Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-09T07:52:22.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Bifurcation in steady laminar mixed convection flow in horizontal ducts

Published online by Cambridge University Press:  20 April 2006

K. Nandakumar ,
Jacob H. Masliyah  and
Hin-Sum Law
K. Nandakumar
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton. T6G 2G6, Canada
Jacob H. Masliyah
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton. T6G 2G6, Canada
Hin-Sum Law
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton. T6G 2G6, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 145 - 161
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, T. B. 1978a Bifurcation phenomena in steady flows of a viscous fluid. I. Theory. Proc. R. Soc. Lond. A 359, 1–26.Google Scholar
Benjamin, T. B. 1978b Bifurcation phenomena in steady flows of a viscous fluid. II. Experiments. Proc. R. Soc. Lond. A 359, 27–43.Google Scholar
Benjamin, T. B. & Mullin, T. 1981 Anomalous modes in the Taylor experiment. Proc. R. Soc. Lond. A 377, 221–249.Google Scholar
Benjamin, T. B. & Mullin, T. 1982 Notes on the multiplicity of flows in the Taylor experiment. J. Fluid Mech. 121, 219–230.Google Scholar
Bergles, A. E. & Simonds, R. R. 1971 Combined forced and free convection for laminar flow in horizontal tubes with uniform heat flux. Intl J. Heat Mass Transfer 14, 1989–2000.Google Scholar
Cheng, K. C. & Hwang, G.-J. 1969 Numerical solution for combined free and forced laminar convection in horizontal rectangular channels. Trans. ASME C: J. Heat Transfer 91, 59–66Google Scholar
Cheng, K. C., Nakayama, J. & Akiyama, M. 1977 Effect of finite and infinite aspect ratios on flow patterns in curved rectangular channels. Int. Symp. on Flow Visualization, Tokyo, Oct. 1977, 109–114.
Cliffe, K. A. 1983 Numerical calculations of two-cell and single-cell Taylor flows. J. Fluid Mech. 135, 219–233.Google Scholar
Dennis, S. C. R. & Ng, M. 1982 Dual solutions for steady laminar flow through a curved tube. Q. J. Mech. Appl. Maths 35, 305–324.Google Scholar
Faris, G. N. & Viskanta, R. 1969 An analysis of combined forced and free convection heat transfer in a horizontal tube. Intl. J. Heat Mass Transfer 12, 1295–1309.Google Scholar
Hwang, G. J. & Cheng, K. C. 1970 Boundary vorticity method for convective heat transfer with secondary flow - applications to the combined free and forced laminar convection in horizontal tubes. Heat Transfer 4, Paper no. NC3.5.Google Scholar
Iqbal, M. & Stachiewicz, J. W. 1966 Influence of tube orientation on combined free and forced laminar convection heat transfer. Trans. ASME C: J. Heat Transfer 88, 109–116Google Scholar
Iqbal, M. & Stachiewicz, J. W. 1967 Variable density effects in combined free and forced convection in inclined tubes. Intl J. Heat Mass Transfer 10, 1625–1629.Google Scholar
Jaluria, Y. 1980 Natural Convection Heat and Mass Transfer. Pergamon.
Kato, K., Watanabe, E., Ogura, T. & Hanzawa, T. 1982 Effect of natural convection on laminar flow heat transfer in horizontal circular tubes. J. Chem. Enging of Japan 15, 335–361.Google Scholar
Keller, H. B. 1977 Numerical Solutions of Bifurcation and Nonlinear Eigenvalue Problems; Applications of Bifurcation Theory (ed. P. H. Rabinowitz), pp. 359–384. Academic.
Lee, Y. & Korpela, S. A. 1983 Multicellular natural convection in a vertical slot. J. Fluid Mech. 126, 91–121.Google Scholar
Masliyah, J. H. 1980 On laminar flow in curved semicircular ducts. J. Fluid Mech. 99, 469–479.Google Scholar
Mccomas, S. T. & Eckert, E. R. G. 1966 Combined free and forced convection in horizontal circular tubes. Trans. ASME C: J. Heat Transfer 88, 147–153Google Scholar
Mori, Y. Futagami, K., Tokuda, S. & Nakamura, M. 1966 Forced convective heat transfer in uniformly heated horizontal tubes (1st Report: experimental study on the effect of buoyancy). Int. J. Heat Mass Transfer 9, 453–463.Google Scholar
Mori, Y. & Futagami, K. 1967 Forced convective heat transfer in uniformly heated horizontal tubes (2nd Report; Theoretical Study). Intl J. Heat Mass Transfer 10, 1801–1813.Google Scholar
Morton, B. R. 1959 Laminar convection in uniformly heated horizontal pipes at low Rayleigh numbers. Q. J. Mech. Appl. Maths 12, 410–120.Google Scholar
Mullin, T. 1982 Mutations of steady cellular flows in the Taylor experiment. J. Fluid Mech. 121, 207–218.Google Scholar
Nandakumar, K. & Masliyah, J. H. 1982 Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 119, 475–490.Google Scholar
Nandakumar, K. & Masliyah, J. H. 1984 Review of swirling flow and heat transfer in coiled and twisted pipes. To appear in Advances in Transport Processes (ed. A. S. Mujumdar & R. A. Mashelkar). Wiley Eastern Ltd..
Newell, P. H. & Bergles, A. E. 1970 Analysis of combined free and forced convection for fully developed laminar flow in horizontal tubes. Trans. ASME C: J. Heat Transfer 90, 83–93.Google Scholar
Patankar, S. V., Ramadhyani, S. & Sparrow, E. M. 1978 Effect of circumferentially nonuniform heating on laminar combined convection in a horizontal tube, Trans. ASME C: J. Heat Transfer 100, 63–70.Google Scholar
Shah, R. K. & London, A. L. 1978 Laminar Flow Forced Convection in Ducts. Academic.
Shannon, R. L. & Depew, C. A. 1968 Combined free and forced convection in a horizontal tube with uniform heat flux. Trans ASME C: J. Heat Transfer 90, 353–357.Google Scholar
Strikwerda, J. C. 1982 Upwind differencing, false scaling and nonphysical solutions to the driven cavity problem. J. Comp. Phys. 47, 303–307.Google Scholar