Transient Thermal Analysis of Natural Convection in Porous and Partially Porous Cavities

REFERENCES

• A. Carotenuto , N. Massarotti , and A. Mauro , A New Methodology for Numerical Simulation of Geothermal Down-Hole Heat Exchangers , Appl. Therm. Eng. , vol. 48 , pp. 225 – 236 , 2012 .
   Web of Science ®Google Scholar
• E. Holzbecher and Y. Yusa , Numerical Experiments on Free and Forced Convection in Porous Media , Int. J. Heat Mass Transfer , vol. 38 , no. 11 , pp. 2109 – 2115 , 1995 .
   Web of Science ®Google Scholar
• F. Arpino and N. Massarotti , Numerical Simulation of Mass and Energy Transport Phenomena in Solid Oxide Fuel Cells , Energy , vol. 34 , no. 12 , pp. 2033 – 2041 , 2009 .
   Web of Science ®Google Scholar
• F. Arpino , N. Massarotti , and A. Mauro , Three-Dimensional Simulation of Heat and Mass Transport Phenomena in Planar SOFCs , Int. J. Hydrogen Energy , vol. 36 , no. 16 , pp. 10288 – 10301 , 2011 .
   Web of Science ®Google Scholar
• F. Arpino , G. Buonanno , M. Scungio , N. Massarotti , and A. Mauro , A Roboust Artificial Compressibility Algorithm for Turbulent Incompressible Flows in Urban Areas, Second International Conference on Computational Methods for Thermal Problems, Dalian, China, 2011 .
   Google Scholar
• A. Mauro , F. Arpino , N. Massarotti , and P. Nithiarasu , A Novel Single Domain Approach for Numerical Modelling Solid Oxide Fuel Cells , Int. J. Numer. Methods Heat Fluid Flow , vol. 20 , no. 5 , pp. 587 – 612 , 2010 .
   Web of Science ®Google Scholar
• D. A. Nield and A. Bejan , Convection in Porous Media, , 3rd ed. , Springer , New York , 2006 .
   Google Scholar
• E. R. Lapwood , Convection of a Fluid in a Porous Medium , Math. Proc. Cambridge Philos. Soc. , vol. 44 , no. 4 , pp. 508 – 521 , 1974 .
   Google Scholar
• R. A. Wooding , Steady State Free Thermal Convection of Fluid in Saturated Permeable Medium, J. Fluid Mech. , vol. 2, pp. 273–285, 1957.
   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 Dyn. , vol. 7 , pp. 23 – 48 , 1996 .
   Web of Science ®Google Scholar
• H. C. Brinkman , A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles , Appl. Sci. Res. , vol. A1 , pp. 27 – 34 , 1947 .
   Google Scholar
• P. H. Forchheimer , Wasserbewegung Durch Boden , Zeitschrift Verein Deutscher Ingenieure , vol. 45 , no. 50 , pp. 1781 – 1788 , 1901 .
   Google Scholar
• F. C. Lai and F. A. Kulacki , Non-Darcy Mixed Convection Along a Vertical Wall in a Saturated Porous Medium , J. Heat Transfer , vol. 113 , no. 1 , pp. 252 – 255 , 1991 .
   Web of Science ®Google Scholar
• T. J. Chung , Computational Fluid Dynamics , Cambridge University Press , Cambridge , 2002 .
   Google Scholar
• P. Nithiarasu , K. N. Seetharamu , and T. Sundararajan , Double-Diffusive Natural Convection in an Enclosure Filled with Saturated Porous Medium a Generalized Non-Darcy Approach , Num. Heat Transfer , vol. 30 , pp. 413 – 426 , 1996 .
   Web of Science ®Google Scholar
• P. Nithiarasu , K. N. Seetharamu , and T. Sundararajan , Natural Convective Heat Transfer in an Enclosure Filled with Fluid Saturated Variable Porosity Medium , Int. J. Heat Mass Transfer , vol. 40 , pp. 3955 – 3967 , 1997 .
   Web of Science ®Google Scholar
• P. Nithiarasu , K. N. Seetharamu , and T. Sundararajan , Effect of Porosity on Natural Convective Heat Transfer in a Fluid Saturated Porous Medium , Int. J. Heat Fluid Flow , vol. 19 , pp. 56 – 58 , 1998 .
   Web of Science ®Google Scholar
• K. S. S. P. Nithiarasu , T. Sundararajan , and K. N. Seetharamu , Bouyancy Driven Flow in a Non-Darcian, Fluid Saturated Porous Enclosure Subjected to Uniform Heat Flux in a Non-Darcian, Fluid-Saturated Porous Enclosure Subjected to Uniform Heat Flux-A Numerical Study , Commun. Numer. Methods Eng. , vol. 15 , pp. 765 – 776 , 1999 .
   Web of Science ®Google Scholar
• F. Arpino , N. Massarotti , A. Mauro , and P. Nithiarasu , Artificial Compressibility-Based CBS Scheme for the Solution of the Generalized Porous Medium Model , Numer. Heat Transfer, Part B Fundam. , vol. 55 , no. 3 , pp. 196 – 218 , 2009 .
   Web of Science ®Google Scholar
• N. Massarotti , P. Nithiarasu , and A. Carotenuto , Microscopic and Macroscopic Approach for Natural Convection in Enclosures Filled with Fluid Saturated Porous Medium , Int. J. Numer. Methods Heat Fluid Flow , vol. 13 , no. 7 , pp. 862 – 886 , 2003 .
   Web of Science ®Google Scholar
• J. F. Mercier , C. Weisman , M. Firdaouss , and P. Le Quéré , Heat Transfer Associated to Natural Convection Flow in a Partly Porous Cavity , J. Heat Transfer , vol. 124 , pp. 130 – 143 , 2002 .
   Web of Science ®Google Scholar
• A. K. Singh , P. Agnihotri , N. P. Singh , and A. K. Singh , Transient and Non-Darcian Effects on Natural Convection Flow in a Vertical Channel Partially Filled with Porous Medium: Analysis with Forchheimer–Brinkman Extended Darcy Model , Int. J. Heat Mass Transfer , vol. 54 , pp. 1111 – 1120 , 2011 .
   Web of Science ®Google Scholar
• M. Hajipour and A. M. Dehkordi , Transient Behavior of Fluid Flow and Heat Transfer in Vertical Channels Partially Filled with Porous Medium: Effects of Inertial Term and Viscous Dissipation , Energy Convers. Manage. , vol. 61 , pp. 1 – 7 , 2012 .
   Web of Science ®Google Scholar
• A. Bejan and A. D. Kraus , Heat Transfer Handbook , John Wiley & Sons , New Jersey , 2003 .
   Google Scholar
• S. Saeid and I. Pop , Transient Free Convection in a Square Cavity Filled with a Porous Medium , Int. J. Heat Mass Transfer , vol. 47 , pp. 1917 – 1924 , 2004 .
   Web of Science ®Google Scholar
• A. J. Chorin , A Numerical Method for Solving Incompressible Viscous Flow Problems , J. Comput. Phys. , vol. 135 , pp. 118 – 125 , 1997 .
   Web of Science ®Google Scholar
• P. Nithiarasu , An Efficient Artificial Compressibility (AC) Scheme Based on Split (CBS) Method for Incompressible Flows , Int. J. Numer. Methods Eng. , vol. 56 , pp. 1815 – 1845 , 2003 .
   Web of Science ®Google Scholar
• A. G. Malan , R. W. Lewis , and P. Nithiarasu , An Improved Unsteady, Unstructured, Artificial Compressibility, Finite Volume Scheme for Viscous Incompressible Flows, Part I: Theory and Implementation , Int. J. Numer. Methods Eng. , vol. 54 , pp. 695 – 714 , 2002 .
   Web of Science ®Google Scholar
• E. Turkel , Review of Preconditioning Methods for Fluid Dynamics, Appl. Numer. Math. , vol. 12, pp. 257–284, 1993.
   Web of Science ®Google Scholar
• J. W. Weiss and W. A. Smith , Preconditioning Applied to Variable and Constant Density Flows , AIAA J. , vol. 33 , pp. 2050 – 2057 , 1995 .
   Google Scholar
• A. L. Gaitonde , A Dual-Time Method for Two-Dimensional Unsteady Incompressible Flow Calculations , Int. J. Numer. Methods Eng. , vol. 41 , pp. 1153 – 1166 , 1998 .
   Web of Science ®Google Scholar
• Y. H. Choi and C. L. Merkle , The Application of Preconditioning in Viscous Flows , J. Comput. Phys. , vol. 105 , pp. 207 – 223 , 1993 .
   Web of Science ®Google Scholar
• E. Turkel , Preconditioning Methods for Solving the Incompressible and Low Speed Compressible Equations , J. Comput. Phys. , vol. 72 , pp. 227 – 298 , 1987 .
   Web of Science ®Google Scholar
• H. Cabak , C. H. Sung , and V. Modi , Explicit Runge–Kutta method for Three-Dimensional Internal Incompressible Flows , AIAA J. , vol. 30 , pp. 2024 – 2031 , 1992 .
   Google Scholar
• P. Tamamidis , G. Zhang , and D. N. Assanis , Comparison of Pressure-Based and Artificial Compressibility Methods for Solving 3D Steady Incompressible Viscous Flows , J. Comput. Phys. , vol. 124 , pp. 1 – 13 , 1996 .
   Web of Science ®Google Scholar
• F. B. Lin and F. Sotiropoulos , Assessment of Artificial Dissipation Models for Three-Dimensional Incompressible Flow Solutions , J. Fluids Eng. (ASME) , vol. 119 , pp. 331 – 340 , 1997 .
   Web of Science ®Google Scholar
• Y. Zhao and B. L. Zhang , A High-Order Characteristics Upwind FV Method for Incompressible Flow and Heat Transfer Simulation on Unstructured Grids , Comput. Methods Appl. Mech. Eng. , vol. 190 , pp. 733 – 756 , 2000 .
   Web of Science ®Google Scholar
• M. T. Manzari , An Explicit Finite Element Algorithm for Convection Heat Transfer Problems , Int. J. Numer. Methods Heat Fluid Flow , vol. 9 , pp. 860 – 877 , 1999 .
   Web of Science ®Google Scholar
• E. Kim , A Mixed Galerkin Method for Computing the Flow Between Eccentric Rotating Cylinders , Int. J. Numer. Methods Fluids , vol. 26 , pp. 877 – 885 , 1998 .
   Web of Science ®Google Scholar
• T. Wasfy , A. C. West , and V. Modi , Parallel Finite Element Computation of Unsteady Incompressible Flows , Int. J. Numer. Methods Fluids , vol. 26 , pp. 17 – 37 , 1998 .
   Web of Science ®Google Scholar
• F. Arpino , A. Carotenuto , N. Massarotti , and A. Mauro , New Solutions for Axial Flow Convection in Porous and Partly Porous Cylindrical Domains , Int. J. Heat Mass Transfer , vol. 57 , no. 1 , pp. 155 – 170 , 2013 .
   Web of Science ®Google Scholar
• F. Arpino , A. Carotenuto , N. Massarotti , and P. Nithiarasu , A Robust Model and Numerical Approach for Solving Solid Oxide Fuel Cell (SOFC) Problems , Int. J. Numer. Methods Heat Fluid Flow , vol. 18 , no. 7–8 , pp. 811 – 834 , 2008 .
   Web of Science ®Google Scholar
• F. Arpino , N. Massarotti , and A. Mauro , A Stable Explicit Fractional Step Procedure for the Solution of Heat and Fluid Flow Through Interfaces Between Saturated Porous Media and Free Fluids in Presence of High Source Terms , Int. J. Numer. Methods Eng. , vol. 83 , no. 6 , pp. 671 – 692 , 2010 .
   Web of Science ®Google Scholar
• F. Arpino , N. Massarotti , and A. Mauro , High Rayleigh Number Laminar-Free Convection in Cavities: New Benchmark Solutions , Numer. Heat Transfer, Part B Fundam. , vol. 58 , no. 2 , pp. 73 – 97 , 2010 .
   Web of Science ®Google Scholar
• F. Arpino , N. Massarotti , and A. Mauro , Efficient Three-Dimensional FEM Based Algorithm for the Solution of Convection in Partly Porous Domains , Int. J. Heat Mass Transfer , vol. 54 , pp. 4495 – 4506 , 2011 .
   Web of Science ®Google Scholar
• F. Arpino , N. Massarotti , A. Mauro , and P. Nithiarasu , Artificial Compressibility Based CBS Solutions for Double Diffusive Natural Convection in Cavities , Int. J. Numer. Methods Heat Fluid Flow , vol. 23 , no. 1 , pp. 205 – 225 , 2013 .
   Web of Science ®Google Scholar
• O. C. Zienkiewicz , R. L. Taylor , and P. Nithiarasu , The Finite Element Method for Fluid Dynamics , 6th ed. , Elsevier, Butterworth and Heinemann , Oxford , USA , 2005 .
   Google Scholar
• K. Morgan and J. Peraire , Unstructured Grid Finite Element Methods for Fluid Mechanics , Reports on Progress in Physics , vol. 61 , no. 9 , 1998 .
   Google Scholar
• R. Lohner , Applied CFD Techniques , John Wiley & Sons , New York , NY , 2001 .
   Google Scholar
• N. Massarotti , F. Arpino , R. W. Lewis , and P. Nithiarasu , Explicit and Semi-Implicit CBS Procedures for Incompressible Viscous Flows, Int. J. Numer. Methods Eng. , vol. 66, no. 10, pp. 1618–1640, 2006.
   Web of Science ®Google Scholar
• A. G. Malan , R. W. Lewis , and P. Nithiarasu , An Improved Unsteady, Unsctructured, Artificial Compressibility, Finite Volume Scheme for Viscous Incompressible Flows: Part II . Appl. Int. J. Numer. Methods Eng. , vol. 54 , pp. 715 – 729 , 2002 .
   Web of Science ®Google Scholar
• S. Whitaker , Diffusion and Dispersion in Porous Media , AIChE J. , vol. 13 , pp. 420 – 427 , 1961 .
   Web of Science ®Google Scholar
• C. T. Hsu and P. Cheng , Thermal Dispersion in a Porous Medium , Int. J. Heat Mass Transfer , vol. 33 , pp. 1589 – 1597 , 1990 .
   Google Scholar
• R. W. Lewis , P. Nithiarasu , and K. N. Seetharamu , Fundamentals of the Finite Element Method for Heat and Fluid Flow , John Wiley & Sons , Chichester , 2004 .
   Google Scholar
• J. S. Shuen , K. H. Chen , and Y. Choi , A Coupled Implicit Method for Chemical Non-Equilibrium Flows at All Speeds , J. Comput. Phys. , vol. 106 , no. 2 , pp. 306 – 318 , 1993 .
   Google Scholar
• S. E. Rogers and D. Kwak , Steady and Unsteady Solutions of the Incompressible Navier–Stokes Equations , AIAA J. , vol. 29 , no. 4 , pp. 603 – 610 , 1991 .
   Google Scholar
• O. C. Zienkiewicz and R. L. Taylor , The Finite Element Method, Vol 3, Fluid Dynamics , Butterworth and Heinemann , Oxford , 2000 .
   Google Scholar
• P. Nithiarasu , R. L. T. Bevan , and K. Murali , An Artificial Compressibility Based Fractional Step Method for Solving Time Dependent Incompressible Flow Equations. Temporal Accuracy and Similarity with a Monolithic Method , Comput. Mech. , vol. 51 , no. 3 , pp. 255 – 260 , 2013 .
   Web of Science ®Google Scholar
• N. Massarotti , P. Nithiarasu , and O. C. Zienkiewicz , Natural Convection in Porous Medium-Fluid Interface Problems , Int. J. Numer. Methods Heat Fluid Flow , vol. 11 , no. 5 , pp. 473 – 490 , 2001 .
   Web of Science ®Google Scholar
• M. A. Christon , P. M. Gresho , and S. B. Sutton , Computational Predictability of Time-Dependent Natural Convection Flows in Enclosures (Including a Benchmark Solution) , Int. J. Numer. Methods Fluids , vol. 40 , pp. 953 – 980 , 2002 .
   Web of Science ®Google Scholar
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   Google Scholar