The complex nature of the convective terms in the fluid flow governing equations has caused many researchers to work on estimating more accurate advection term magnitudes by employing better approximate expressions. The trend of progress has been to include more physics of flow in the approximations. However, there is no archival evidence that reports the direct implementation of buoyancy as a physical influence in the advection term modeling. In this work, the influence of buoyancy in an efficient advection term expression is investigated in a control volume context with a collocated grid arrangement. The accuracy of the results obtained by both excluding and including the buoyancy term is evaluated through application to the natural convection heat transfer problem in a cavity at different Rayleigh numbers.
Issue Section:
Technical Papers
1.
Kelleher, M. D., and Yovanovich, M. M., 1981, “Heat Transfer in Electronic Equipment,” ASME HTD-Vol. 20.
2.
Yovanovich, M. M., 1991, “Theory and Applications of Constriction and Spreading Resistance Concepts for Microelectronic Thermal Management,” Cooling Techniques for Computers, ed., W. Aung, Hemisphere Publ. Corp., Washington, DC, pp. 277–332.
3.
Yovanovich, M. M., Lee, S., and Gayowsky, T. J., 1992, “Approximate Analytic Solution of Laminar Forced Convection from an Isothermal Plate,” AIAA Pap., 92-0248.
4.
Yovanovich, M. M., 1983, “Non-Iterative Control Volume Approach to One-Dimensional Steady Conduction with Convection—Applications to Extended Surfaces, Heat Transfer in Electronic Equipment,” Proc., ASME Symposium, Boston, MA, pp. 59–69.
5.
Ahmed
, G. R.
, and Yovanovich
, M. M.
, 1992
, “Numerical Study of Natural Convection from Discrete Heat Sources in a Vertical Square Enclosure
,” J. Thermophys. Heat Transfer
, 6
, pp. 121
–12
; also, AIAA Paper 90-0256.6.
Wang
, C. S.
, Yovanovich
, M. M.
, and Culham
, J. R.
, 1999
, “Modeling Natural Convection from Horizontal Isothermal Annular Heat Sinks
,” ASME J. Electron. Packag.
, 121
, pp. 44
–49
.7.
Yovanovich, M. M., 1993, “General Expression for Laminar Forced and Natural Convection Heat Transfer from Isothermal Flat Plates for all Prandtl Numbers,” AIAA Pap., 93-2750.
8.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publ. Co., New York, NY.
9.
Spalding
, D. B.
, 1972
, “A Novel Finite-Difference Formulation for Differential Expressions Involving both First and Second Derivatives
,” Int. J. Numer. Methods Eng.
, 4
, pp. 551
–559
.10.
Raithby
, G. D.
, and Torrance
, K. E.
, 1974
, “Upstream-Weighted Differencing Schemes and their Application to Elliptic Problems Involving Fluid Flow
,” Comput. Fluids
, 2
, pp. 191
–206
.11.
Raithby
, G. D.
, 1976
, “Skew Upstream Differencing Schemes for Problems Involving Fluid Flow
,” Comput. Methods Appl. Mech. Eng.
, 9
, pp. 153
–164
.12.
Van Doormal, J. P., and Raithby, G. D., 1987, “Evaluation of New Techniques for the Calculation of Internal Recirculating Flows,” AIAA Pap., 87-0059.
13.
Leonard
, B. P.
, 1979
, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation
,” Comput. Methods Appl. Mech. Eng.
, 19
, pp. 59
–98
.14.
Pollard
, A.
, and Siu
, A.
, 1982
, “The Calculation of Some Laminar Flows Using Various Discretization Schemes
,” Comput. Methods Appl. Mech. Eng.
, 35
, pp. 293
–313
.15.
Hughes, T. J. R., and Brooks, A., 1979, “A Multi-dimensional Upwind Scheme with no Cross Wind Diffusion,” Proc., ASME Symposium on Finite Element Methods for Convection Dominated Flows, New York, NY, pp. 19–35.
16.
Rhie
, C. M.
, and Chow
, W. L.
, 1983
, “Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation
,” AIAA J.
, 21
(11
), pp. 1525
–1532
.17.
Schneider
, G. E.
, and Raw
, M. J.
, 1986
, “A Skewed, positive Influence Coefficient Upwinding Procedure for Control-Volume-Based Finite-Element Convection-Diffusion Computation
,” Numer. Heat Transfer, Part A
, 9
, pp. 1
–26
.18.
Prakash
, C.
, 1987
, “Examination of the Upwind (Donor-Cell) Formulation in Control Volume Finite-Element Methods for Fluid Flow and Heat Transfer
,” Numer. Heat Transfer, Part A
, 11
, pp. 401
–416
.19.
Blackwell, B., and Pepper, D. W., 1992, “Benchmark Problems for Heat Transfer Codes,” ASME HTD-Vol. 222.
20.
Darbandi, M., and Schneider, G. E., 1999, “The Influence of Buoyancy on the Correct Algebraic Modeling of Advection,” Proc., 7th Annual Conference of the CFD Society of Canada (Halifax, Canada), CFDSC, Ottawa, ON, Canada, pp. 4-15–4-23.
21.
Schneider
, G. E.
, and Raw
, M. J.
, 1987
, “Control Volume Finite Element Method for Heat Transfer and Fluid Flow Using Co-located Variables—1. Computational Procedure
,” Numer. Heat Transfer
, 11
(4
), pp. 363
–390
.22.
Armfield, S. W., 1990, “Finite Difference Solutions of the Navier-Stokes Equations on Staggered and Nonstaggered Grids,” Proc., Fourth International Conference, Griffith University, Brisbane, Hemisphere Publ. Corp., New York, NY, pp. 287–294.
23.
Schneider
, G. E.
, Raithby
, G. D.
, and Yovanovich
, M. M.
, 1978
, “Finite-Element Solution Procedures for Solving the Incompressible, Navier-Stokes Equations Using Equal Order Variable Interpolation
,” Numer. Heat Transfer
, 1
, pp. 433
–451
.24.
Karimian, S. M. H., and Schneider, G. E., 1994, “Numerical Solution of Two Dimensional Incompressible Navier-Stokes Equations: Treatment of Velocity-Pressure Coupling,” AIAA Pap., 94-2359.
25.
Darbandi
, M.
, and Schneider
, G. E.
, 1997
, “Momentum Variable Procedure for Solving Compressible and Incompressible Flows
,” AIAA J.
, 35
(12
), pp. 1801
–1805
; also, AIAA Paper 96-0605.26.
De Vahl Davis
, G.
, 1983
, “Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution
,” Int. J. Numer. Methods Fluids
, 3
, pp. 249
–264
.27.
Hortmann
, M.
, Peric
, M.
, and Scheuerer
, G.
, 1990
, “Finite Volume Multigrid Prediction of Laminar Natural Convection: Bench-Mark Solutions
,” Int. J. Numer. Methods Fluids
, 11
, pp. 189
–207
.28.
Elder
, J. W.
, 1965
, “Turbulent Free Convection in a Vertical Slot,” Part 1
, J. Fluid Mech.
, 23
, pp. 99
–111
.29.
Darbandi
, M.
, and Schneider
, G. E.
, 1999
, “Application of an All-Speed Flow Algorithm to Heat Transfer Problems
,” Numer. Heat Transfer, Part A
, 35
, pp. 695
–715
.Copyright © 2003
by ASME
You do not currently have access to this content.
