Summary
The fully developed laminar mixed convection flow in a vertical tube of constant surface temperature is investigated assuming that (i) the effect of viscous dissipation is significant, (ii) the Boussinesq approximation holds, and (iii) the average flow velocity U m (as an experimentally accessible quantity) is prescribed. It is shown that under such conditions both upward (U m > 0) and downward (U m < 0) laminar flow solutions may exist. Whereas the downward flow solutions exist for any prescribed U m < 0, upward flows only exist below a maximum value U m,max of U m . Moreover, a nontrivial flow configuration is possible also for U m = 0. A remarkable feature of the problem is that for U m < U m,max, even two solution branches (dual solutions) exist, which merge when U m approaches its maximum value U m,max. The mechanical and thermal characteristics of the flow configurations associated with the dual solutions are discussed in the paper in detail.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aung W. and Worku G. (1986). Theory of fully developed, combined convection including flow reversal. J. Heat Transf. 108: 485–488
Hamadah T. T. and Wirtz R. A. (1991). Analysis of laminar fully developed mixed convection in a vertical channel with opposing buoyancy. J. Heat Transf. 113: 507–510
Al-Nimr M. A. and El-Shaarawi I. (1995). Analytical solution for transient laminar fully developed free convection in vertical channels. Heat Mass Transf. 30: 241–248
Barletta A. (1999). Combined forced and free convection with viscous dissipation in a vertical circular duct. Int. J. Heat Mass Transf. 42: 2243–2253
Barletta A. and Rossi di Schio E. (2001). Effect of viscous dissipation on mixed convection heat transfer in a vertical tube with uniform wall heat flux. Heat Mass Transf. 38: 129–140
Chamkha A. J. (2002). On laminar hydromagnetic mixed convection flow in a vertical channel with symmetric and asymmetric wall heating conditions. Int. J. Heat and Mass Transf. 45: 2509–2525
Chamkha A. J., Groşan T. and Pop I. (2002). Fully developed free convection of a micropolar fluid in a vertical channel. Int. Comm. Heat Mass Transf. 29: 1119–1127
Boulama K. and Galanis N. (2004). Analytical solution for fully developed mixed convection between parallel vertical plates with heat and mass transfer. J. Heat Transf. 126: 381–388
Barletta A., Magyari E. and Keller B. (2005). Dual mixed convection flows in a vertical channel. Int. J. Heat Mass Transf. 48: 4835–4845
Wilks G. and Barmley J. S. (1981). Dual solutions in mixed convection. Proc. R. Soc. Edinb. A 87: 349–358
Merkin J. H. (1985). On dual solutions occurring in mixed convection in a porous medium. J. Engng. Math. 20: 171–179
Mahmood T. and Merkin J. H. (1988). Similarity solutions in axisymmetric mixed-convection boundary-layer flow. J. Engng. Math. 22: 73–92
Ridha A. (1996). Aiding flows non-unique similarity solutions of mixed-convection boundary-layer equations. ZAMP 47: 341–352
Bejan A. (1993). Heat transfer. Wiley, New York, 643
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barletta, A., Lazzari, S. & Magyari, E. Uni- and bidirectional mixed convection flow regimes described by dual solutions in a vertical duct. Acta Mechanica 194, 83–102 (2007). https://doi.org/10.1007/s00707-007-0467-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-007-0467-3