Begell House Inc.
Journal of Porous Media
JPM
1091-028X
8
4
2005
TRANSPORT ACROSS ATOMIC PORES
343-345
10.1615/JPorMedia.v8.i4.10
Massoud
Kaviany
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109
Porous Solid Model to Describe Heat-Mass Transfer near Phase Transition Interface in Crystal Growth from Melt Simulations
347-354
10.1615/JPorMedia.v8.i4.20
In simulating the process of crystal growing from the melt it is of crucial importance to describe correctly convective heat-mass transfer in the melt, especially at the crystallization front. Most models use the Navier-Stokes equation in the Boussinesq approximation. The approximation is based on all properties of the melt being independent of pressure and represents the heat-mass transfer process very well when the flow is laminar.In dealing with non-stationary models, however, account should be taken of the presence of a transitional boundary layer near the crystallization front whose thermal properties may differ greatly from those of a pure melt. As a rule it is assumed that the thickness of the layer with transitional properties is small and all properties of the material being simulated are changed abruptly at the interface. In reality, the boundary layer thickness depends on the crystallization front velocity and temperature gradients in the region and may be not so small. As the properties of the melt in this region differ from those of the rest of the melt an additional term appears in the equation to describe the frictional force which impedes the flow along the crystallization boundary.A model where the additional frictional force originating in the boundary layer near the crystallization front is described in terms of porous solid approximation is presented. The force is proportional to the crystallization front velocity and the Solid-to-liquid phase ratio in the boundary layer region, the share of each phase is calculated using the specific enthalpy value for the melt in the region.
Coriolis Effect on Flow Stability in Mushy Layers Solidifying in a Microgravity Enviroment
355-364
10.1615/JPorMedia.v8.i4.30
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
The stability of the flow of interstitial liquid in a rotating mushy layer driven by expansion or contraction upon solidification is presented. A truncated system of governing equations corresponding to the near-eu-tectic limit is analyzed and the key mechanisms controlling the stability are identified. It is found that rotation stabilizes the flow driven by expansion upon solidification.
Transverse Dispersion in Open-Cellular Metallic Foams
365-378
10.1615/JPorMedia.v8.i4.40
Johan G.
Fourie
British Columbia Institute of Technology, 3700 Willingdon Avenue, Burnaby BC, Canada V5G 3H2
Jean P.
Du Plessis
Department of Applied Mathematics, University of Stellenbosch, Private Bag X1, Matieland 7602 South Africa
Experimental transverse dispersion data was obtained from the observation of the macroscopic spreading of a neutrally buoyant tracer introduced into water traversing open-cellular aluminum foam samples. In the Peclet number range of 780−3900 used in this study, the contribution of molecular diffusion to the spreading of the tracer element was negligible. Digital images of the tracer distributions in the water entering and exiting the foam samples were recorded and analyzed. Tracer concentration distributions obtained from the digital images were indirectly related to transverse mass dispersion coefficients through the solution of the differential dispersion equation. Subsequently, transverse mass dispersion data was correlated in terms of a dimensionless dispersion parameter that takes into account the morphological properties of the foam.
Computer Simulation of Ordinary Gas Transfer in Tubes
379-391
10.1615/JPorMedia.v8.i4.50
Mohammad-Hasan
Abbasi
Department of Materials Engineering, Isfahan University of Technology, 84156 Isfahan, Iran
Transfer of pure gas particles in cylindrical tubes under a pressure gradient is formulated on the basis of an ordinary diffusion regime. The pressure distribution in the tube is derived, and a parameter called the transported gas fraction is introduced. It has been shown theoretically that this parameter is a function of the particle mean free path at the mean pressure and the tube length. A computer simulation was then used to verify the results of the formulation. It is shown that the results of the formulation and simulation are in good agreement within certain conditions, i.e., when the tube length is at least five times greater than the particle mean free path at the mean pressure.
Thermosolutal Convection in a Ferromagnetic Fluid Saturating a Porous Medium
393-408
10.1615/JPorMedia.v8.i4.60
Divya
Department of Applied Sciences, National Institute of Technology, Hamirpur, (H.P.)-177 005, India
R. C.
Sharma
Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla 171 005, India
Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
The thermosolutal convection in ferrofluid saturating a porous medium is considered for a ferromagnetic fluid layer heated and soluted from below in the presence of a uniform magnetic field. Using the linearized stability theory and normal mode analysis, the exact solutions are obtained for the case of two free boundaries. For the case of stationary convection, the medium permeability and non-buoyancy magnetization both have destabilizing effects on the system, whereas a stable solute gradient has a stabilizing effect on the system. The critical magnetic thermal Rayleigh number for the onset of instability is also determined. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of a stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were nonexistent in its absence. A sufficient condition for the nonexistence of overstability is also obtained.
Simultaneous Thermal and Mass Diffusion on Three-Dimensional Mixed Convection Flow through a Porous Medium
409-417
10.1615/JPorMedia.v8.i4.70
Pawan Kumar
Sharma
Department of Applied Mathematics Amity School of Engineering and Technology, 580 Delhi-Palam Vihar Road, U&I Building, Beijwasan, New Delhi, India
The effect of simultaneous thermal and mass diffusion on mixed convection flow through a porous medium bounded by an infinite vertical flat porous plate with transverse sinusoidal suction of the fluid at the plate has been analyzed. The problem becomes three-dimensional due to periodic suction velocity. Assuming the free-stream velocity to be uniform, the closed-form solutions are obtained for the velocity, skin frictions, concentration, and temperature distribution. During the course of the discussion, the effects of Re (Reynolds number or suction parameter), Sc (Schmidt number), and k (permeability of porous medium) have been presented.
Effect of the Macroscopic Local Inertial Term on the Non-Newtonian Free-Convection Flow in Channels Filled with Porous Materials
419-430
10.1615/JPorMedia.v8.i4.80
M. M.
Abuzaid
Mechanical Engineering Department, Jordan University of Science and Technology, Irbid 22110, Jordan
Taha K.
Aldoss
Mechanical Engineering Department, Jordan University of Science and Technology, Irbid 22110, Jordan
The transient behavior of non-Newtonian free-convection flow in open-ended vertical parallel-plate channels filled with porous materials is investigated numerically. The role of the macroscopic local inertial term in the momentum equation is studied. It is found that the effect of the macroscopic local inertial term becomes more significant as the power law index n and the modified Darcy number Da* increase, and as the modified Forchheimer Γ and Fourier γ numbers decrease. The macroscopic local inertial term plays no role when Da* < 104over the entire ranges of n, Γ, and γ. Also, it is found that the macroscopic local inertial term plays no role when Γ > 104 over wide ranges of Da*, γ, and n. The modified Fourier number γ has insignificant effect on the channel transient behavior at large values of γ. It is found that the effect of the macroscopic local inertial term is very sensitive to the Forchheimer number at high values of Darcy number and power law index. Also, there is an upper limit for n, beyond which changing the power law index has insignificant effect on the local inertial term.