Laminar convective heat transfer of a bingham plastic in a circular pipe with uniform wall heat flux: The graetz problem extended

Journal of Heat Transfer

Volumn 121, Issue 3, 1999, Pages 556-563

  Min, T ^a   Yoo, J Y ^a  

^a Seoul National University   (South Korea)

Author keywords

Forced convection; Materials Processing and Manufacturing Process; Non Newtonian Flows and Systems

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HEAT FLUX; HEAT LOSSES; LAMINAR FLOW; NUSSELT NUMBER; PIPE FLOW; PROBLEM SOLVING; VISCOUS FLOW; WALL FLOW; YIELD STRESS;

BINGHAM PLASTIC; BRINKMAN NUMBER; PECLET PROBLEM;

HEAT CONVECTION;

BINGHAM FLUID; FORCED CONVECTION; HEAT TRANSFER; LAMINAR FLOW; PIPE FLOW;

EID: 0033410192     PISSN: 00221481     EISSN: 15288943     Source Type: Journal    
DOI: 10.1115/1.2826016     Document Type: Article

References (21)

1. Shah, R. K., and London, A. L., 1978, “Laminar Flow Forced Convection in Ducts,” Advances in Heat Transfer, Supplement 1, Academic Press, New York.
2. Siegel, R., Sparrow, E. M., and Hallman, T. M., 1958, “Steady Laminar Heat Transfer in a Circular Tube with Prescribed Wall Heat Flux,” Applied Scientific Research, Sect. A7, pp. 386-392.
3. Vradis, G. G, Dougher, J., and Kumar, S., 1993, “Entrance Pipe and Heat Transfer for a Bingham Plastic,” Intetnational Journal of Heat and Mass Transfer, Vol. 36, pp. 543-552.
4. Vradis, G. C., and Ötiigen, M. V., 1997, “The Axisymmetric Sudden Expansion Flow of a Non-Newtonian Viscoplastic Fluid,” ASME Journal of Fluids Engineering, Vol. 119, pp. 193-200.
5. Wissler, E. H., and Schechter, R. S., 1959, “The Graetz-Nusselt Problem (with Extension) for a Bingham Plastic,” Chemical Engineering Progress Symposium Series 29, Vol. 55, pp. 203-208.
6. Beek, W. J., and Eggink, R., 1962, “Heat Transfer to Non-Newtonian Fluids in Laminar Flow through Circular Pipes,” De Ingenieur, Vol. 74, No. 35, pp. 81-89 (in Dutch).
7. Bird, R. B., Armstrong, R. C., and Hassager, O., 1987, Dynamics of Polymerie Liquids, (Vol. 1, Fluid Mechanics), John Wiley and Sons, New York.
8. Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960, Transport Phenomena, John Wiley and Sons, New York.
9. Blackwell, B. F., 1985, “Numerical Solution of the Graetz Problem for a Bingham Plastic in Laminar Tube Flow With Constant Wall Temperature,” ASME Journal of Heat Transfer, Vol. 107, pp. 466-468.
10. Finlayson, B. A., 1972, The Method of Weighted Residuals and Variational Principles, Academic Press, New York.
11. Hsu, C. J., 1967, “An Exact Mathematical Solution for Entrance-Region Laminar Heat Transfer with Axial Conduction,” Applied Scientific Research, Vol. 17, pp. 359-376.
12. Johnston, P. R., 1991, “Axial Conduction and the Graetz Problem for a Bingham Plastic in Laminar Tube Flow,” International Journal of Heat and Mass Transfer, Vol. 34, pp. 1209-1217.
13. Kakaf, S., Shah, R. K., and Aung, W., 1987, Handbook of Single-Phase Convective Heat Transfer, John Wiley and Sons, New York
14. Kays, W. M., and Crawford, M. E., 1993, Convective Heat and Mass Transfer, 3rd Ed., McGraw-Hill, New York.
15. LeCroy, R. C., and Eraslan, A. H., 1969, “The Solution of Temperature Development in the Entrance Region of an MHD Channel by the B. G. Galerkin Method,” ASME Journal of Heat Transfer, Vol. 91, pp. 212-220.
16. Min, T., Yoo, J. Y., and Choi, H., 1997a, “Laminar Convective Heat Transfer of a Bingham Plastic in a Circular Pipe—I. Analytical Approach—Thermally Fully Developed Flow and Thermally Developing Flow (the Graetz Problem Extended),” International Journal of Heat and Mass Transfer, Vol. 40, pp. 3025-3037.
17. Min, T., Yoo, J. Y., Choi, H. G., and Choi, H., 1997b, “Laminar Convective Heat Transfer of a Bingham Plastic in a Circular Pipe—II. Numerical Approach— Hydrodynamically Developing Flow and Simultaneously Developing Flow,” International Journal of Heat and Mass Transfer, Vol. 40, pp. 3689-3701.
18. Ou, J. W., and Cheng, K. C., 1973, “Viscous Dissipation Effects on Thermal Entrance Region Heat Transfer in Pipes with Uniform Wall Heat Flux,” Applied Scientific Research, Vol. 28, pp. 289-301.
19. Pirkle, J. C., and Sigillito, V. G., 1972, “Laminar Heat Transfer with Axial Conduction,” Applied Scientific Research, Vol. 26, pp. 108-112.
20. Sellars, J. R., Tribus, M., and Klein, J. S., 1956, “Heat Transfer to Laminar Flow in a Round Tube or Flat Conduit—The Graetz Problem Extended,” ASME Transactions, Vol. 78, pp. 441-448.
21. Shah, R. K., 1975, “Thermal Entry Length Solutions for the Circular Tube and Parallel Plates,” Proceedings of National Heat and Mass Transfer Conference, 3rd, Indian Institute of Technology, Bombay, Vol. 1, Paper No. HMT-11-75.