Finite element modelling of flow, heat and mass transfer in fluid saturated porous media

SummaryIn this article, a short review of numerical modelling of porous medium flow, heat and mass transfer is presented. The focus of the article is mainly on the use of finite element method and velocity correction algorithm. In addition to a detailed discussion on the velocity correction scheme, some essential fundamental and application problems are solved and results are presented. Many of these results are compared against available experimental and numerical data.

[1]  H. Brinkman.  A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles , 1949 .

[2]  S. Ergun.  Fluid flow through packed columns , 1952 .

[3]  R. F. Benenati,et al.  Void fraction distribution in beds of spheres , 1962 .

[4]  S. Whitaker.  Diffusion and dispersion in porous media , 1967 .

[5]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[6]  B. Chan,et al.  Natural convection in enclosed porous media with rectangular boundaries , 1970 .

[7]  G. Comini,et al.  Finite element solution of incompressible Navier-Stokes equations , 1982 .

[8]  J. Z. Zhu,et al.  The finite element method , 1977 .

[9]  George M. Homsy,et al.  Convection in a porous cavity , 1978, Journal of Fluid Mechanics.

[10]  P. Tyvand,et al.  Nonlinear thermal convection in anisotropic porous media , 1979, Journal of Fluid Mechanics.

[11]  H. Inaba,et al.  An experimental study of transient heat transfer characteristics in a porous layer enclosed between two opposing vertical surfaces with different temperatures , 1981 .

[12]  O. A. Plumb,et al.  Non-darcy natural convection from heated surfaces in saturated porous media , 1981 .

[13]  C. L. Tien,et al.  Boundary and inertia effects on flow and heat transfer in porous media , 1981 .

[14]  C. Hickox,et al.  A numerical study of natural convection in a vertical, annular, porous layer , 1985 .

[15]  S. Giuliani,et al.  Finite element solution of the unsteady Navier-Stokes equations by a fractional step method , 1982 .

[16]  F. Kulacki,et al.  Natural convection in a vertical porous annulus , 1984 .

[17]  Kambiz Vafai,et al.  Convective flow and heat transfer in variable-porosity media , 1984, Journal of Fluid Mechanics.

[18]  C. L. Tien,et al.  An Experimental Investigation of Heat Transfer in Variable Porosity Media , 1985 .

[19]  F. Kulacki,et al.  Natural convection in porous media , 1985, Journal of Fluid Mechanics.

[20]  Adrian Bejan,et al.  Heat and mass transfer by natural convection in a porous medium , 1985 .

[21]  E. Subramanian,et al.  A boundary-layer analysis for natural convection in vertical porous enclosures—use of the Brinkman-extended Darcy model , 1985 .

[22]  O. V. Trevisan,et al.  Natural convection with combined heat and mass transfer buoyancy effects in a porous medium , 1985 .

[23]  V. Prasad.  Numerical study of natural convection in a vertical, porous annulus with constant heat flux on the inner wall , 1986 .

[24]  Nishimura Tatsuo,et al.  Numerical analysis of natural convection in a rectangular enclosure horizontally divided into fluid and porous regions , 1986 .

[25]  H. Bau,et al.  Thermal Convection Around a Heat Source Embedded in a Box Containing a Saturated Porous Medium , 1988 .

[26]  R. Viskanta,et al.  Natural convection in vertical enclosures containing simultaneously fluid and porous layers , 1988, Journal of Fluid Mechanics.

[27]  Kambiz Vafai,et al.  Convective and Radiative Heat Transfer in Porous Media , 1989 .

[28]  K. Vafai,et al.  Forced Convection in a Channel Filled With a Porous Medium: An Exact Solution , 1989 .

[29]  G. Lauriat,et al.  Non-darcian effects on natural convection in a vertical porous enclosure , 1989 .

[30]  P. Cheng,et al.  Thermal dispersion in a porous medium , 1990 .

[31]  B. Ramaswamy.  Efficient Finite Element Method for Two-Dimensional Fluid Flow and Heat Transfer Problems , 1990 .

[32]  Mohamed M. Hafez,et al.  Finite element solution of compressible Navier-Stokes equations , 1991 .

[33]  J. Ni,et al.  NATURAL CONVECTION IN A VERTICAL ENCLOSURE FILLED WITH ANISOTROPIC POROUS MEDIA , 1991 .

[34]  M. Kaviany.  Principles of heat transfer in porous media , 1991 .

[35]  A Numerical Solution of Variable Porosity Effects on Natural Convection in a Packed-Sphere Cavity , 1991 .

[36]  Vijay K. Garg,et al.  A variable property analysis of alloy solidification using the anisotropic porous medium approach , 1992 .

[37]  J. E. Akin,et al.  Semi‐implicit and explicit finite element schemes for coupled fluid/thermal problems , 1992 .

[38]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[39]  J. L. Lage.  EFFECT OF THE CONVECTIVE INERTIA TERM ON BENARD CONVECTION IN A POROUS MEDIUM , 1992 .

[40]  J. L. Lage.  On the Theoretical Prediction of Transient Heat Transfer Within a Rectangular Fluid-Saturated Porous Medium Enclosure , 1993 .

[41]  Chang Wen-Jeng,et al.  Natural convection in a vertical cylinder filled with anisotropic porous media , 1993 .

[42]  Farid Alavyoon,et al.  On natural convection in vertical porous enclosures due to prescribed fluxes of heat and mass at the vertical boundaries , 1993 .

[43]  A. Shenoy.  Non-Newtonian fluid heat transfer in porous media , 1994 .

[44]  Y. R. Chang,et al.  Measurement of opposing heated line jets discharged at an angle to a confined crossflow , 1994 .

[45]  Kimura Shigeo,et al.  On natural convection in vertical porous enclosures due to opposing fluxes of heat and mass prescribed at the vertical walls , 1994 .

[46]  Chang Wen-Jeng,et al.  Natural convection in a finite wall rectangular cavity filled with an anisotropic porous medium , 1994 .

[47]  K. N. Seetharamu,et al.  Convective heat transfer in axisymmetric porous bodies , 1995 .

[48]  E. Bilgen,et al.  Multiple solutions for double-diffusive convection in a vertical porous enclosure , 1995 .

[49]  D. Misra,et al.  A comparative study of porous media models in a differentially heated square cavity using a finite element method , 1995 .

[50]  O. Zienkiewicz,et al.  A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme , 1995 .

[51]  Ramon Codina,et al.  A general algorithm for compressible and incompressible flow—Part II. tests on the explicit form , 1995 .

[52]  G. Degan.  Convective heat transfer in a vertical anisotropic porous layer , 1995 .

[53]  Kankanhalli N. Seetharamu,et al.  DOUBLE-DIFFUSIVE NATURAL CONVECTION IN AN ENCLOSURE FILLED WITH FLUID-SATURATED POROUS MEDIUM: A GENERALIZED NON-DARCY APPROACH , 1996 .

[54]  K. Vafai,et al.  Closure statements on the Brinkman-Forchheimer-extended Darcy model , 1996 .

[55]  C. Hickox,et al.  Simulation of Coupled Viscous and Porous Flow Problems , 1996 .

[56]  J. L. Lage,et al.  Forced convection in a fluid-saturated porous-medium channel with isothermal or isoflux boundaries , 1996, Journal of Fluid Mechanics.

[57]  K. N. Seetharamu,et al.  Natural convective heat transfer in a fluid saturated variable porosity medium , 1997 .

[58]  K. N. Seetharamu,et al.  Non-Darcy double-diffusive natural convection in axisymmetric fluid saturated porous cavities , 1997 .

[59]  P. Vasseur,et al.  Boundary-layer regime in a vertical porous layer with anisotropic permeability and boundary effects , 1997 .

[60]  K. Vafai,et al.  Non-Darcian effects on double-diffusive convection within a porous medium , 1997 .

[61]  K. N. Seetharamu,et al.  Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall , 1997 .

[62]  Kankanhalli N. Seetharamu,et al.  Finite element analysis of heat transfer by natural convection in porous media in vertical enclosures: Investigations in Darcy and non‐Darcy regimes , 1997 .

[63]  P. Vasseur,et al.  Natural Convection in a Rectangular Cavity Filled with an Anisotropic Porous Medium , 1998 .

[64]  Kankanhalli N. Seetharamu,et al.  Finite element analysis of transient natural convection in an odd‐shaped enclosure , 1998 .

[65]  K. N. Seetharamu,et al.  Effect of porosity on natural convective heat transfer in a fluid saturated porous medium , 1998 .

[66]  Finite element analysis of pollutant transport in water-saturated soil , 1998 .

[67]  V. Eswaran,et al.  NUMERICAL STUDY OF HEAT AND MASS TRANSFER IN AN ANISOTROPIC POROUS ENCLOSURE DUE TO CONSTANT HEATING AND COOLING , 1998 .

[68]  P. Nithiarasu,et al.  A new semi-implicit time stepping procedure for buoyancy driven flow in a fluid saturated porous medium , 1998 .

[69]  K. N. Seetharamu,et al.  Buoyancy driven flow in a non-Darcian, fluid-saturated porous enclosure subjected to uniform heat flux-a numerical study , 1999 .

[70]  Ali J. Chamkha,et al.  Mixed convection flow in a lid-driven enclosure filled with a fluid-saturated porous medium , 1999 .

[71]  O. Zienkiewicz,et al.  The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems , 1999 .

[72]  Jay M. Khodadadi,et al.  Pseudosteady-state natural convection inside spherical containers partially filled with a porous medium , 1999 .

[73]  K. N. Seetharamu,et al.  Numerical investigation of buoyancy driven flow in a fluid saturated non-Darcian porous medium , 1999 .

[74]  P. Nithiarasu.  Finite element modeling of a leaking third component migration from a heat source buried into a fluid saturated porous medium , 1999 .

[75]  T. C. Jue.  Analysis of heat and fluid flow in partially divided fluid saturated porous cavities , 2000 .

[76]  Kankanhalli N. Seetharamu,et al.  Non-Darcy natural convection in a hydrodynamically and thermally anisotropic porous medium , 2000 .

[77]  P. Nithiarasu.  A comparative study on the performance of two time stepping schemes for convection in a fluid saturated porous medium , 2001 .

[78]  J. Szmelter.  Incompressible flow and the finite element method , 2001 .

[79]  K. Muralidhar,et al.  Analysis of flow and heat transfer in a regenerator mesh using a non-Darcy thermally non-equilibrium model , 2001 .

[80]  O. C. Zienkiewicz,et al.  Natural convection in porous medium‐fluid interface problems ‐ A finite element analysis by using the CBS procedure , 2001 .

[81]  C Thompson,et al.  Applied CFD techniques: An introduction based on finite element methods , 2002 .

[82]  Arnaud G. Malan,et al.  An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part I. Theory and implementation , 2002 .