
Muhammad
Sajid
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
I.
Ahmad
Department of Mathematics, Azad Kashmir University, Muzaffarabad 13100, Pakistan
M.
Ayub
Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, Pakistan
901-910
Unsteady Boundary Layer Flow Due to a Stretching Sheet in a Porous Medium with Partial Slip
The present paper is concerned with the influence of partial slip on the unsteady boundary layer flow induced by a stretching sheet in a porous medium. The problem is formulated and solved using a homotopy analysis method. The obtained solution is accurate and valid for all the values of time. The effects of dimensionless time, porosity, and slip parameters on the velocity are analyzed.
Muhammad
Sajid
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
I.
Ahmad
Department of Mathematics, Azad Kashmir University, Muzaffarabad 13100, Pakistan
911-917
Exact Solutions for the Accelerated Flows of a Generalized Second-Grade Fluid between Two Sidewalls Perpendicular to the Plate
This paper is concerned with the exact solutions for the accelerated flows of a generalized second-grade fluid through a porous medium with a fractional derivative model. The fractional calculus approach is taken into account in the constitutive relationship of a non-Newtonian fluid model. Two characteristic examples, which are flow due to a constantly accelerating plate and flow due to variable accelerating plate between two sidewalls perpendicular to the plate, are considered. Employing the Fourier sine transforms and the theory of the Laplace transform for fractional calculus, the exact solutions are obtained. The solutions for a second-grade fluid appear as the limiting cases of the presented solutions by setting β = 1. Furthermore, in the absence of sidewalls, all solutions that have been constructed reduce to the known solutions of second-grade and Newtonian fluids corresponding to the motion over an infinite flat plate.
Masood
Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
919-926