Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
7
4
2004
Development of Boundary Layers in Transient Buoyant Convection about a Vertical Plate in a Porous Medium
Transient natural convection over a vertical plate in a porous medium is considered. The Brinkman-extended Darcy flow model is adopted. The Rayleigh number is large to render a boundary layer-type flow pattern. An order-of-magnitude analysis is performed. Numerical solutions are secured over broad ranges of nondimensional parameters. The results indicate that, for high Darcy and Rayleigh numbers, the porous system shows a double boundary layer structure (δm > δT), similar to the pure fluid system. In the opposite limit of low Darcy and Rayleigh numbers, the Darcy term effect is notable in the thermal and momentum boundary layers, and the present results are in accord with the Darcy model. In the intermediate parameter region, ε3/2J1/2Pr Ra1/2Da J1/2σ1/2Pr and (ε/J)1/2 Ra1/2Da 3/2J1/2Pr, the Darcy term effect is seen only in the outer momentum boundary layer for transient periods. At very small times (t JKσ/εκe, K/εvf), the Darcy term effect is very small in both the thermal and momentum boundary layers even for low Darcy numbers. The early-time boundary layer structure of the porous system is akin to that based on the pure-fluid model. In all of the parameter regions, with high heat capacity ratio σ, the ratio of δm to δT for small times is larger than that of the steady state.
K. H.
Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon 305-701, (South) Korea
Sung Jin
Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehakro, Yuseong-ku, Daejeon 305-701, Rep. of Korea
Jae Min
Hyun
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon, South Korea
12
Free Convection in a Thermally Stratified Non-Darcian Wavy Porous Enclosure
Natural convection from a wavy vertical wall to a thermally stratified porous enclosure under non-Darcian assumptions has been analyzed numerically by the finite element method. The effect of inertial forces due to non-Darcian Forchheimer term, thermal stratification level, vertical wavy wall amplitude, wave phase, roughness parameter, and Rayleigh number on the convection process has been analyzed. Interestingly, features such as multiple circulation zones in flow field, thermal boundary layer along the lower segment of wavy wall, and appearance of cold region with large stratification are noticed in the temperature field. Nearly a 90% variation in Nu is possible with varying phase of the wavy surface. In the presence of thermal stratification, the maximum influence of non-Darcian forces is noticed when wave phase of the wavy wall is around 300°.
B. V. Rathish
Kumar
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur,
Kanpur-208016, India
Shalini
Department of Mathematics and Scientific Computing, Indian Institute of Technology, Kanpur, 208016 India
18
Double-Diffusive Natural Convection Induced by a Wavy Surface in a Stratified Porous Medium
In this study, heat and mass transfer near a vertical wavy surface embedded in a mass and thermally stratified porous medium has been employed. The complex wavy surface is transformed to a flat plate by a suitable coordinate transformation, and the obtained boundary layer equations are solved by the local nonsimilarity method under a MAT-LAB setup. Influence of the buoyancy ratio, Lewis number, amplitude-wavelength ratio, and thermal and mass stratification levels on the local Nusselt and local Sherwood numbers are analyzed. Presence of mass and/or thermal stratification in the porous domain decreases both the heat and mass transfer from the wavy surface into the porous medium. The amplitude of harmonic curves for the local Sherwood and local Nusselt numbers tend to decrease away from the leading edge of vertical surface either on increasing thermal or mass stratification, or on decreasing buoyancy ratio. Further, these curves also droop downward with mass or/and thermal stratification. Both the average Nusselt and average Sherwood numbers are found to be constantly smaller than those of the corresponding flat plate.
B. V. Rathish
Kumar
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur,
Kanpur-208016, India
Shalini
Department of Mathematics and Scientific Computing, Indian Institute of Technology, Kanpur, 208016 India
10
Free Convection in a Shallow Annular Cavity Filled with a Porous Medium
In this paper we use asymptotic analysis to examine free convection in a shallow annular cavity filled with a fluid-saturated porous medium. The sidewalls of the cavity are maintained at different temperatures and the upper and lower boundaries are insulating. Results are obtained in the limit as the aspect ratio A, defined as the ratio of the height of the annular cavity to its width, goes to zero. This problem was first studied by Pop, Rees, and Storesletten (J. Porous Media, vol. 1, pp. 227-241, 1998) who considered the case when δ = O(1/A) where δ is the ratio of the inner cylinder radius to the height of the cavity. The results of Pop et al. are extended in this paper by considering convection in the limit as A → 0 with δ = O(1). The results indicate that curvature effects strongly influence the nature of convection in shallow annular cavities.
D. M.
Leppinen
Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
D. Andrew S.
Rees
Department of Mechanical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
L.
Storesletten
Department of Mathematics, Agder University College, Serviceboks 422, 4604 Kristiansand, Norway
14
Convection and Dispersion in a Naturally Fractured Reservoir
In this work, theoretical and experimental studies are presented on the natural convection flow in a naturally fractured reservoir, produced by a vertical geothermal gradient. The present approach considers finite oil-filled, tilted fractures with small aspect ratios, with a fluid thermal conductivity assumed to be very small compared with the thermal conductivity of the rock matrix. These assumptions are fully justified for actual Mexican naturally fractured reservoirs. Finite tilted porous layers saturated with oil have also been considered. In all the cases studied, convection occurs under any vertical temperature gradient. In addition, the diffusion and dispersion of nitrogen (N2) is studied, with this substance located initially at the top of the fracture. In these types of flows, the influence of convection over diffusion and dispersion of passive substances is extremely small.
E.
Luna
Instituto Mexicano del Petroleo, YNF. 07730 Mexico D.F., Mexico
A.
Medina
Instituto Mexicano del Petroleo, YNF. 07730 Mexico D.F., Mexico
C.
Perez-Rosales
Instituto Mexicano del Petroleo, YNF. 07730 Mexico D.F., Mexico
Cesar
Trevino
Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 Mexico D.F., Mexico
14
The Soret Coefficient in Porous Media
We describe in this paper how we measured the thermodiffusion coefficient DT and the isothermal diffusion coefficient D in a free liquid and in a porous medium. Next we compute their ratio in order to resolve the question, "Is the Soret coefficient the same in a free fluid and in a porous medium?"
J. K.
Platten
University of Mons-Hainaut, Belgium
P.
Costeseque
Institut de Mecanique des Fluides de Toulouse, IMFT, Toulouse, France
14
Non-Darcy Free Convection from a Vertical Plate with Time-Periodic Surface Temperature Oscillations
In this article, the linearized theory is used to study the effect of small amplitude time-dependent surface temperature oscillations on free convection to a vertical plate embedded in a non-Darcy porous medium. Forchheimer extension is considered in the flow equations. The time-dependent perturbations are used to transform the governing equations to two groups — similar and nonsimilar, respectively. For the nonsimilar equations, the second-level local nonsimilarity method is used to convert it to a set of ordinary differential equations. The numerical solutions are obtained in the complex domain for a range of the non-Darcy parameter D and the frequency variable ξ.
Mohamed F.
El-Amin
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, 81258; King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
8