Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
5
2
2002
A Coupled Approach to Predict Microscopic Temperature Distribution Inside a Unit Cell of Nonisothermal Laminar Flow in Periodic Porous Media
A method to compute the microscopic temperature distribution inside a unit cell for a laminar flow of an incompressible fluid in periodic porous media is presented in this paper. Previous approaches have only exploited the similarity of the periodic unit cells to assume the microscopic unit cell problem regardless of its comformity with the macroscopic energy balance. In this article, we consider both the similarity and compatibility with the macroscopic temperature distribution to pose the nonisothermal unit cell problem. The natural mode temperature solution of the macroscopic energy balance equation is used as the macroscopic solution to derive the unit cell problem. Aperiodic unit cell problem with arbitrary structures has been formulated. Its consistency with energy conservation at both the microscopic and macroscopic levels has been examined. Taylor's dispersion solution is found to be a special case of this unit cell solutions. The potential of this method is demonstrated by performing a numerical simulation of nonisothermal laminar Incompressible flow through a two-dimensional in-line cylindrical unit cell. From simulation results, the total effective thermal conductivity of the unit cell is calculated and compared with reported experimental results. The good agreement confirms the validity of this approach. This inverse unit cell approach makes it possible to evaluate the influence of the heat capacity ratio of the fluid and the solid which was not possible to study with previous numerical unit cell approaches.
Kuang-Ting
Hsiao
Department of Mechanical Engineering, University of Delaware, Newark, DE 19716
Suresh G.
Advani
Center for Composite Materials, Department of Mechanical Engineering, University of Delaware, Newark, DE 19716
17
Numerical Study of Natural Convection in a Vertical Cylindrical Annulus Using a Non-Darcy Equation
A numerical Investigation of transient free convection in a vertical cylindrical annulus filled with a fluid saturated porous medium with the inner wall heated to a uniform temperature, the outer wall cooled to a uniform temperature and maintaining top and bottom boundaries at adiabatic condition, bos been carried out. A finite difference implicit method which incorporates upwind differencing for nonlinear convective terms and the successive line over relaxation (SLOR) method for convergence are used to solve the coupled nonlinear governing equations. Heat transfer rate and flow fields are obtained for wide range of Rayleigh numbers Ra ranging from 103 to 106, Darcy numbers Da ranging from 10-1 to 10-3, radii ratio l in the range 1 Ј l Ј 10, and aspect ratio A in the range 1 Ј A Ј 2. The numerical results indicate that the temperature and velocity fields are significantly modified and the beat transfer rate is decreased as the Darcy number decreases. The temperature and velocity fields are significantly modified by the radii ratio. The rate of heat transfer increases with an increase in radii ratio. At a high Rayleigh number the curvature effect on heat transfer is insignificant. The numerical results further indicate that an increase in viscosity ratio (L) reduces the Nusselt number by enhancing the contribution of the viscous diffusion term.
B. M. R.
Prasanna
Department of Mathematics, Siddaganga Institute of Technology, Tumkur 572 103, India
M.
Venkatachalappa
UGC Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore 560 001, India
16
Aiding and Opposing Mixed Convection from a Cylinder in a Saturated Porous Medium
Numerical solutions are presented for mixed convection from a cylinder embedded in a saturated porous medium. Both aiding and opposing flow conditions are considered. Numerical calculations using the finite difference method with body-fitted coordinates have covered a wide range of governing parameters (i.e., 10 Ј Re Ј 100, 0 Ј Gr Ј 400 and Pr = 0.7). The present results agree well with the previous study by Badr and Pop (1988) for flows at a small Reynolds number and a small mixed convection parameter Gr/Re. However, significant discrepancies have been found between the two studies for flows at a high Reynolds number and a high mixed convection parameter Gr/Re. In addition, oscillatory flows are observed for opposing flows at high Gr/Re, which were not revealed in the previous study (Badr and Pop, 1988). Several reasons are offered to explain the discrepancies found.
M. J.
Zhou
School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019
F. C.
Lai
School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019
10
Moderate Time Scale Linear Stability of Moderate Stefan Number Convection In Rotating Mushy Layers
The solidification of a binary alloy in a mushy layer subject to Coriolis effects is considered. A near-eutectic approximation and large far-field temperature is employed in order to study the dynamics of the mushy layer with a Stefan number of unit order of magnitude. The linear stability theory is used to investigate analytically the Coriolis effect in a rotating mushy layer for both stationary and oscillatory convection for a new time scale proposed by the author. The linear theory established that in contrast to the problem of a stationary mushy layer, rotating the mushy layer has a stabilizing effect on convection. In addition it was found that the critical Rayleigh number and wave number are independent of the Toylor number for the case of oscillatory convection.
Saneshan
Govender
School of Mechanical Engineering, University of Kwa-Zulu; School of Mechanical Engineering, University of Natal, Durban, South Africa; Eskom Holdings Ltd, Engineering Department (Gas Division), Eskom Enterprises Park, Simba Road, Sunninghill, Johannesburg
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
9
Drying of Porous Particles in Fluidized Beds: Modeling and Experiments
A mathematical model describing the drying of porous particles in a batch-fluidized bed was developed. This model takes into account the bubble, interstitial gas and solid phases, and is based on the conservation laws of mass and energy and on empirical correlations for heat and mass transfer between the phases. Solid particles were considered perfectly mixed in the fluidized bed while interstitial gas and bubble phase were assumed to be in plug-flow. The mathematical model comprises a set of non-linear differential equations that was solved numerically. Experiments using alumina particles were carried out in a fluidized bed dryer in order to collect data for the estimation of the model parameters. It was observed that the experimental data of outlet gas temperature, solid temperature and moisture content in the solids agree well with those obtained by the model simulation.
L. A.
Calcada
DTQ/IT/UFRRJ, CP: 74501, 23581-970, Seropedica, RJ, Brazil
11
Effect of Variable Gravity Field on Thermal Instability in a Porous Medium with Inclined Temperature Gradient and Vertical Throughflow
The onset of convection in a horizontal fluid saturated isotropic porous layer with inclined temperature gradient and vertical throughflow, subject to a gravity field varying linearly with distance in the layer, is investigated. The resulting eigenvalue problem is solved using the Galerkin technique. It is seen that when the variable gravity parameter is positive, an increase in the vertical throughflow in the direction of the gravity vector always stabilizes the system. Further, an increase in the throughflow in the direction opposing gravity delays the onset of convection when the variable gravity parameter is negative.
Sherin M.
Alex
Department of Mathematics, Anna University, Chennai (Madras), India
Prabhamani R.
Patil
Department of Mathematics, Anna University, Chennai (Madras), India
11
On a Couple-Stress Fluid Heated from Below in a Porous Medium in the Presence of a Magnetic Field and Rotation
A layer of couple-stress fluid heated from below in a porous medium is considered in the presence of a uniform vertical magnetic field and uniform vertical rotation. For the case of stationary convection, the rotation postpones the onset of convection. The magnetic field and couple-stress may hasten the onset of convection in the presence of rotation while In the absence of rotation, they always postpone the onset of convection. The medium permeability hastens the onset of convection in the absence of rotation while in presence of rotation, it may postpone the onset of convection. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The rotation and magnetic field are found to introduce oscillatory modes In the system which were nonexistent in their absence. A sufficient condition for the nonexistence of ovestabllity is also obtained.
Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
R. C.
Sharma
Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla 171 005, India
Mohinder
Pal
Department of Mathematics, Government Degree College, Nadaun, (H.P.) 177 033, India
10
Nonsimilarity Solutions for Mixed Convection Flow Along Nonisothermal Vertical Plate Embedded in Porous Media with Variable Permeability
An analysis is performed for mixed convection flows through a fluid saturated porous medium adjacent to a vertical surface with the heating condition of power law variation in wall temperature. The entire mixed convection regime is covered by the single parameter c = [1 + (Rax + Pex)1/2]-1 from the pure forced convection limit (c = 1) to the pure free convection limit (c = 0). In modeling the flows through porous media, non-slip boundary condition, the variation of permeability and thermal conductivity due to packing of particles are taken into consideration. A finite difference scheme was used to solve the system of transformed governing equations. Velocity and temperature profiles, and local Nusselt number are presented. It is found that as c decreases from 1 to 0, the thermal boundary layer thickness increases first and then decreases. Numerical results show that the variation of permeability effect has significant influences on velocity, temperature profiles and heat transfer rates from vertical surface.
Gh. M.
Omer
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
I. A.
Hassanien
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
9