Begell House Inc.
Journal of Porous Media
JPM
1091-028X
14
6
2011
NATURAL CONVECTION IN A TRAPEZOIDAL ENCLOSURE FILLED WITH A NON-DARCIAN POROUS MEDIUM
467-480
10.1615/JPorMedia.v14.i6.10
Bader Alshriaan
Al-Azmi
Mechanical Engineering Department, Kuwait University, Al-Safat 13060, Kuwait
natural convection
numerical
porous medium
trapezoid
generalized model
Natural convection in a trapezoidal enclosure filled with a porous medium is analyzed numerically in this investigation. Three different configurations are tested to determine which configuration exhibits optimum heat transfer characteristics. The vertical walls are subjected to a temperature gradient while the horizontal walls are kept insulated. The transport equations are solved using the finite-element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing the results with previously published results. The importance of non-Darcian effects on convection in a trapezoidal enclosure is analyzed in this work. Different flow models for porous media, such as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and average heat transfer. The implications of Rayleigh number, inclination angle, porosity, Darcy number, and the ratio of solid thermal conductivity to the fluid thermal conductivity on the flow structure and heat transfer characteristics are investigated in detail.
SLIP EFFECTS ON THE OSCILLATORY FLOW IN A POROUS MEDIUM
481-493
10.1615/JPorMedia.v14.i6.20
Tasawar
Hayat
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science,
King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia
M. Faheem
Afzaal
Imperial College London, University of Birmingham, Department of Mathematics, Quaid-i-Azam University
Constantin
Fetecau
Academy of Romanian Scientists, Bucuresti 050094, Romania
Awatif A.
Hendi
Department of Physics, Faculty of Sciences, King Saud University, P. O. Box 1846, Riyadh 11321, Saudi Arabia
exact solutions
viscous fluid
magnetohydrodynamic (MHD) flow
porous medium
wall slip
Exact solutions of the Stokes' second problem in the presence of a slip condition are established. Two types of boundary conditions are considered. An incompressible magnetohydrodynamic fluid occupies the porous space. Both steady and transient solutions in each case of boundary oscillations are derived by Laplace transform treatment. Graphs are sketched for the pertinent parameters and discussed.
EFFECTS OF THE REACTION RATE AND THE LARGE SIZE DEFORMABLE AEROSOLS ON DISPERSION IN ATMOSPHERIC FLOW REGARDED AS THE TURBULENT FLUID SATURATED POROUS MEDIA
495-506
10.1615/JPorMedia.v14.i6.30
N.
Rudraiah
National Research Institute for Applied Mathematics, 492/G, 7th Cross, 7th Block (West), Jayanagar, Bangalore 560 082, and UGC-DSA Centre in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore 560 001, India
N.
Devaraju
UGC-Center for Advanced Studies in Fluid Mechanics, Department of Mathematics, Bangalore University; National Research Institute for Applied Mathematics, 462/G, 7th Cross, 7th Block (West), Jayana-gar, Bangalore 560 070, India
dispersion
aerosols
deformation
atmosphere
This paper describes the use of Taylor's analysis to study the dispersion of large size aerosols as the mixture of deformable agglomeration and coalescence of aerosols in the atmosphere. A proper theory is developed incorporating the resistance offered by sparsely packed aerosols following the Darcy-Brinkman model, including elastic deformation. Analytical solutions for velocity are obtained using a regular perturbation technique. Concentration distribution is determined using the advection of concentration by the atmospheric turbulent fluid in the presence of an irreversible first-order chemical reaction and a source in the boundary condition. It is shown that the aerosols are dispersed relative to a plane moving with the mean speed of atmospheric turbulent fluid as well as the mean speed of agglomeration of aerosol with a relative diffusion coefficient, D β, called the Taylor dispersion coefficient. This D β is numerically computed and the results reveal that D β increases with an increase in Re and Pe, but decreases with an increase in σρ, β1, and R1, where Re is the Reynolds number, σρ is the porous parameter, R1 is the deformation parameter, and β1 is the reaction rate parameter. This decrease in D β, with an increase in the porous parameter and an increase in the reaction rate parameter is favorable for the formation of clouds in the atmosphere.
ESTIMATING APPARENT DIFFUSION COEFFICIENT AND TORTUOSITY IN PACKED SAND COLUMNS BY TRACERS EXPERIMENTS
507-520
10.1615/JPorMedia.v14.i6.40
Andrea
Zoia
Laboratory of Flow and Transport Simulation, Commission of Atomic Energy CEA Saclay, DEN/DANS/DM2/SFME/LSET
Christelle
Latrille
Laboratory of Radionuclide Migration Measurements and Modeling, Commission of Atomic Energy CEA Saclay, DEN/DAN/DPC/SECR/L3MR
diffusion coefficient
column experiment
tortuosity
dichromatic X-ray spectrometry
hydrodynamic dispersion
temporal moment
In this work we analyze the spatial and temporal features of the transport parameters characterizing the apparent diffusion coefficient and tortuosity along an experimental setup. To perform this study, we resort to the BEETI device, consisting of a vertical column filled with porous materials and of a dichromatic X-ray spectrometer for detecting solute distribution. X-ray measures are noninvasive and nondestructive, and thus allow determining the solute concentration profiles at several locations along the column, as a function of time. Once the concentration profiles are experimentally measured, the transport parameters υ (x) and D (x) are determined at each location by means of the method of temporal moments. Two sets of experimental runs are performed (at high and low flow rates, respectively), in order to single out the effects of mechanical dispersion and molecular diffusion on the overall solute dispersion. Further manipulations allow finally deriving the spatial evolution of the apparent molecular diffusion coefficient and of the tortuosity. The estimated tortuosity values are compared with literature results and show good agreement. This analysis relies on the hypothesis that the traversed porous medium is sufficiently homogeneous and can be used as a benchmark in view of testing our experimental device on more complex soils.
FLOW AND HEAT TRANSFER DUE TO STRETCHING SURFACE IN AN ANISOTROPIC POROUS MEDIUM FILLED WITH A VISCOELASTIC FLUID
523-532
10.1615/JPorMedia.v14.i6.50
Tasawar
Hayat
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science,
King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia
M.
Mustafa
Department of Mathematics, Quaid-I-Azam University
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Saleem
Obaidat
King Saud University
series solution
viscoelastic fluid
heat transfer
This paper presents a theoretical analysis of the steady boundary layer flow and heat transfer induced by a linearly stretching surface in an anisotropic porous medium filled with a viscoelastic fluid. The governing partial differential equations are converted into a set of ordinary differential equations by the use of similarity transformation. The flow is, therefore, governed by the dimensionless anisotropic parameter, a; Darcy number, Da*; dimensionless viscoelastic parameter, K; viscosity ratio parameter, M; and Prandtl number, Pr. The resulting ordinary differential equations are successfully solved analytically using the homotopy analysis method. The variations of the skin-friction coefficient and the local Nusselt number as functions of the governing parameters are presented in tables and graphs. The results presented in this paper reveal that the solution of the present problem is given by Eq. (31), which is shown to be convergent in the whole region of the similarity variable η when hf = −0.5 and hθ = −1.6.
EFFECT OF TEMPERATURE MODULATION ON THE ONSET OF CONVECTION IN A HELE-SHAW CELL
533-539
10.1615/JPorMedia.v14.i6.60
K.
Souhar
Laboratory of Energy Engineering, Materials and Systems, ENSA, Ibn Zohr University, Morocco
S.
Aniss
Laboratory of Mechanics, Faculty of Sciences Ain Chock, Hassan II University, Morocco
M. T.
Ouazzani
University Hassan II, Faculty of Sciences Ain-Chock, Laboratory of Mechanics, Casablanca, Morocco
Hele-shaw cell
convection
temperature modulation
The convective stability of a horizontal Hele-Shaw liquid layer is investigated when the time-dependent periodic temperature, Tm + Ts cos(ω*t*), is applied on the horizontal walls. Here, the stationary component of the applied temperature gradient is set to zero. The objective of the present study is to find the critical conditions under which thermal convection starts and to show that it is possible to advance or to delay the onset of convection by proper tuning of the modulation frequency. Thus, the Floquet theory and a technique of converting a boundary value problem toward an initial value problem are used to solve the linear system of equations corresponding to the onset of convection. We show that in the limit of low and high dimensionless frequency, ω < 0.5 and ω > 50, the basic state tends to a stable equilibrium configuration and for the intermediate dimensionless frequency, ω = 9.68, the system is potentially unstable. Here, only the harmonic solutions exist. The results obtained from an asymptotic study for low and high dimensionless frequencies are in good agreement with the numerical results.
POROSITY FOR FRACTAL MEDIA
541-544
10.1615/JPorMedia.v14.i6.70
Guo-cheng
Wu
Key Laboratory of Numerical Simulation of Sichuan Province, and College of Mathematics and Information Science, Neijiang Normal University
fractals
fractional measure
porosity
The flow and transport properties of fractal porous media, such as flow resistance, permeability, and dispersion conductivity, have gradually attracted much attention in the past decades. The properties may be closely related to the microstructures of the media and strongly depend on the structure of the pore space. Porosity is an important and fundamental parameter for porous materials. The classical definition of porosity was practical on a large scale, but not very effective especially when physical properties are considered on the nano-scale. In this paper, a measurable definition and a new theoretical model for a spherical fractal medium are developed based on the fractal characters of porous media and fractional integrals. The model can well describe the porosity for all scales, and it is especially useful for fractal porous materials and composite manufacturing.
HPM-PADE METHOD ON NATURAL CONVECTION OF DARCIAN FLUID ABOUT A VERTICAL FULL CONE EMBEDDED IN POROUS MEDIA
545-553
10.1615/JPorMedia.v14.i6.80
H.
Bararnia
Department of Mechanical Engineering, Babol University of Technology
E.
Ghasemi
Department of Mechanical Engineering, Babol University of Technology
Soheil
Soleimanikutanaei
Babol Noshirvani University of Technology
Amin
Barari
Aalborg University
Davood
Ganji (D.D. Ganji)
Babol University
porous media
heat transfer
HFM-Fade
vertical full cone
natural convection
Darcian fluid
In this paper, fluid flow and heat transfer of a vertical full cone embedded in porous media have been studied. A similarity solution for a full cone subjected to wall temperature boundary conditions gives us a nonlinear ordinary differential equation (ODE), which has been solved through the homotopy perturbation method (HPM) and the Fade approximation. The obtained analytical solution in comparison with the numerical ones represents remarkable accuracy. The results also indicate that HFM-Fade can provide us with a convenient way to control and adjust the convergence region. Finally, the Nusselt number, which is an important parameter in heat transfer, has been calculated by HFM-Fade.
THERMAL NON-EQUILIBRIUM MODELING OF COUPLED HEAT AND MASS TRANSFER IN BULK ADSORPTION SYSTEM OF POROUS MEDIA
555-563
10.1615/JPorMedia.v14.i6.90
Xuewei
Zhang
Huazhong University of Science and Technology, School of Energy and Power Engineering, Wuhan 430074
Wei
Liu
School of Energy and Power Engineering, Huazhong University of Science & Tecnology, 1037 Luo Yu Rd. Hongshan District, Wuhan 430074, China
heat and mass transfer
non-equilibrium
porous media
pressure swing adsorption
carbon dioxide
According to the volume-averaging method, a two-dimensional thermal non-equilibrium mathematical model was developed to simulate the coupled heat and mass transfer in porous media with strong adsorption, in which local fluid and solid temperatures were dealt with separately. The temperature-dependent Langmuir isotherm was applied to describe the equilibrium characteristics of binary gas CO2 adsorbed by zeolite 13X. The adsorption-generated heat was considered in the energy equation of the solid matrix. The coupling of two energy equations was made by considering the interfacial heat transfer term. The adsorption feature of a packed bed filled with porous adsorbent and the effects of bulk flow velocity, particle diameter, effective thermal conductivity of solids, and specific heat of adsorbent on product concentration were investigated numerically. The numerical simulation shows that the heat transfer characteristic has notable effects on the quantity of adsorption and the purity of the product. High adsorption efficiency can be achieved by improving the adsorbent physical properties and reducing the temperature span of the pressure swing adsorption process. Experimental data reported by other researchers validate the accuracy of the present model.