Md. Abdul Hyea and Md. Mizanur Rahmanb* aDepartments of Mathematics & Statistics, Bangladesh University of Business & Technology,Dhaka-1216, Bangladesh
bDepartment of Mathematics, Faculty of Applied Science and Technology, Islamic University, Kushita-7003, Bangladesh
Download Citation:
|
Download PDF
Non-isothermal flow through a rotating curved duct with square cross section is studied numerically by using the spectral method, and covering a wide range of the Taylor number, Tr, 0 ≤ Tr ≤ 2000 and Dean number, Dn, 0 ≤ Dn ≤ 2000. A temperature difference is applied across the vertical sidewalls for Grashof number Gr = 500, where the outer wall is heated and the inner one cooled. The rotation (Coriolis force) of the duct about the center of curvature is imposed. The Steady solutions are obtained by using Newton-Raphson iteration method and the Dean numbers are also discussed in detail. Then, in order to investigate the non-linear behavior of the steady and unsteady solutions, there is no stable steady solution, time evolution calculations as well as power spectrum of the periodic oscillations are obtained, and it is also found that for larger Dn, the unsteady flow undergoes in the scenario “steady → periodic → chaotic → steady”, if Tr is increased. Finally spectral analysis and phase space are found to be very useful investigation of the Non-isothermal fluid flow behavior.ABSTRACT
Keywords:
Curved duct; Taylor number; Dean number; secondary flow; curvature; time evolution.
Share this article with your colleagues
[1] Berger, S. A., Talbot, L., and Yao, L. S. 1983. Flow in Curved Pipes. Annu. Rev. Fluid. Mech., 35: 461-512.REFERENCES
[2] Nandakumar, K. and Masliyah, J. H. 1986. Swirling Flow and Heat Transfer in Coiled and Twisted Pipes. Adv. Transport Process, 4: 49-112.
[3] Gottlieb, D. and Orazag, S. A. 1977. “Numerical Analysis of Spectral Methods”. Society for Industrial and Applied Mathematics. Philadelphia.
[4] Winters, K. H. 1987. A Bifurcation Study of Laminar Flow in a Curved Tube of Rectangular Cross-section. J. Fluid Mech, 180: 343-369.
[5] Mess, P. A. J., Nandakumar, K., and Masliyah J. H. 1996. Steady Spatial Oscillations in a Curved Duct of Square Cross-section. Phy. Fluids, 8, 12: 3264-3270.
[6] Chandratilleke, T. T. and Nursubyakto. 2003. Numerical Prediction of Secondary Flow and Convective Heat Transfer in Externally Heated Curved Rectangular Ducts. Int. J. Thermal Sci., 42: 187-198.
[7] Mondal, R. N., Kaga, Y., Hyakutake, T., and Yanase, S. 2006a. Effects of curvature and Convectiv heat Transfer in Curved Square Duct Flows. Trans. ASME, Journal of Fluids Engineering, 128, 9: 1013-1022.
[8] Yanse, S., Mondal, R. N., and Kaga, Y. 2005. Numerical Study of Non-isothermal Flow with Convective Heat Transfer in a Curved Rectangular Duct. Int. J. Thermal Sci., 44: 1047-1060.
[9] Ludwieg, H. 1951. Die Ausgebildete Kanalatromung in Einem Rotierenden System. Ingenieu-archiv, 19: 296-308.
[10] Miyazaki, H. 1973. Combined Free and Force Convection Heat Transfer and Fluid Flow In Rotating Curved Rectangular Tubes. Trans. ASME C: J. Heat Transfer, 95: 64-71.
[11] Wang, L. Q. and Cheng, K. C. 1996. Flow Transitions and combined Free and Forced Convective Heat Transfer in Rotating Curved Channels: the Case of Positive Rotation. Phys. Of Fluids, 8: 1553-1573.
[12] Selmi, M. and Namdakumar, K. 1999. Bifurcation Study of the Flow Through Rotating Curved Ducts. Phys. Of Fluids, 11: 2030-2043.
[13] Yamamoto, K., Yanse, S., and Alam, M. M. 1999. Flow Through a Rotating Curved Duct with Square Cross-section. J. Phys. Soc. Japan, 68: 1173-1184.
[14] Yang, T. and Wang, L. 2003. Bifurcation and Stability of Forced Convection in Rotating Curved Ducts of Square Cross Section. Int. J. Heat Mass Transfer, 46: 613-629.
[15] Mondal, R. N., Alam M. M., and Yanase, S. 2007. Numerical Prediction of non-isothermal flows through a rotating Curved duct with square cross section. Thommasat Int. J. Sci and Tech., 12, 3: 24-43.
ARTICLE INFORMATION
Received:
2013-04-12
Revised:
2014-06-05
Accepted:
2014-06-23
Available Online:
2014-12-01
Hye, Md.A., Rahman, Md.M. 2014. A numerical study on Non-Isothermal flow through a rotating curved duct with square cross section. International Journal of Applied Science and Engineering, 12, 241–256. https://doi.org/10.6703/IJASE.2014.12(4).241
Cite this article:
