Implementation of the Stress Jump Condition in a Control-Volume Finite-Element Method for the Simulation of Laminar Coupled Flows in Adjacent Open and Porous Domains

REFERENCES

• J. Bear , Dynamics of Fluids in Porous Media , Dover , New York , 1988 .
   Google Scholar
• M. Kaviany , Principles of Heat Transfer in Porous Media, , 2nd ed. , Springer-Verlag , New York , 1995 .
   Google Scholar
• D. A. Nield and A. Bejan , Convection in Porous Media, , 3rd ed. , Springer-Verlag , New York , 2006 .
   Google Scholar
• G. S. Beavers and D. D. Joseph , Boundary Conditions of a Naturally Permeable wall , J. Fluid Mech. , vol. 30 , pp. 197 – 207 , 1967 .
   Web of Science ®Google Scholar
• G. I. Taylor , A Model for the Boundary Condition of a Porous Material , J. Fluid Mech. , vol. 49 , pp. 319 – 326 , 1971 .
   Web of Science ®Google Scholar
• S. Richardson , A Model for the Boundary Condition of a Porous Material , J. Fluid Mech. , vol. 49 , part 2 , pp. 327 – 336 , 1971 .
   Web of Science ®Google Scholar
• G. H. Neale and W. K. Nader , Practical Significance of Brinkman's Extension on Darcy Flow: Coupled Parallel Flows with a Channel and a Bounding Porous Medium, Can. J. Chem. Eng. , vol. 52, pp. 475–478, 1974.
   Web of Science ®Google Scholar
• K. Vafai and C. L. Tien , Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media , Int. J. Heat Mass Transfer , vol. 24 , pp. 195 – 203 , 1981 .
   Web of Science ®Google Scholar
• K. Vafai and R. Thiyagaraja , Analysis of Flow and Heat Transfer at the Interface Region of a Porous Medium , Int. J. Heat Mass Transfer , vol. 30 , pp. 1391 – 1405 , 1987 .
   Web of Science ®Google Scholar
• K. Vafai and S. J. Kim , Fluid Mechanics at the Interface Region between a Porous Medium and a Fluid Layer—An Exact Solution , Int. J. Heat Fluid Flow , vol. 11 , pp. 254 – 256 , 1990 .
   Web of Science ®Google Scholar
• J. Y. Jang and J. L. Chen , Forced Convection in a Parallel Plate Channel Partially Filled with a High Porosity Medium , Int. Commun. Heat Mass Transfer , vol. 19 , p. 263 – 273 , 1992 .
   Web of Science ®Google Scholar
• J. A. Ochoa-Tapia and S. Whitaker , Momentum Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid I: Theoretical Development , Int. J. Heat Mass Transfer , vol. 38 , pp. 2635 – 2646 , 1995 .
   Web of Science ®Google Scholar
• J. A. Ochoa-Tapia and S. Whitaker , Momentum Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid II: Comparison with Experiment , Int. J. Heat Mass Transfer , vol. 40 , pp. 2647 – 2655 , 1995 .
   Google Scholar
• A. V. Kuznetsov , Analytical Investigation of the Fluid Flow at the Interface Region between a Porous Medium and a Clear Fluid in Channels Partially Filled with a Porous Medium , Appli. Sci. Res. , vol. 56 , pp. 53 – 67 , 1996 .
   Google Scholar
• A. V. Kuznetsov , Influence of the Stress Jump Condition at the Porous-Medium/Clear Fluid Interface on a Flow at a Porous Wall , Int. Commun. Heat Mass Transfer , vol. 24 , pp. 401 – 410 , 1997 .
   Google Scholar
• J. A. Ochoa-Tapia and S. Whitaker , Heat Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid , Int. J. Heat Mass Transfer , vol. 40 , pp. 2691 – 2707 , 1997 .
   Web of Science ®Google Scholar
• J. A. Ochoa-Tapia and S. Whitaker , Heat Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid: The One Equation Model , J. Porous Media , vol. 1 , pp. 31 – 46 , 1998 .
   Web of Science ®Google Scholar
• A. V. Kuznetsov , Analytical Investigation of Couette Flow in a Composite Channel Partially Filled with a Porous Medium and Partially Filled with a Clear Fluid , Int. J. Heat Mass Transfer , vol. 41 , pp. 2556 – 2560 , 1998 .
   Google Scholar
• A. V. Kuznetsov , Analytical Study of the Fluid Flow and Heat Transfer During Forced Convection in a Composite Channel Partially Filled with a Brinkman-Forchheimer Porous Medium, Flow , Turbulence Combustion , vol. 60 , pp. 173 – 192 , 1998 .
   Web of Science ®Google Scholar
• J. A. Ochoa-Tapia and S. Whitaker , Momentum Jump Condition at the Boundary between a Porous Medium and a Homogeneous Fluid: Inertial Effects , J. Porous Media , vol. 1 , pp. 201 – 217 , 1998 .
   Web of Science ®Google Scholar
• M. K. Alkam and M. A. Al-Nimr , Transient Non-Darcian Forced Convection Flow in a Pipe Partially Filled with a Porous Material , Int. J. Heat Mass Transfer , vol. 41 , pp. 347 – 356 , 1998 .
   Web of Science ®Google Scholar
• A. V. Kuznetsov , Fluid Mechanics and Heat Transfer in the Interface Region between a Porous Medium and a Fluid Layer: A Boundary Layer Solution , J. Porous Media , vol. 2 , pp. 309 – 321 , 1999 .
   Web of Science ®Google Scholar
• B. Alazmi and K. Vafai , Analysis of Variants within the Porous Media Transport Models , ASME J. Heat Transfer , vol. 122 , pp. 303 – 326 , 2000 .
   Web of Science ®Google Scholar
• B. Alazmi and K. Vafai , Analysis of Fluid Flow and Heat Transfer Interfacial Conditions between a Porous Medium and a Fluid Layer , Int. J. Heat Mass Transfer , vol. 44 , pp. 1735 – 1749 , 2001 .
   Web of Science ®Google Scholar
• D. F. James and A. M. J. Davis , Flow at the Interface of a Model Fibrous Porous Medium, J. Fluid Mech. , vol. 426, pp. 47–72, 2001.
   Google Scholar
• B. Goyeau , D. Lhuillier , D. Gobin , and M. G. Velarde , Momentum Transport at a Fluid-Porous Interface , Int. J. Heat Mass Transfer , vol. 46 , pp. 4071 – 4081 , 2003 .
   Web of Science ®Google Scholar
• M. Chandesris and D. Jamet , Boundary Conditions at a Planar Fluid-Porous Interface for a Poiseuille Flow , Int. J. Heat Mass Transfer , vol. 49 , pp. 2137 – 2150 , 2006 .
   Web of Science ®Google Scholar
• M. Chandesris and D. Jamet , Boundary Conditions at a Fluid-Porous Interface: An a Priori Estimation of the Stress Jump Coefficients , Int. J. Heat Mass Transfer , vol. 50 , pp. 3422 – 3436 , 2007 .
   Web of Science ®Google Scholar
• A. G. Salinger , R. Aris , and J. J. Derby , Finite Element Formulations for Large-Scale, Coupled Flows in Adjacent Porous and Open Fluid Domains , Int. J. Numer. Meth. Fluids vol. 18 , pp. 1185 – 1209 , 1994 .
   Web of Science ®Google Scholar
• D. K. Gartling , C. E. Hickox , and R. C. Givler , Simulation of Coupled Viscous and Porous Flow Problems , Comput. Fluid Dynam. , vol. 7 , pp. 23 – 48 , 1996 .
   Web of Science ®Google Scholar
• R. A. Silva and M. J. S. De Lemos , Numerical Analysis of the Stress Jump Interface Condition for Laminar Flow over a Porous Layer , Numer. Heat Transfer A , vol. 43 , pp. 603 – 617 , 2003 .
   Web of Science ®Google Scholar
• V. A. F. Costa , L. A. Oliveira , B. R. Baliga , and A. C. M. Sousa , Simulation of Coupled Flows in Adjacent Porous and Open Domains Using a Control Volume Finite Element Method , Numer. Heat Transfer A , vol. 45 , pp. 675 – 697 , 2004 .
   Web of Science ®Google Scholar
• L. Betchen , A. G. Straatman , and B. E. Thompson , A Nonequilibrium Finite-Volume Model for Conjugate Fluid/Porous/Solid Domains , Numer. Heat Transfer A , vol. 49 , pp. 543 – 565 , 2006 .
   Web of Science ®Google Scholar
• P. Yu , T. S. Lee , Y. Zheng , and H. T. Low , A Numerical Method for Flows in Porous and Homogenous Fluid Domains Coupled at the Interface by Stress Jump , Int. J. Numer. Meth. Fluids , vol. 53 , pp. 1755 – 1775 , 2007 .
   Web of Science ®Google Scholar
• G. K. Batchelor , An Introduction to Fluid Dynamics , Cambridge University Press , Cambridge , U.K. , 1967 .
   Google Scholar
• F. M. White , Viscous Fluid Flow, , 2nd ed. , McGraw-Hill , New York , 1991 .
   Google Scholar
• D. A. Nield , The Limitations of the Brinkman-Forchheimer Equations in Modeling Flow in a Saturated Porous Medium and at an Interface , Int. J. Heat Fluid Flow , vol. 12 , pp. 269 – 272 , 1991 .
   Web of Science ®Google Scholar
• S. Whitaker , The Forchheimer Equation: A Theoretical Development , Transp. Porous Media , vol. 25 , pp. 26 – 61 , 1996 .
   Google Scholar
• V. A. F. Costa and L. A. Oliveira , A Control Volume Based Finite Element Method for Two-Dimensional Steady Fluid Flow, Heat Transfer, and Related Phenomena , Proc. III Encontro de Mecânica Computacional , vol. 2 , pp. F10.1 – F10.15 , F. C. T. da Universidade de Coimbra , Coimbra , Portugal , 1992 .
   Google Scholar
• V. A. F. Costa , L. A. Oliveira , and A. R. Figueiredo , A Control Volume Based Finite Element Method for Three-Dimensional Incompressible Turbulent Fluid Flow, Heat Transfer, and Related Phenomena , Int. J. Numer. Meth. Fluids , vol. 21 , pp. 591 – 613 , 1995 .
   Google Scholar
• V. A. F. Costa , Numerical Modeling of Three-Dimensional Incompressible Flows through a Control Volume Finite Element Method (in Portuguese) , Ph.D. thesis , F. C. T. da Universidade de Coimbra , Coimbra , Portugal , 1995 .
   Google Scholar
• C. Masson , H. J. Saabas , and B. R. Baliga , Co-Located Equal-Order Control-Volume Finite Element Method for Two-Dimensional Axisymmetric Incompressible Fluid Flow , Int. J. Num. Meth. Fluids , vol. 18 , pp. 1 – 26 , 1994 .
   Web of Science ®Google Scholar
• H. J. Saabas and B. R. Baliga , Co-located Equal-Order Control-Volume Finite-Element Method for Multidimensional, Incompressible, Fluid Flow—Part I: Formulation , Numer. Heat Transfer B , vol. 26 , pp. 381 – 407 , 1994 .
   Web of Science ®Google Scholar
• B. R. Baliga , Control-Volume Finite Element Methods for Fluid Flow and Heat Transfer, in W. J. Minkowycz , and E. M. Sparrow (eds.), Advances in Numerical Heat Transfer , vol. 1, chap. 3, Taylor & Francis , New York, 1997.
   Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere/McGraw-Hill , Washington , DC , 1980 .
   Google Scholar
• S. Whitaker , The Method of Volume Averaging , Kluwer , Dordrecht , The Netherlands , 1999 .
   Google Scholar
• F. A. L. Dullien , Porous Media: Fluid Transport and Pore Structure, , 2nd ed. , Academic Press , New York , 1992 .
   Google Scholar
• S. Ergun , Fluid Flow Through Packed Columns , Chem. Eng. Prog. , vol. 48 , pp. 89 – 94 , 1952 .
   Web of Science ®Google Scholar
• I. F. Macdonald , M. S. El-Sayed , K. Mow , and F. A. L. Dullien , Flow through Porous Media—Ergun Equation Revisited , Ind. Eng. Chem. Fund. , vol. 18 , pp. 199 – 208 , 1979 .
   Web of Science ®Google Scholar
• J. P. du Plessis , Analytical Quantification of Coefficients in the Ergun equation for Fluid Friction in a Packed Bed , Transp. Porous Media , vol. 16 , pp. 189 – 207 , 1994 .
   Google Scholar
• C. Prakash , and S. V. Patankar , A Control-Volume-Based Finite-Element Method for Solving the Navier-Stokes Equations Using Equal-Order Velocity-Pressure Interpolation , Numer. Heat Transfer , vol. 8 , pp. 259 – 280 , 1985 .
   Web of Science ®Google Scholar
• C. M. Rhie , and W. L. Chow , Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , AIAA J. , vol. 21 , pp. 1525 – 1532 , 1983 .
   Google Scholar
• M. Peric , R. Kessler , and G. Scheurer , Comparison of Finite Volume Numerical Methods with Staggered and Co-located Grids , Comput. Fluids , vol. 16 , pp. 389 – 403 , 1988 .
   Web of Science ®Google Scholar
• S. V. Patankar , C. H. Liu , and E. M. Sparrow , Fully Developed Flow and Heat Transfer in Ducts Heaving Streamwise-Periodic Variations of Cross-Sectional Area , ASME J. Heat Transfer , vol. 99 , pp. 180 – 186 , 1977 .
   Web of Science ®Google Scholar
• K. K. Chawla , Composite Materials: Science and Engineering, , 2nd ed. , Springer-Verlag , New York , 1998 .
   Google Scholar