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Original Articles

NATURAL CONVECTION IN A SQUARE ENCLOSURE BY A FINITE-ELEMENT, PENALTY FUNCTION METHOD USING PRIMITIVE FLUID VARIABLES

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Pages 315-330 | Published online: 27 Feb 2007

REFERENCES

  • J. O. Wilkes and S. W. Churchill , The Finite-Difference Computation of Natural Convection in a Rectangular Enclosure , AIChE J. , vol. 12 , no. 1 , pp. 161 – 166 , 1966 .
  • J. W. Elder Numerical Experiments with Free Convection in a Vertical Slot , J. Fluid Mech. , vol. 24 , pt. 4 , pp. 823 – 843 , 1966 .
  • G. De Vahl Davis , Laminar Natural Convection in an Enclosed Rectangular Cavity , Int. J. Heat Mass Transfer , vol. 11 , pp. 1675 – 1692 , 1968 .
  • A. Rubel and F. Landis , Numerical Study of Natural Convection in a Vertical Rectangular Enclosure , Phys. Fluids , vol. 12 , suppl. 2 , pp. 208 – 213 , 1969 .
  • R. K. MacGregor and A. F. Emery , Free Convection through Vertical Plane Layers-Moderate and High Prandtl Number Fluids , Trans. ASME, J. Heat Transfer , vol. 91 , pp. 391 – 401 , 1969 .
  • M. E. Newell and F. W. Schmidt , Heat Transfer by Laminar Natural Convection Within Rectangular Enclosures , Trans. ASME, J. Heat Transfer , vol. 92 , pp. 159 – 167 , 1970 .
  • C. Quon , High Rayleigh Number Convection in an Enclosure—A Numerical Study, Phys. Fluids , vol. 15, no. 1, pp. 12–19, 1972.
  • D. E. Cormack , L. G. Leal , and J. H. Seinfeld , Natural Convection in a Shallow Cavity with Differentially Heated End Walls. Part 2. Numerical Solutions , J. Fluid Mech. , vol. 65 , pt. 2 , pp. 231 – 246 , 1974 .
  • O. C. Zienkiewicz , The Finite Element Method, , 3d ed., McGraw-Hill , New York , 1977 .
  • G. Strang and G. J. Fix , An Analysis of the Finite Element Method , Prentice-Hall , Englewood Cliffs , N.J. , 1973 .
  • D. J. Tritton , Physical Fluid Dynamics , Van Nostrand Reinhold , New York , 1977 .
  • A. E. Gill , The Boundary-Layer Regime for Convection in a Rectangular Cavity , J. Fluid Mech. , vol. 26 , pt. 3 , pp. 515 – 536 , 1966 .
  • C. Taylor and P. Hood , A Numerical Solution of the Navier-Stokes Equations using the Finite Element Technique , Comput. Fluids , vol. 1 , pp. 73 – 100 , 1973 .
  • D. K. Gartling and E. B. Becker , Finite Element Analysis of Viscous Incompressible Flow , Methods Appl. Mech. Ens. , vol. 8 , pp. 51 – 60 and 127 – 138 , 1976 .
  • M. Kawahara , N. Yoshimura , K. Nagagawa , and H. Ohsaka , Steady and Unsteady Finite Element Analysis of Incompressible Viscous Fluid , Int. J. Numer. Methods Eng. , vol. 10 , pp. 437 – 456 , 1976 .
  • O. C. Zienkiewicz , R. H. Gallagher , and P. Hood , Newtonian and Non-Newtonian Viscous Incompressible Flow. Temperature Induced Flows , in J. R. Whiteman (ed.), The Mathematics of Finite Elements and Applications , vol. 2 , Academic Press , New York , 1976 .
  • D. K. Gartling , Convective Heat Transfer Analysis by the Finite Element Method , Comput. Methods Appl. Mech. Eng. , vol. 12 , no. 3 , pp. 365 – 382 , 1977 .
  • R. Temam and F. Thomasset , Solution of the Navier-Stokes Equations by Finite Element Methods , Proc. 4th Int. Conf. Numer. Methods Fluid Mech. , pp. 392 – 395 , 1974 .
  • J. N. Reddy , On the Finite Element Method with Penalty for Incompressible Fluid Flow Problems , presented at the Third Conference on the Mathematics of Finite Elements and Applications , Brunei Univ. , England , Apr. 1978 .
  • J. C. Heinrich , R. S. Marshall , and O. C. Zienkiewicz , Penalty Function Solution of Steady-State Navier-Stokes Equations , Dept. of Civil Engineering Rept. C/R/308/78 , Univ. College of Swansea , Wales , 1978 .
  • O. C. Zienkiewicz and P. N. Godbole , Viscous Incompressible Flow with Special Reference to Non-Newtonian (Plastic) Fluids , in R. H. Gallagher , J. T. Oden , C. Taylor , and O. C. Zienkiewicz (eds.), Finite Elements in Fluids , vol. 1 , Wiley , New York , 1975 .
  • B. A. Finlayson , The Method of Weighted Residuals and Variational Principles , Academic Press , New York , 1972 .
  • T. J. R. Hughes , R. L. Taylor , and J. F. Levy , High Reynolds Number, Steady, Incompressible Flows by a Finite Element Method , in R. H. Gallagher , J. T. Oden , C. Taylor , and O. C. Zienkiewicz (eds.), Finite Elements in Fluids , vol. 3 , Wiley , New York , 1978 .
  • R. L. Taylor , Computer Procedures for Finite Element Analysis , in O. C. Zienkiewicz (ed.), The Finite Element Method, , 3d ed., chap. 24 , McGraw-Hill , New York , 1977 .
  • O. C. Zienkiewicz and E. Hinton , Reduced Integration, Function Smoothing and Non-Comformity in Finite Element Analysis (with Special Reference to Thick Plates ), J. Franklin Inst. , vol. 302 , pp. 443 – 461 , 1977 .
  • J. W. Elder , Laminar Free Convection in a Vertical Slot, J. Fluid Mech. , vol. 23, pt. 1, pp. 77–98, 1965.
  • J. C. Heinrich , R. S. Marshall , and O. C. Zienkiewicz , Penalty Function Solution of Coupled Convective and Conductive Heat Transfer , presented at the International Conference on Laminar and Turbulent Flow , Swansea, Wales , 1978 .
  • C. Quon , Free Convection in an Enclosure Revisited , Trans. ASME, J. Heat Transfer , vol. 99 , pp. 340 – 341 , 1977 .
  • R. G. Brooks and S. D. Probert , Heat Transfer between Parallel Walls An Interferometric Investigation , J. Mech. Eng. Sci. , vol. 14 , no. 2 , pp. 107 – 127 , 1972 .

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