Begell House Inc.
Journal of Porous Media
JPM
1091-028X
18
6
2015
NATURAL CONVECTION FROM A CYLINDER IN SQUARE POROUS ENCLOSURE FILLED WITH NANOFLUIDS
559-567
10.1615/JPorMedia.v18.i6.10
Habibis
Saleh
School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia
Ishak
Hashim
School of Mathematical Sciences & Solar Energy Research Institute, Faculty of Science
& Technology, Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor DE, Malaysia
nanofluids
natural convection
Darcy's law
The problem of natural convection induced by a temperature difference between an outer porous enclosure and an inner circular cylinder is studied in this paper. The fluid in the porous enclosure is a water-based nanofluids containing Ag, Cu, Al2O3, or TiO2 nanoparticles. The coupled momentum and energy equations have been solved numerically over a wide range of values of the solid volume fraction, the Rayleigh number, the cylinder radius, and various temperature conditions of the bottom wall. It is found that there exists an optimum cylinder radius, below which the increasing cylinder radius increases the strength of flow circulation and above which the cylinder radius decreases the strength of flow circulation. The heat transfer rate increases linearly by increasing the nanoparticles concentration for all cylinder radius and Rayleigh number.
EFFECT OF THERMAL RADIATION ON MIXED CONVECTION FLOW OF A NANOFLUID ABOUT A SOLID SPHERE IN A SATURATED POROUS MEDIUM UNDER CONVECTIVE BOUNDARY CONDITION
569-584
10.1615/JPorMedia.v18.i6.20
S.M.M.
EL-Kabeir
Department of Mathematics, Salman bin Abdulaziz University, College of Science and Humanity Studies, Al-Kharj, 11942, Saudi Arabia; Department of Mathematics, Aswan University, Faculty of Science, 81528, Egypt
M.
Modather
Department of Mathematics, Salman bin Abdulaziz University, College of Science and Humanity Studies, Al-Kharj, 11942, Saudi Arabia; Department of Mathematics, Aswan University, Faculty of Science, 81528, Egypt
Ahmed M.
Rashad
Department of Mathematics, Aswan University, Faculty of Science, Aswan, 81528, Egypt
mixed convection
porous medium
solid sphere
nanofluids
thermal radiation
convective boundary condition
This work focuses on the numerical modeling of a steady mixed convection boundary layer flow of a nanofluid about a solid sphere embedded in a porous medium with convective surface in the presence of the thermal radiation effect using the Brinkman-extended Darcy model. A model is developed to analyze the behavior of nanofluids, taking into account the nanoparticle volume fraction parameter, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. An appropriate transformation is employed, and the transformed equations are solved numerically using an efficient implicit iterative tri-diagonal finite difference method. Comparisons to previously published works are performed, and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the local skin-friction coefficient and local Nusselt number are illustrated graphically to show interesting features of the solutions. It is concluded that both the local skin-friction coefficient and local Nusselt number decreased due to increases in Darcy number, while they are increased as in either the mixed convection parameter, Biot number, or thermal radiation parameter increase. In addition, an increase in the values of the nanoparticle volume fraction produced enhances in the local skin friction and reductions in the local Nusselt number.
NATURAL CONVECTION IN A CUBICAL POROUS CAVITY SATURATED WITH NANOFLUID USING TIWARI AND DAS' NANOFLUID MODEL
585-596
10.1615/JPorMedia.v18.i6.30
Mikhail A.
Sheremet
Department of Theoretical Mechanics, Tomsk State University, 634050, Tomsk, Russia; Institute of Power Engineering, Tomsk Polytechnic University, 634050, Tomsk, Russia
Teodor
Grosan
Faculty of Mathematics and Computer Science, Babes-Bolyai University, 400084 Cluj-Napoca,
Romania
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
natural convection
cubical cavity
porous medium
nanofluids
numerical method
Natural convection in a cubical differentially heated porous cavity filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless vector potential functions and temperature taking into account the Darcyâˆ’Boussinesq approximation. The Tiwari and Das' nanofluid model with new, more realistic empirical correlations for the physical properties of the nanofluids has been used for numerical analysis. The governing equations have been solved numerically on the basis of a second-order accurate finite difference method with nonuniform mesh. The results have been presented in terms of the three-dimensional velocity and temperature fields, streamlines, and isotherms at middle cross section, average and local Nusselt numbers at hot wall for a wide range of key parameters.
ONSET OF DOUBLE DIFFUSIVE REACTION-CONVECTION IN AN ANISOTROPIC POROUS LAYER WITH INTERNAL HEAT SOURCE
597-612
10.1615/JPorMedia.v18.i6.40
S . N.
Gaikwad
Department of Mathematics, Gulbarga University, Jnana Ganga, Gulbarga-585106, India
M.
Dhanraj
Department of Mathematics, Gulbarga University, Jnana Ganga Campus, Gulbarga - 585 106, Karnataka, India
double diffusive convection
internal Rayleigh number
chemical reaction
anisotropy
porous layer
heat mass transfer
The effect of internal heat source on the onset of double diffusive reaction-convection in an anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated analytically using both linear and weak nonlinear stability analyses. The linear analysis is based on the usual normal mode method. The Darcy model is employed for the momentum equation. The effects of internal Rayleigh number, Damkohler number, mechanical anisotropy parameter, thermal anisotropy parameter, Lewis number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the effects of internal Rayleigh number and mechanical anisotropy parameter have destabilizing effect, while the thermal anisotropy parameter has stabilizing effect on the stationary, oscillatory, and finite amplitude convection. The Damkohler number has destabilizing effect in the case of stationary mode, with stabilizing effect in the case of oscillatory and finite amplitude modes. A weak nonlinear analysis based on truncated representation of Fourier series is performed to find heat and mass transfer. Further, the transient behavior of the Nusselt number and Sherwood number is studied by solving the finite amplitude equations using the Runge-Kutta method.
NATURAL CONVECTION ABOVE A HORIZONTAL PLATE IN A NANOFLUID-SATURATED POROUS MEDIUM WITH OR WITHOUT A MAGNETIC FIELD
613-628
10.1615/JPorMedia.v18.i6.50
Kaustav
Pradhan
Indian Institute of Technology Kharagpur
Abhijit
Guha
Mechanical Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur, Pin 721302, India
MHD
natural convection
porous medium
nanofluid
horizontal plate
A generalized similarity theory is developed for natural convection over a horizontal plate in a nanofluid-saturated porous medium in the presence of a vertical magnetic field. The paper highlights three important aspects: role of the wall boundary condition of the nanoparticles, the magnetic field, and the porous medium. Two different boundary conditions are imposed on the nanoparticle volume fraction, one where the nanoparticle volume fraction at the wall is actively controlled and another where the nanoparticle flux is set equal to zero at the surface. It is shown that a similarity theory can be formulated for the case of a uniform magnetic field when natural convection takes place in a Darcian porous medium (which is in contrast to magnetohydrodynamic natural convection in a normal fluid for which similarity solutions exist only for a specific power law variation of the magnetic field along the plate). It is observed that the applied magnetic field reduces the velocity in the boundary layer. Consequently, the temperature of the nanofluid and the nanoparticle volume fraction near the plate is greater than that in the absence of a magnetic field. The Nusselt number and Sherwood number for a nanofluid are found to decrease with an increase in the value of the magnetic parameter. The effect of the nanofluid parameters Nr, Nb, and Nt on the velocity, temperature and nanoparticle volume fraction within the boundary layer is also investigated. The effect of the nanofluid parameters on the Nusselt and Sherwood numbers is complicated and is illustrated through tables. It is shown that the wall boundary condition of the nanoparticles has a profound effect on the computed values of Nusselt and Sherwood numbers.
ONSET OF THERMAL CONVECTION IN A ROTATING NANOFLUID LAYER SATURATING A DARCY-BRINKMAN POROUS MEDIUM: A MORE REALISTIC MODEL
629-635
10.1615/JPorMedia.v18.i6.60
Gian C.
Rana
Department of Mathematics, NSCBM Government College, Hamirpur-177005, Himachal
Pradesh, India
Ramesh
Chand
Department of Mathematics, Government Degree College Sugh-Bhatoli, Himachal Pradesh,
India
nanofluid
rotation
thermal convection
Darcy-Brinkman porous medium
In this paper, we investigate analytically the thermal convection in a rotating nanofluid layer saturating a Darcy-Brinkman porous medium by using a more realistic linear stability analysis model. In this model, we assume that the nanoparticle concentration flux is zero on the boundaries and we can put values of temperature at the boundaries. The assumed boundary conditions neutralize the possibility of oscillatory convection, and only stationary convection occurs in the absence of rotation. But in the presence of rotation, oscillatory convection occurs due to the Coriolis effect. This paper is the extension of our previous paper in which we put both temperature and nanoparticle volume fraction at the boundaries of the nanofluid layer.
GEOMETRICAL CHARACTERIZATION OF KELVIN-LIKE METAL FOAMS FOR DIFFERENT STRUT SHAPES AND POROSITY
637-652
10.1615/JPorMedia.v18.i6.70
Prashant
Kumar
IUSTI, CNRS UMR 7343, Aix-Marseille University, Marseille, France
Frederic
Topin
Polytech Marseille, Laboratoire IUSTI, UMR CNRS 7343, Technopole de Chateau Gombert, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
Lounes
Tadrist
Aix-Marseille Universite, CNRS, Laboratoire IUSTI, UMR 7343, Marseille 13453, France
foam geometry
characterization
metal foam
structure
strut morphology
specific surface
Kelvin cell foams are an idealization of replication foams and nowadays are also materialized for various industrial purposes. There are several works dealing with thermo-hydraulic properties of foams in relation to their structure. The thermo-hydraulic behavior of open-cell foams depends on their microscopic structure. Various ideal periodic isotropic structures of tetrakaidecahedron shapes with constant cross section of the ligament having circular, square, diamond, hexagon, and star strut shapes with various orientations are studied. Computer aided design (CAD) modeling has been used to produce various shapes in the porosity range from 60 to 95%. A generalized analytical model has been proposed in order to obtain geometrical parameters correctly as they have substantial influence on thermal and hydraulic phenomena, where strut geometry is of primary importance. Various relationships between different geometrical parameters and porosities are presented. The analytical results are compared with experimental data from the literature. An excellent agreement has been observed between the predicted correlations, data obtained from CAD measurements, and experiments.