Begell House Inc.
Journal of Porous Media
JPM
1091-028X
19
8
2016
HEAT SINK WITH MULTILAYER OF POROUS MEDIA
659-667
10.1615/JPorMedia.v19.i8.10
Arun
Karunanithi
Department of Mechanical Engineering, University of Texas at Dallas, Dallas, TX 75080, USA
Fatemeh
Hassanipour
Department of Mechanical Engineering, University of Texas at Dallas, Richardson, TX, 75080
porous media
forced convection heat transfer
heat sink
This study presents a new miniature porous heat sink system for dissipating high heat flux in electronic devices. Previous studies have shown that stacked multilayer mini/micro channel heat sinks have advantages over traditional single layered channels in terms of both pressure drop and thermal resistance. Instead of square or rectangular channels, in this work, a stacked multilayer of porous media is used, where the porosity varies from one layer to the next layer (porosity scaling) along with the heat transfer direction. This work studies numerically both the pressure drop and thermal resistance for the proposed approach. The results are compared with the case of uniform porosities and also with the case when layers of a multichannel are used instead of porous media layers.
SORET AND DUFOUR EFFECTS ON MHD NATURAL CONVECTIVE HEAT AND SOLUTE TRANSFER IN A FLUID-SATURATED POROUS CAVITY
669-686
10.1615/JPorMedia.v19.i8.20
Balla Chandra
Shekar
Department of Mathematics, Osmania University, Hyderabad, Telangana State, India
Naikoti
Kishan
Osmania University, Hyderabad, India
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates, 10021
MHD
Soret and Dufour effects
cavity
porous media
finite element method
The present problem addresses double-diffusive magnetohydrodynamic free convection in an inclined square cavity filled with a fluid-saturated porous medium under the influence of Soret and Dufour effects. The inclined cavity makes an angle with the horizontal plane. A uniform magnetic field inclined with the same angle of inclination of the cavity is applied. At the two horizontal walls of the cavity, the heat and solute transverse gradients are applied, and lateral walls of the cavity are regarded as insulated and impermeable. Using the appropriate dimensionless quantities, the governing equations with boundary conditions are transformed to nondimensional form. The governing partial differential equations are solved by the finite element method of Galerkin's weighted residual scheme. Numerical results are obtained for different values of the Rayleigh number, Lewis number, buoyancy ratio, magnetic field parameter, Soret number, and Dufour number. The overall investigation of variation of streamlines, isotherms, isoconcentration, Nusselt number, and Sherwood number is presented graphically.
DETERMINATION OF NON-DARCY FLOW BEHAVIOR IN A TIGHT FORMATION
687-700
10.1615/JPorMedia.v19.i8.30
Yu
Shi
Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, Canada, S4S 0A2
Zhengming
Yang
Institute of Porous Flow and Fluid Mechanics, UCAS, Hebei, 065007, China; PetroChina Research Institute of Petroleum Exploration and Development, Langfang, 065007, China
Daoyong
Yang
Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of
Regina, Regina, Saskatchewan, Canada, S4S 0A2
non-Darcy flow
tight formation
threshold pressure gradient
pore throat distribution
modified Hagen-Poiseuille equation
A novel technique has been experimentally and theoretically developed and applied to quantify the non-Darcy behavior caused by boundary flow that adheres to the grain of the rock in tight oil formations. Experimentally, constant-rate mercury injection experiments are conducted to determine the distribution of the pore throat as a function of its radius for three core samples. The threshold pressure gradient is then obtained through a permeability test with water for an additional three core samples collected from the same formation. Theoretically, the total flow rate model is derived by integrating the flow rate of an individual throat with respect to its distribution function, while the modified Hagenâˆ’Poiseuille equation, which considers the effect of boundary flow in the microscale, is employed to characterize single-phase flow in low-permeability sandstone formations. Once the permeability and pressure gradient with non-Darcy effect have been obtained for the single-phase flow, the relative permeability equation of two-phase flow is correspondingly developed based on the modified capillary tube model. It is found from experimental results and theoretical models that both permeability and threshold pressure gradient are nonlinear functions of the pressure gradient in single-phase flow when the pressure gradient ranges from 0.0086 to 0.4323 MPa/m. Meanwhile, a larger pressure gradient is required to overcome the negative resistance due to the non-Darcy flow on the relative permeability curve. At water saturation of 60.2%, the oil relative permeability can be increased by 13.4%, while water cut is decreased by 17.2% with an increase of pressure gradient from 0.0200 MPa/m to its maximum threshold pressure gradient (i.e., 0.4323 MPa/m).
APPLICATION OF FINITE ELEMENT METHOD TO UNSTEADY MAGNETOHYDRODYNAMIC FREE-CONVECTION FLOW PAST A VERTICALLY INCLINED POROUS PLATE INCLUDING THERMAL DIFFUSION AND DIFFUSION THERMO EFFECTS
701-722
10.1615/JPorMedia.v19.i8.40
R. Srinivasa
Raju
Department of Mathematics, GITAM University, Hyderabad Campus, Rudraram, Medak (Dt),
502329, Telangana State, India
B. Mahesh
Reddy
Department of Mathematics, Bandari Srinivas Institute of Technology, Gollapally (Village), Chevella (Mandal), Ranga Reddy (District), 501503, Telangana State, India
Mohammad Mehdi
Rashidi
Tongji University
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
thermal diffusion
diffusion thermo
porous medium
magnetohydrodynamics
finite element method
In this analysis, thermal diffusion (Soret) and diffusion thermo (Dufour) effects have been discussed on unsteady magnetohydrodynamic free-convection heat and mass transfer flow on a viscous, incompressible, electrically conducting fluid past a semi-infinite inclined vertical porous plate, moving with a uniform velocity with chemical reaction and thermal radiation. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. It is assumed that the effect of viscous dissipation is negligible in the energy equation and there is a first-order chemical reaction between the diffusing species and the fluid. The non-linear partial differential equations governing the flow have been solved numerically using the finite element method (FEM). We have examined the effects of different controlling parameters, namely, Soret number, Dufour number, magnetic field parameter, Grashof number for heat and mass transfer, permeability parameter, thermal radiation parameter, Prandtl number, Schmidt number, angle of inclination of the plate, and chemical reaction parameter on the flow field and heat transfer characteristics. Graphical display of the numerical examination is performed to illustrate the influence of various flow parameters on the velocity, temperature and concentration profiles, skin-friction, rate of heat, and mass transfer coefficients. The present study has several applications in coating and suspensions, paper production, heat exchangers technology, materials processing exploiting, drying, evaporation at the surface of water body, etc.
ONSET OF BUOYANCY-DRIVEN CONVECTION IN A CYLINDRICAL POROUS LAYER SATURATED WITH LARGE VISCOSITY VARIATION LIQUID
723-735
10.1615/JPorMedia.v19.i8.50
Jong Dae
Lee
Department of Chemical Engineering, Chungbuk National University, Chungbuk 28644, Republic of Korea
Min Chan
Kim
Department of Chemical Engineering, Jeju National University, Jeju 63243, Republic of Korea
buoyancy-driven convection
porous medium
cylindrical geometry
viscosity variation effect
linear stability analysis
A stability analysis on the buoyancy-driven convection under the transient concentration fields is conducted in an initially quiescent, liquid-saturated, and cylindrical porous layer with gas diffusion from below. Darcy's law and the Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The viscosity variation of liquid with the dissolved concentration is approximated by employing the Frankâˆ’Kamenetskii approximation. The linear stability equations are derived in the selfsimilar domain and solved without the quasi-steady-state approximation. The present predictions suggest the critical RaD, which is quite different from the previous ones. The onset time becomes shorter with increasing RaD and follows the asymptotic relation derived in the infinite horizontal porous layer. The viscosity variation effect makes the system unstable and accelerates the onset of convection.
NATURAL CONVECTION OF MICROPOLAR NANOFLUIDS IN A RECTANGULAR ENCLOSURE SATURATED WITH ANISOTROPIC POROUS MEDIA
737-750
10.1615/JPorMedia.v19.i8.60
Sameh Elsayed
Ahmed
Department of Mathematics, Faculty of Science, Abha, King Khalid University, Saudi Arabia; Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
Ahmed M.
Rashad
Department of Mathematics, Aswan University, Faculty of Science, Aswan, 81528, Egypt
porous media
natural convection
rectangular enclosure
micropolar nanofluid
SIMPLE
The problem of natural convection flow and heat transfer of micropolar nanofluid inside a rectangular enclosure saturated with anisotropic porous medium is investigated numerically. All the walls of the enclosure are adiabatic except the bottom wall, which is partially heated and cooled by sinusoidal temperature profiles. An Al2O3/water nanofluid model has been utilized into the micropolar theory with experimental forms of thermo-physical nanofluid properties for both situations of hydrodynamically isotropic and anisotropic medium. The mathematical model of the proposed micropolar nanofluid flow regime consists of a set of partial differential equations along with the corresponding boundary conditions and these equations were solved numerically using the finite volume method with SIMPLE algorithm. The obtained results are presented in terms of streamlines and isotherms as well as local Nusselt number. It is found that a good enhancement in the rate of heat transfer can be obtained by increasing the nanoparticle volume fraction. For the anisotropic porous medium case, the increase in the permeability ratio leads to decrease the fluid activity, vortex strength, and the flow direction is reversed.