A Numerical method for three-dimensional parabolic flow and heat transfer in straight ducts of irregular cross section

Computational Thermal Sciences

Volumn 1, Issue 3, 2009, Pages 259-288

  Jesuthasan, Nirmalakanth ^a   Baliga, Bantwal Rabi ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC APPROXIMATION; AXIAL DIRECTION; CO-LOCATED; CONTROL VOLUMES; CROSS SECTION; DEPENDENT VARIABLES; DISCRETIZED EQUATIONS; DOWNSTREAM NODES; ENERGY CONSERVATION EQUATIONS; EXIT PLANES; FLOW AND HEAT TRANSFER; INTERPOLATION FUNCTION; IRREGULAR CROSS-SECTIONS; LAMINAR FORCED CONVECTIONS; PARABOLIC PROBLEMS; SIZE SELECTION; SQUARE CROSS SECTION; STEP SIZE; STEP-BY-STEP; STRAIGHT DUCT; TRIANGULAR CROSS-SECTIONS;

DUCTS; NUMBER THEORY; NUMERICAL METHODS; PRISMS; PROBLEM SOLVING;

THREE DIMENSIONAL;

EID: 78651525898     PISSN: 19402503     EISSN: 19402554     Source Type: Journal    
DOI: 10.1615/ComputThermalScien.v1.i3.20     Document Type: Article

References (39)

1. Akbari, M. and Behzadmehr, A., Developing mixed convection of a nanofluid in a horizontal tube with uniform heat flux, Int. J. Num. Methods Heat Fluid Flow, vol.17, pp. 566-586, 2007.
2. Baliga, B. R. and Atabaki, N., Control-volume-based finite difference and finite element methods, Handbook of Numerical Heat Transfer, 2nd ed., W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy, Eds., Chapter 6, Wiley, Hoboken, NJ, 2006.
3. Baliga, B. R. and Patankar, S. V., A new finite-element formulation for convectiondiffusion problems, Numer. Heat Transfer, vol.3, pp. 393-409, 1980.
4. Beavers, G. S., Sparrow, E. M., and Magnuson, R. A., Experiments on hydrodynami-cally developing flow in rectangular ducts of arbitrary aspect ratio, Int. J. Heat Mass Transfer, vol.13, pp. 689-702, 1970.
5. Brennen, C. E., Fundamentals of Multiphase Flow, Cambridge University Press, Cambridge, England, 2005.
6. Briley, W. R., Numerical method for predicting three-dimensional steady viscous flow in ducts, J. Comp. Physics, vol.14, pp. 8-28, 1974.
7. Caretto, L. S., Curr, R. M., and Spalding, D. B., Two numerical methods for threedimensional boundary layers, Comput. Methods Appl. Mech. Eng., vol.1, pp. 39-57, 1972.
8. Carlson, G. A. and Hornbeck, R. W., A numerical solution of laminar entrance flow in a square duct, J. Appl. Mech., vol.40, pp. 25-30, 1973.
9. Chandrupatla, A. R. and Sastri, V. M. K., Constant wall temperature entry length laminar flow of and heat transfer to a non-Newtonian fluid in a square duct, in Proc. 6th Int. Heat Transfer Conf., Toronto, pp. 323-328, 1978.
10. Choudhury, D. and Patankar, S. V., Combined forced and free laminar convection in the entrance region of an inclined isothermal tube, ASME J. Heat Transfer, vol.110, pp. 901-909, 1988.
11. Crowe, C. T., Multiphase Flow Handbook, Taylor & Francis, Boca Raton, 2006.
12. Daungthongsuk, W. andWongwises, S., A critical review of convective heat transfer of nanofluids, Renewable Sustainable Energy Rev., vol.11, pp. 797-817, 2007. (Pubitemid 44829992)
13. Del Giudice, S., Strada, M., and Comini, G., Three-dimensional laminar flow in ducts, Numer. Heat Transfer, vol.4, pp. 215-228, 1981.
14. Elias, S. R., Stubley, G. D., and Raithby, G. D., An adaptive agglomeration method for additive correction multigrid, Int. J. Num. Methods in Eng., vol.40, pp. 887-903, 1997.
15. Fleming, D. P. and Sparrow, E. M., Flow in the hydrodynamic entrance region of ducts of arbitrary cross-section, ASME J. Heat Transfer, vol.91, pp. 345-354, 1969.
16. Goldstein, R. J. and Kreid, D. K., Measurements of laminar flow development in a square duct using laser-Doppler flowmeter, ASME J. Appl. Mech., vol.34, pp. 813-818, 1967.
17. Jothiprasad, G., Mavriplis, D. J., and Caughey, D. A., Higher-order time integration schemes for the unsteady Navier-Stokes equations on unstructured grids, J. Comput. Phys., vol.191, pp. 542-566, 2003.
18. Kays, W. M. and London, A. L., Compact Heat Exchangers, 3rd ed., McGraw-Hill, New York, 1984.
19. Launder, B. E. and Sandham, N. D., Closure Strategies for Turbulent and Transitional Flows, Cambridge Univ. Press, Cambridge, England, 2002.
20. Liu, J. T., Peng, X. F., and Yan, W. M., Numerical study of fluid flow and heat transfer in microchannel cooling passages, Int. J. Heat Mass Transfer, vol.50, pp. 1855-1864, 2007.
21. Masson, C., Saabas, H. J., and Baliga, B. R., Co-located equal-order control-volume finite element method for two-dimensional axisymmetric incompressible flow, Int. J. Num. Methods in Fluids, vol.18, pp. 1-26, 1994.
22. Morini, G. L., Single-phase convective heat transfer in microchannels: A review of experimental results, Int. J. Thermal Sci., vol.43, pp. 631-651, 2004.
23. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
24. Patankar, S. V. and Baliga, B. R., A new finite-difference scheme for parabolic differential equations, Num. Heat Transfer, vol.1, pp. 27-37, 1978.
25. Patankar, S. V., Ramadhyani, S., and Sparrow, E. M., Effect of circumferentially nonuniform heating on laminar combined convection in a horizontal tube, ASME J. Heat Transfer, vol.100, pp. 63-70, 1978.
26. Patankar, S. V. and Spalding, D. B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat Mass Transfer, vol.15, pp. 1787-1806, 1972.
27. Peng, X. F. and Petersen, G. P., Convective heat transfer and flow friction for water flow in microchannel structures, Int. J. Heat Mass Transfer, vol.39, pp. 2599-2608, 1996.
28. Prakash, C. and Patankar, S. V., 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.
29. Pratap, V. S. and Spalding, D. B., Fluid flow and heat transfer in three-dimensional duct flows, Int. J. Heat Mass Transfer, vol.19, pp. 1183-1188, 1976.
30. Raithby, G. D., Skew upstream difference schemes for problems involving fluid flow, Comput. Methods Appl. Mech. Eng., vol.9, pp. 153-164, 1976.
31. Rhie, C. M. and Chow,W. L., Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA J., vol.21, pp. 1525-1532, 1983.
32. Roberts, D. W. and Forester, C. K., Parabolic procedure for flows in ducts of arbitrary cross-section, AIAA J., vol.17, pp. 33-40, 1979.
33. Saabas, H. J. and Baliga, B. R., A co-located equal-order control-volume finite element method for multidimensional, incompressible fluid flow-Part I: Formulation, Numer. Heat Transfer, Part B, vol.26, pp. 381-407, 1994.
34. Schneider, G. E. and Raw, M. J., A skewed positive influence coefficient upwind procedure for control-volume-based finite element convection-diffusion computation, Num. Heat Transfer, vol.9, pp. 1-26, 1986.
35. Shah, R. K. and London, A. L., Laminar Flow Forced Convection in Ducts, Advances in Heat Transfer, Supp. 1, Academic Press, New York, 1978.
36. Spalding, D. B., A novel finite-difference formulation for differential expressions involving both first and second derivatives, Int. J. Numer. Methods Eng., vol.4, pp. 551-559, 1972.
37. Thompson, B. R., Maynes, D., and Webb, B. W., Characterization of the hydrodynamically developing flow in a microtube using MTV, ASME J. Fluids Eng., vol.127, pp. 1003-1012, 2005.
38. Venditti, D. and Baliga, B. R., An h-adaptive strategy for CVFEM simulations of viscous incompressible flow, CFD 98: Proc. 6th Ann. Conf. CFD Society of Canada, Part VIII, pp. 65-70, Quebec City, 1998.
39. Wilcox, D., Turbulence Modeling for CFD, DCW Industries, La Cañada, CA, 1993.