ANALYSIS OF AIDING AND OPPOSING MIXED COVECTION IN VERTICAL SEMICIRCULAR DUCTS

A. A Busedra

doi:10.66411/jer.v8i8.150

Authors

A.A.Busedra Mech. Eng. Dept., University of Garyounis, Benghazi, Libya Author

DOI:

https://doi.org/10.66411/jer.v8i8.150

Keywords:

Heat flux, Mixed convection, Laminar, Vertical semicircular ducts

Abstract

Laminar fully developed mixed convection in vertical semicircular ducts with upward and downward flows is investigated. Numerical solutions, obtained by using a control volume based finite difference approach, are presented for solving the governing equations. Results are obtained for the two limiting thermal boundary conditions; uniform heat input axially with uniform peripheral wall temperature (H1) and uniform heat input axially with uniform wall heat flux circumferentially (H2). These results include the velocity and temperature fields and data for the friction factor and Nusselt number. In aiding and opposing flows, the velocity and temperature distributions, due to the free convection effect, become different from the one corresponding to pure forced convection. At high Gr, the concentration of the isovel contours near the duct wall, for both thermal boundary conditions, leads to increased wall shear. In addition, the high concentration of isotherms near the wall shows high temperature gradient. The isovels for H2 are found to be slightly more concentrated near the wall which resulted in a slight increase in the wall shear as compared with the H1case. Due to the disappearance of the thermal stratification in H2 at higher values of Gr, it is noted that, when aiding the flow upward, (fRe)H2 exceeds (fRe)H1, and it reverses with NuH1 > NuH2, for any value of Gr. However, when the flow is downward, the values of the friction factor and Nussult number decrease as Gr increases for both H1 and H2 thermal boundary conditions

References

[1] Hallman, T.M, Combined Forced and Free – Laminar Heat Transfer in Vertical Tubes with Uniform Internal Heat Generation, ASME Transactions, 78, 1831- 1841, 1956. DOI: https://doi.org/10.1115/1.4014198

[2] Morton, B. R, Laminar Convection in Uniformly Heated Vertical Pipes, Journal of Fluid Mechanics, 8, (1960), 227-240. DOI: https://doi.org/10.1017/S0022112060000566

[3] Martin A. and J. Shadday, Combined Forced / Free Convection Through Vertical Tubes at High Grashof Numbers, Proceedings of the 8th International Heat Transfer Conference, 3, (1986), 1433-1437. DOI: https://doi.org/10.1615/IHTC8.2940

[4] Aung W. and G. Worku, Theory of Fully Developed, Combined Convection Including Flow Reversal, Journal of Heat Transfer, 108, (1986), 485-488. DOI: https://doi.org/10.1115/1.3246958

[5] Cheng C. H., H. S. Kuo, and W. H. Huang, Flow Reversal and Heat Transfer of Fully Developed Mixed Convection in Vertical Channels, Journal of Thermo physics Heat Transfer, 4, (1990), 375-383. DOI: https://doi.org/10.2514/3.190

[6] Habhci S. and S. Acharya, Laminar Mixed Convection in Symmetrically or Asymmetrically Heated Vertical Channel, Numerical Heat Transfer, Part A, 9, (1986), 605-618. DOI: https://doi.org/10.1080/10407788608913496

[7] Iqbal M. amd B. D. Aggarwala, Combined Free and Forced Convection Through Vertical Rectangular Channel with Unequal Heating from Sides, Journal of Applied Mechanics, 93, (1971), 829-833. DOI: https://doi.org/10.1115/1.3408961

[8] Cheng C. H. and C. J. Weng, Flow of Combined Convection in a Vertical Rectangular Duct with Unequally Isothermal Walls, International Communication Journal of Heat and Mass Transfer, 18, (1991), 127-140. DOI: https://doi.org/10.1016/0735-1933(91)90014-U

[9] Aggarwala B. D. and M. Iqbal, On Limiting Nusselt Numbers from Membrane Analogy for Combined Free and Forced Convection Through Vertical Ducts, International Journal of Heat and Mass Transfer, 12, (1969), 737-748. DOI: https://doi.org/10.1016/0017-9310(69)90007-6

[10] Iqbal M., B. D. Aggarwala, and A. G. Fowler, Laminar Combined Free and Forced Convection in Vertical Non-Circular Ducts Under Uniform Heat Flux, International Journal of Heat and Mass Transfer, 12, (1969), 1123-1139. DOI: https://doi.org/10.1016/0017-9310(69)90120-3

[11] Velusamy K. and V. K. Garg, Laminar Mixed Convection in Vertical Elliptic Ducts, International Journal of Heat Transfer, 39, (1996), 745-752. DOI: https://doi.org/10.1016/0017-9310(95)00163-8

[12] Maitra D. and K. S. Raju, Combined Free and Forced Convection Laminar Heat Transfer in a Vertical Annulus, Journal of Heat Transfer, 97, (1975), 135-137. DOI: https://doi.org/10.1115/1.3450263

[13] Manglik R. M. and A. E. Bergles, Laminar Flow Heat Transfer in a Semi-circular Tube with Uniform Wall Temperature, International Journal of Heat and Mass Transfer, 30, no. 3, (1988), 625-636. DOI: https://doi.org/10.1016/0017-9310(88)90044-0

[14] Trupp A. C. and A. C. Y. Lau, Fully Developed Laminar Heat Transfer in a Circular Sector Duct with Isothermal Walls, Journal of Heat Transfer, 106, (1984), 467-469. DOI: https://doi.org/10.1115/1.3246696

[15] Lei Q. M. and A. C. Trupp, Further Analysis of Laminar Flow Heat Transfer in Circular Sector Ducts, ASME Journal of Heat Transfer, 111, (1989), 1088-1090. DOI: https://doi.org/10.1115/1.3250773

[16] Lei Q. M. and A. C. Trupp, Forced Convection of Thermally Developed Laminar Flow in Circular Sector Ducts, Journal of Heat Transfer, 33, no. 8, (1990), 1675- 1683. DOI: https://doi.org/10.1016/0017-9310(90)90023-N

[17] Nandakumar K., J. H. Masliyah, and H. S. Law, Bifurcation in Steady Laminar Mixed Convection Flow in Horizontal Ducts, Journal of Fluid Mechanics, 152, (1985), 145-161. DOI: https://doi.org/10.1017/S0022112085000611

[18] Lei Q. M. and A. C. Trupp, Prediction of Laminar Mixed Convection in a Horizontal Semicircular Duct, 6th Miami International Symposium on Heat and Mass transfer, 4, (Dec. 1990), 10-12.

[19] Chinporncharoenpong C., A. C. Trupp, and H. M. Soliman, Effect of Gravitational Force Orientation on Laminar Mixed Convection for a Horizontal Semicircular Duct, Proceedings of the 3rd World Conference on Experimental Heat Transfer, fluid Mechanics and Thermodynamics, 1, (1993), 815-822. DOI: https://doi.org/10.1016/B978-0-444-81619-1.50099-X

[20] Chinporncharoenpong C., A. C. Trupp, and H. M. Soliman, Laminar Mixed Convection in Horizontal Circular Sector Ducts, Proceedings of the Tenth International Heat Transfer Conference, 5, (1994), 447-452. DOI: https://doi.org/10.1615/IHTC10.3220

[21] Busedra A. A. and H. M. Soliman, Analysis of Laminar Mixed Convection in Inclined Semicircular ducts Under Buoyancy Assisted and Opposed Conditions, Numerical Heat Transfer, Part A, 36, (1999), 527-544. DOI: https://doi.org/10.1080/104077899274660

[22] Lei Q. M. and A. C. Trupp, Experimental Study of Laminar Mixed Convection in the Enrance Region of a Horizontal Semicircular Duct, International Journal of Heat and Mass Transfer, 34, (1991), 2361-2372. DOI: https://doi.org/10.1016/0017-9310(91)90061-I

[23] Busedra A. A. and H. M. Soliman, Experimental Investigation of Laminar Mixed Convection in an Inclined Semicircular Duct, International Journal of Heat and Mass Transfer, 34 (7), (2000), 1103– 1111. DOI: https://doi.org/10.1016/S0017-9310(99)00208-2

[24] Dong Z. F. and M. A. Ebadian, Analysis of Combined Natural and Forced Convection in Vertical Semicircular Ducts with Radial Internal Fins, Numerical Heat Transfer, Part A, 27, (1995), 359-372. DOI: https://doi.org/10.1080/10407789508913706

[25] Shah R. K. and A. L. London, Laminar Flow Forced Convection in Ducts, Academic Press, New York, (1978).

[26] Patankar S. V, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, (1980).

[27] Patankar S. V. and D. B. Spalding, A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows, International Journal of Heat and Mass Transfer, 15, (1972), 1787-1806. DOI: https://doi.org/10.1016/0017-9310(72)90054-3

[28] Sparrow E. M. and A. Haji-Sheikh, Flow and Heat Transfer in Ducts of Arbitrary Shape with Arbitrary Thermal Boundary Conditions, Journal of Heat Transfer, 88, (1966), 351-358. DOI: https://doi.org/10.1115/1.3691570