NUMERICAL STUDY OF COMBINED CONVECTION HEAT TRANSFER FOR THERMALLY DEVELOPING UPWARD FLOW IN A VERTICAL CYLINDER

Abstract

The problem of the laminar upward mixed convection heat transfer for thermally developing air flow in the entrance region of a vertical circular cylinder under buoyancy effect and wall heat flux boundary condition has been numerically investigated. An implicit finite difference method and the Gauss elimination technique have been used to solve the governing partial differential equations of motion (Navier Stocks equations) for two-dimensional model. This investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m2 to 400 W/m2. The results present the dimensionless temperature profile, dimensionless velocity profile, dimensionless surface temperature along the cylinder, and the local Nusselt number variation with the dimensionless axial distance Z+. The dimensionless velocity and temperature profile results have revealed that the secondary flow created by natural convection have a significant effect on the heat transfer process. The results have also shown an increase in the Nusselt number values as the heat flux increases. The results have been compared with the available experimental study and with the available analytical solution for pure forced convection in terms of the local Nusselt number. The comparison has shown satisfactory agreement.

Keywords

Dates

  • Submission Date2006-11-13
  • Revision Date2007-01-24
  • Acceptance Date2007-09-27

DOI Reference

10.2298/TSCI0802089M

References

  1. Bergles, A. E., Simonds, R. R., Combined Forced and Free Convection for Laminar Flow in a Horizontal Tube with Uniform Heat Flux, Int. J. Heat and Mass Transfer, 14 (1971), 12, pp.1989-2000
  2. Aung, W., Mixed Convection in Internal Flow, in: Handbook of Single-Phase Convective Heat Transfer (Eds. S. Kakac, R. K. Shah, W. Aung), John Wiley and Sons, Inc., New York, USA, 1987, pp. 15.1-15.51
  3. Yousef, W. W., Tarasuk, J. D., Free Convection Effects on Laminar Forced Convective Heat Transfer in a Horizontal Isothermal Tube, J. Heat Transfer, ASME Trans., 104 (1982), 2, pp. 145-152
  4. Hallman, T. M., Combined Forced and Free Laminar Heat Transfer in Vertical Tubes with Uniform Heat Generation, J. Heat Transfer, ASME Trans., 78 (1956), 8, pp. 1831-1841
  5. Mori, Y., et al., Forced Convective Heat Transfer in Uniformly Heated Horizontal Tubes, J. Heat and Mass Transfer, 9 (1966), 5, pp. 453- 463
  6. Kemeny, G. A., Somers, E. V., Combined Free and Forced Convective Flow in Vertical Circular Tubes - Experiments with Water and Oil, ASME paper, No. 61-WA-161 (1961), pp. 1-7
  7. Marner, W. J., McMillan, H. K., Combined Free and Forced Convection Laminar in a Vertical Tube with Constant Wall Temperature, J. Heat Transfer, ASME Trans., 92 (1970), Ser. C(4), pp. 559-561
  8. Zeldin, B., Schmidt, F. W, Developing Flow with Combined Forced-Free Convection in an Isothermal Vertical Tube, J. Heat Transfer, ASME Trans., 94 (1972), Ser. C(2), pp. 211-223
  9. Jackson, J. D., Cotton, M. A., Axcell, B. P., Studies of Mixed Convection in Vertical Tubes, Int. J. Heat and Fluid Flow, 10 (1989), 1, pp. 2-15
  10. Barozzi, G. S., Zanchini, E., Mariotti, M., Experimental Investigation of Combined Forced and Free Convection in Horizontal and Inclined Tubes, Meccanica, 20 (1985), 1, pp. 18-27
  11. Orfi, J., Galanis, N., Nguyen, C. T., Simultaneous Development of a Laminar Flow Inside an Inclined Tube with Mixed Convection (in French), Revue Générale de Thermique, 36 (1997), 2, pp. 83-92
  12. Wang, M., Tsuji, T., Nagano, Y., Mixed Convection with Flow Reversed in the Thermal Entrance Region of Vertical Pipes, J. Heat Transfer, ASME Trans., 37 (1994), 15, pp. 2305-2319
  13. Joye, D. D., Jacobs, S. W., Back Flow in the Inlet Region of Opposing Mixed Convection Heat Transfer in a Vertical Tube, Proceedings, 10th International Heat Transfer Conference, Brighten, UK, 1994, paper 12-NM-26, pp. 489-494
  14. Nesreddine, H., Galanis, N., Nguyen, C. T., Variable-Property Effects in Laminar Aiding and Opposing Mixed Convection of Air in Vertical Tubes, Numer. Heat Transf., Part A, 31 (1997), 1, pp. 53-69
  15. Nesreddine, H., Galanis, N., Nguyen, C. T., Effects of Axial Diffusion on Laminar Heat Transfer with Low Peclet Numbers in the Entrance Region of Thin Vertical Tubes, Numer. Heat Transf., Part A, 33 (1998), 5, pp. 247-266
  16. Laplante, G., Bernier, M. A., Opposing Mixed Convection in Vertical Pipes with Wall Heat Conduction, Int. J. Heat and Mass Transfer, 40 (1997), 15, pp. 3527-3536
  17. EzEddine, S., Anouar, S., Mohamed Salah, S., Combined Gas Radiation and Laminar Mixed Convection in Vertical Circular Tubes, Int. J. Heat and Fluid Flow, 24 (2003), 5, pp. 736-746
  18. Su, Y. C., Chung, J. N., Linear Stability Analysis of Mixed Convection Flow in a Vertical Pipe, Journal of Fluid Mechanics, 422 (2004), 11, pp. 141-166
  19. Nguyen, C. T., et al., Transient Laminar Mixed Convection Flow in a Vertical Tube under High Grashof Number Condition, J. Heat Transfer, ASME Trans., 21 (2004), 3, pp. 133-139
  20. Nguyen, C. T., et al., Numerical Investigation of Flow Reversal and Instability in Mixed Laminar Vertical Tube Flow, Int. J. Thermal Sciences, 43 (2004), 3, pp. 797-808
  21. Mohammed, H. A; Salman, Y. K., Combined Natural and Forced Convection Heat Transfer for Assisting Thermally Developing Flow in a Uniformly Heated Vertical Circular Cylinder, Int. J. Communications in Heat and Mass Transfer, 34 (2007), 4, pp. 474-491
  22. Voicu, I., et al., Mixed Convection in a Vertical Double Pipe Heat Exchanger, Int. J. Thermal Sciences, 46 (2007), 6, pp. 540-550
  23. Kakac, S., Shah, R. K., Aung, W., Handbook of Single Phase Convective Heat Transfer, John Wiley and Sons Inc., New York, USA, 1987
  24. Shah, R. K., London, A. L., Laminar Flow Forced Convection in Ducts, Advances in Heat Transfer, Supplement 1, Academic Press, New York, USA, 1978
Volume 12, Issue 2, Pages89 -102