Begell House Inc.
Journal of Porous Media
JPM
1091-028X
17
8
2014
ON THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN A LAYER OF NANOFLUID UNDER ROTATION SATURATING A POROUS MEDIUM
657-667
G. C.
Rana
Department of Mathematics, Government College Hamirpur, Himachal Pradesh, India
R. C.
Thakur
Department of Mathematics, Govt. College, Dhaliara-177103, District Kangra Himachal Pradesh, India
S. K.
Kango
Department of Mathematics, Govt. College, Haripur-177 103, District Kullu Himachal Pradesh, India
In this study, the double-diffusive convection in a horizontal layer of nanofluid under rotation in a porous medium is presented. For the porous medium, the Darcy model is employed. The base fluid of the nanofluid is itself a binary fluid like salty water. The nanofluid describes the effects of thermophoresis and Brownian diffusion. From the linear stability analysis based upon normal modes analysis method, the dispersion relation accounting for the effect of various parameters is derived. For the case of stationary convection, it is observed that rotation and solute gradient have a stabilizing effect on the system. Rotation plays an important role in the thermal instability of fluid layer and has applications in rotating machineries such as nuclear reactors, petroleum industry, biomechanics, etc. The influences of thermo-nanofluid Lewis number, thermosolutal Lewis number, and Soret and Dufour parameter on the stability of stationary convection are presented graphically and discussed. A very good agreement is found between the present paper and earlier published results.
FLOW AND HEAT TRANSFER IN A POROUS MEDIUM SATURATED BY A MICROPOLAR FLUID BETWEEN PARALLEL PERMEABLE DISKS
669-684
Jawali C.
Umavathi
Department of Mathematics, Gulbarga University, Kalaburgi-585106, Karnataka, India
M
Shekar
Department of Mathematics, Gulbarga University, Gulbarga 585 106, Karnataka, India
In this paper, the flow and heat transfer in a porous medium saturated by a micropolar fluid between two parallel permeable disks with uniform suction or injection through the surface of the disks is studied analytically using differential transform methods. It is assumed that the Darcy−Brinkman model is considered for the flow through the porous medium. The governing nonlinear partial differential equations of motion are transformed into a dimensionless form through von Karman's similarity transformation. The approximate solutions of these equations are obtained in the form of series with easily computable terms using differential transformations. The effects of the Reynolds number, the Darcy number, the vortex viscosity parameter, and the Prandtl number on the flow field and temperature distributions are determined and discussed. The results show that for different values of the Darcy number and vortex viscosity parameter, the shear stress is more for suction velocity and less for injection velocity, respectively. It is also found that the rate of heat transfer increases as Reynolds number increases for both suction and injection parameter. As the Darcy number and vortex viscosity parameter increases, the rate of heat transfer decreases for injection and increases for suction.
NONLINEAR ELECTROHYDROMAGNETIC STABILITY OF CONDUCTING FLUID FLOWING THROUGH POROUS MEDIUM DOWN AN INCLINED PLANE
685-703
Mohamed F.
El-Sayed
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis (Roxy), Cairo, Egypt; Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraidah 51452, Saudi Arabia
M. H. M.
Moussa
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
Ahmed A. A.
Hassan
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis Cairo, Egypt
N. M.
Hafez
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
The nonlinear stability of a conducting viscous film flowing through porous medium down an inclined plane in the presence of electromagnetic field is investigated under an induction-free approximation. Using the momentum integral method a nonlinear evolution equation for the development of the free surface is derived. A normal mode approach and the method of multiple scales are used to obtain the linear and nonlinear solutions. The linear stability analysis of the evolution equation shows that the electric field destabilizes the film flow while magnetic field stabilizes it at not too large an electric field, and these effects are stronger in the presence of porous medium than in its absence, whereas the porosity of porous medium and the medium permeability destabilize the film flow. The weakly nonlinear study reveals that both the subcritical instability and supercritical stable are possible for this type of thin film flow. The influence of magnetic field on the flow is strong, and its effect in the absence of porous medium is stronger than in the presence of porous medium, while the influence of electric field parameter on the flow is feeble in both cases of absence or presence of porous medium. The behaviors of threshold amplitude and nonlinear wave speed in both subcritical unstable and supercritical stable regions under the effects of all physical parameters have been discussed in detail.
ANALYSIS OF GAS PERMEABILITY FOR LIQUID PHASE-SINTERED POROUS SiC COMPACT
705-713
Hikaru
Maeda
Department of Chemistry, Biotechnology, and Chemical Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan
Yoshihiro
Hirata
Department of Chemistry, Biotechnology, and Chemical Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan
Soichiro
Sameshima
Department of Chemistry, Biotechnology, and Chemical Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan
Taro
Shimonosono
Kagoshima University
A submicrometer−sized SiC powder was densified with Al2O3−Y2O3 additives by liquid phase sintering during hot-pressing at 1400−1900° C. Gas permeability of N2, CO2, and O2 gases in SiC with 18−36% open porosity was measured at room temperature. The transportation of gas introduced occurred above a critical minimum pressure. The gas flux increased linearly with an increase of the applied pressure gradient. The Knudsen numbers (Kn = λ/r, where λ and r are the molecular mean-free path of gas molecules and the pore radius of SiC compact, respectively) for the porous SiC compacts were in the range of 0.1−0.3, suggesting the transition range between the viscous flow and the Knudsen flow. A theoretical gas permeability coefficient was derived from the Poiseuille equation which describes a viscous flow. The measured permeability coefficient was in the same order of magnitude by the theoretical prediction. The permeability of gas depends basically on pore structure (pore size, porosity, deviated angle of pore channels against ideal straight pores), viscosity of gas molecules, average pressure in a porous ceramics, and temperature. The permeability coefficient calculated by the Knudsen equation was two orders of magnitude smaller than that of the measured permeability coefficient, reflecting a small contribution of Knudsen flow to the flux of gas permeation.
EMERGENCE OF TAPERED DUCTS IN VASCULAR DESIGNS WITH LAMINAR AND TURBULENT FLOWS
715-722
Erdal
Cetkin
Izmir Institute of Technology, Department of Mechanical Engineering, Urla, Izmir 35430, Turkey
Here we show that tapered ducts emerge in volumetrically bathed porous materials to decrease the resistance to the flow in laminar and turbulent flow regimes. The fluid enters the volume from one point and it is distributed to the entire volume. After bathing the volume, it is collected and leaves the volume from another point, i.e., two trees matched canopy to canopy. This paper shows that the flow architecture (i.e., design of the void spaces in a porous material) should be changed to obtain the minimum resistance to the flow as its size increases. Tapering the ducts decreases the order of the transition size, i.e., the size for changing from one construct to another to obtain the minimum pressure drop. The decrease in the pressure drop is 16% and 38% with the tapered ducts when the flow is laminar and turbulent, respectively. In addition, the volume ratios and the shape of the tapered ducts are documented. There is no design existing in nature with diameters of constant size in order to distribute and/or collect heat, fluid, and/or stress such as bones, rivers, veins, and tree branches. The emergence of the tapered ducts in designed porous materials is natural.
SOUND WAVES PROPAGATION WITHIN POROUS LAYERS USING FORCHHEIMER'S MODEL
723-730
Hamzeh M.
Duwairi
Mechanical Engineering Department, Faculty of Engineering and Technology, The University of Jordan, 11942, Amman, Jordan
A fully nonlinear wave analysis is performed for an acoustic wave which propagates through an isentropic porous medium under the boundary layer approximations. It is found that the main three parameters that govern the propagation process are reduced frequency parameter, Re = ρKω/µ; Forchheimer's number, Fr = a/√Kω; and porosity, ε. The propagation process takes place under isentropic conditions and the sound disturbance is under monofrequency and harmonic conditions. It is found that as porosity e is increased, the attenuations and phase shift for both forward and backward sound waves is decreased; this is due to unfavorable acoustic wave propagation in plain medium. The effect of increasing the reduced frequency number, Re, is found to decrease attenuation and increase phase shift velocities; this is also due to the movement of porous medium to the plain medium limit and due to low viscous damping effects. The effect of increasing Forchheimer's number is found to decrease attenuation and increase phase shift for both forward and backward sound waves.
RESISTANCE TO CREEPING FLOW AND PERMEABILITY OF STACKED SPHERES
731-740
Ryszard
Blazejewski
Dept. of Hydraulic and Sanitary Engineering, University of Life Sciences, Piatkowska St. 94a, 60-649 Poznan, Poland
S.
Murat-Blazejewska
Dept. of Land Reclamation and Env. Eng., University of Life Sciences, Piatkowska St. 94a, 60-649 Poznan, Poland
Six regularly packed beds (simple cubic, orthorhombic I and II, tetragonal sphenoidal, and rhombohedral I and II), treated as unit cells made of monosized spheres, were analyzed. A formula to calculate permeability of such beds at creeping flow conditions was proposed. It is based on similar assumptions as the Kozeny−Carman equation, but instead of mean porosity and tortuosity, their local values were taken into account. Two different values of the pore shape factors, regarding triangular and square pores, according to Boussinesq, were applied. The new formula, in its integral form, agrees better with experiments than those given by Slichter, Kozeny and Carman, Martin et al. as well as Franzen; it underestimates the analyzed packings' permeabilities by less than 22%, on average by 13%.
DERIVATION OF THE DARCY-SCALE FILTRATION EQUATION FOR POWER-LAW FLUIDS WITH THE VOLUME AVERAGING METHOD
741-750
Xiao-Hong
Wang
Department of Thermal Science and Energy Engineering, University of Science and Technology
of China, Hefei, Anhui 230026, China
Jiang-Tao
Jia
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
Zhi-Feng
Liu
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
Long-De
Jin
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
The large-scale continuum models for transport of power-law fluids in porous media are derived from the pore-scale control equations using the volume averaging method. The averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The closure problem for the power-law fluid flow is assumed to be analogous to the Newtonian fluid flow. Then a tensorial form of Darcy-scale filtration equation is obtained and the power-law relation between the averaged velocity and the gradient of the averaged pressure are confirmed. Different from Newtonian fluids, the apparent permeability significantly depends upon the filtration velocity direction for higher-dimensional flow (d ≥ 2). Numerical test also validates this conclusion.