Begell House Inc.
Journal of Porous Media
JPM
1091-028X
3
2
2000
Gas-Liquid Countercurrent Flows Through Packed Towers
16
10.1615/JPorMedia.v3.i2.10
Shijie
Liu
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada T6G 2G6
Jun
Long
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada T6G 2G6
The volume-averaged governing equations for multiphase flows in porous media proposed by Liu (1999a) are applied to the study of gas-liquid countercurrent flows in packed towers. Model parameters are proposed for two-phase flows by extending the model of saturated single-phase flows in porous media. Numerical solutions are obtained for developed axisymmetrical flows in packed columns. Flow velocity profiles of both phases, pressure drops, and liquid holdup distributions are obtained. All of the predictions agree well with published experimental results. It is thus demonstrated that the volume-averaged governing equations are satisfactory for describing two-phase flows in packed columns.
Diffusion-Controlled Catalytic Reaction on a Monolithic Catalytic Converter
8
10.1615/JPorMedia.v3.i2.20
Akira
Nakayama
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561, Japan; School of Civil Engineering and Architecture, Wuhan Polytechnic University,
Wuhan, Hubei 430023, China
Fujio
Kuwahara
Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561 Japan
An analytical study has been conducted to investigate the diffusion controlled catalytic reaction, which takes place as the gas flows through a monolithic catalytic converter. The microchannels in the honeycomb monolith are modeled by a collection of circular tubes, which then enables us to focus on a reactive flow through a single tube from a microscopic view. Closed form expressions have been derived for the axial developments of the bulk mean gas temperature, the catalytic surface temperature and the bulk mean concentration.
On the Transition Between Aiding and Opposing Double-Diffusive Flows in a Vertical Porous Cavity
16
10.1615/JPorMedia.v3.i2.30
Abdelkhalk
Amahmid
Faculty of Sciences Semlalia, Physics Department, UFR TMF, BP 2390, Marrakesh, Morocco
Mohammed
Hasnaoui
University Cadi Ayyad, Faculty of Sciences Semlali
Mahmoud
Mamou
National Research Council of Canada, Ottawa, Ontario, Canada, K1A 0R6
Patrick
Vasseur
Ecole Polytechnique, Université de Montréal, C.P. 6079, Succ. "Centre ville", Montréal,
Québec H3C 3A7, Canada
Double-diffusive natural convection in a vertical porous layer induced by horizontal gradients of heat and mass is studied analytically and numerically using the Darcy model with the Boussinesq approximation. The governing parameters of the problem are the Rayleigh number, RT the Lewis number, Le, the buoyancy ratio, N, and the aspect ratio of the porous matrix, A. An approximate analytical solution to the present problem is obtained on the basis of the parallel flow approximation. Two types of solutions are found to exist for the situation in which thermal and solutal buoyancy forces oppose each other and are of comparable intensity. The domains of existence of each type of solution are delineated in terms of the buoyancy ratio, N, and the Lewis number, Le. Solving numerically the full governing equations, it is demonstrated that multiple steady-state solutions are possible and they are found to agree with the analytical solution. The results obtained in this article complete the results available in the literature concerning this subject.
Application of the UNIFAES Discretization Scheme to Mixed Convection in a Porous Layer with a Cavity, Using the Darcy Model
16
10.1615/JPorMedia.v3.i2.40
Jorge
Llagostera
Faculdade de Engenharia Mecanica, Departamento de Energia, Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6122, 13090-970, Campinas-SP, Brazil
Jose R.
Figueiredo
Faculdade de Engenharia Mecanica, Departamento de Energia, Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6122, 13090-970, Campinas-SP, Brazil
Results of numerical simulations are presented on mixed convection in a two-dimensional, horizontal, saturated porous layer, with a cavity of varying depth on the bottom surface, heated from below. The problem formulation was based on the Darcy model to relate the velocity and the pressure fields, and on the Boussinesq hypothesis for the buoyancy effects. The convective-diffusive fluxes at the volume boundaries were represented using the unified finite approach exponential-type scheme (UNIFAES), with the power-law approximation to reduce the computing time. The conditions established by Rivas (1972) for the order of accuracy of the differencing schemes to be maintained in irregular grids allowed reliable accuracy estimates to be obtained. The steady-state regime was studied for Peclet numbers 1, 10, and 100; Rayleigh numbers between 1 and 2000; and cavity aspect ratios 0, 0.5, 1, and 2. Tabulated results for average Nusselt number and maximum and minimum stream function values are reported for the cases simulated. Maps of streamlines and isothermal lines are presented. For deep cavities, multiple steady-state solutions are reported.
Simultaneous Heat and Mass Transfer by Natural Convection from a Cone and a Wedge in Porous Media
10
10.1615/JPorMedia.v3.i2.50
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box
10021, Ras Al Khaimah, United Arab Emirates
A.-R.A.
Khaled
King Abdulaziz University
Osamah
Al-Hawaj
Department of Mechanical and Industrial Engineering, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait
The problem of steady, laminar, hydromagnetic simultaneous heat and mass transfer by natural convection flow over a vertical cone and a wedge embedded in a uniform porous medium is investigated. Two cases of thermal boundary conditions, namely the uniform wall temperature (UWT) and the uniform wall heat flux (UHF), are considered. A nonsimilarity transformation for each case is employed to transform the governing differential equations to a form whereby they produce their own initial conditions. The transformed equations for each case are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the influence of the magnetic field, porous medium inertia effects; heat generation or absorption; lateral wall mass flux; concentration to thermal buoyancy ratio; and the Lewis number on the fluid velocity, temperature, and concentration as well as the Nusselt and the Sherwood numbers is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed. It is concluded that while the local Nusselt number decreases owing to the imposition of the magnetic field, it increases as a result of the fluid's absorption effects. Also, both the local Nusselt and Sherwood numbers increase as the buoyancy ratio increases. This is true for both uniform wall temperature and heat flux thermal conditions. Furthermore, including the porous medium inertia effect in the mathematical model is predicted to decrease the local Nusselt number for both the isothermal and isoflux wall cases.
Transient Natural Convection in Differentially Heated Porous Enclosures
14
10.1615/JPorMedia.v3.i2.60
A. A.
Merrikh
Department of Mechanical Engineering, Eastern Mediterranean University, G. Magosa, T.R.N.C. Mersin 10, Turkey
A. A.
Mohamad
Department of Mechanical Engineering, Eastern Mediterranean University, Magosa, T.R.N.C. Mersin 10, Turkey
The problem of steady, laminar, hydromagnetic simultaneous heat and mass transfer by natural convection flow over a vertical cone and a wedge embedded in a uniform porous medium is investigated. Two cases of thermal boundary conditions, namely the uniform wall temperature (UWT) and the uniform wall heat flux (UHF), are considered. A nonsimilarity transformation for each case is employed to transform the governing differential equations to a form whereby they produce their own initial conditions. The transformed equations for each case are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the influence of the magnetic field, porous medium inertia effects; heat generation or absorption; lateral wall mass flux; concentration to thermal buoyancy ratio; and the Lewis number on the fluid velocity, temperature, and concentration as well as the Nusselt and the Sherwood numbers is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed. It is concluded that while the local Nusselt number decreases owing to the imposition of the magnetic field, it increases as a result of the fluid's absorption effects. Also, both the local Nusselt and Sherwood numbers increase as the buoyancy ratio increases. This is true for both uniform wall temperature and heat flux thermal conditions. Furthermore, including the porous medium inertia effect in the mathematical model is predicted to decrease the local Nusselt number for both the isothermal and isoflux wall cases.
Nonsimilar Solutions for Mixed Convection in Non-Newtonian Fluids Along a Wedge with Variable Surface Heat Flux in a Porous Medium
4
10.1615/JPorMedia.v3.i2.70
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
Mahesh
Kumari
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
Combined Heat and Mass Transfer in Mixed Convection Adjacent to a VWT/VWC or VHF/VMF Cone in a Porous Medium: The Entire Regime
8
10.1615/JPorMedia.v3.i2.80
K.A.
Yih
Department of Fundamental Science, China Air Force Aeronautical and Technical School, Gang-shan, Kaohsiung, Taiwan 90395-2, ROC