A finite element free convection model for the side wall heated cavity

Abstract This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the ‘bench mark'solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10 3 –10 6 ) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed.

[1]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[2]  G. D. Davis.  Natural convection of air in a square cavity: A bench mark numerical solution , 1983 .

[3]  Bantwal R. Baliga,et al.  CO-LOCATED EQUAL-ORDER CONTROL-VOLUME FINITE-ELEMENT METHOD FOR MULTIDIMENSIONAL, INCOMPRESSIBLE, FLUID FLOW—PART II: VERIFICATION , 1994 .

[4]  B. R. Baliga,et al.  A CONTROL VOLUME FINITE-ELEMENT METHOD FOR TWO-DIMENSIONAL FLUID FLOW AND HEAT TRANSFER , 1983 .

[5]  B. R. Baliga,et al.  A NEW FINITE-ELEMENT FORMULATION FOR CONVECTION-DIFFUSION PROBLEMS , 1980 .

[6]  M. Yovanovich,et al.  Finite-element solution procedures for solving the incompressible, Navier-Stokes equations using equal order variable interpolation , 1978 .

[7]  O. Zienkiewicz,et al.  Natural Convection in a Square Enclosure by a Finite-Element, Penalty Function Method Using Primitive Fluid Variables , 1978 .

[8]  Suhas V. Patankar,et al.  A CONTROL VOLUME-BASED FINITE-ELEMENT METHOD FOR SOLVING THE NAVIER-STOKES EQUATIONS USING EQUAL-ORDER VELOCITY-PRESSURE INTERPOLATION , 1984 .

[9]  G. Ren,et al.  A finite element solution of the time-dependent incompressible Navier-Stokes equations using a modified velocity correction method , 1993 .

[10]  R. J. Schnipke,et al.  An equal-order velocity-pressure formulation that does not exhibit spurious pressure modes , 1986 .

[11]  E. Oñate,et al.  Finite volumes and finite elements: Two ‘good friends’ , 1994 .

[12]  G. de Vahl Davis,et al.  Natural convection in a square cavity: A comparison exercise , 1983 .

[13]  Mutsuto Kawahara,et al.  A FINITE ELEMENT SCHEME BASED ON THE VELOCITY CORRECTION METHOD FOR THE SOLUTION OF THE TIME-DEPENDENT INCOMPRESSIBLE NAVIER-STOKES EQUATIONS , 1991 .

[14]  C. Prakash,et al.  AN IMPROVED CONTROL VOLUME FINITE-ELEMENT METHOD IFOR HEAT AND MASS TRANSFER, AND FOR FLUID FLOW USING EQUAL-ORDER VELOCITY-PRESSURE INTERPOLATION , 1986 .

[15]  R. Kessler,et al.  Comparison of finite-volume numerical methods with staggered and colocated grids , 1988 .

[16]  Philip M. Gresho,et al.  On the theory of semi‐implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory , 1990 .