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Laminar mixed convection in a vertical flat channel with constant wall temperature

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Thermophysics and Aeromechanics Aims and scope

Abstract

The problem of laminar mixed convection is considered in a flat vertical channel with upward and downward flow and liquid heating, i.e., for the cases of coincidence of the directions of free and forced convection, as well as their opposite directions. The system of equations of motion, continuity, and energy is solved by the finite difference method. Data on the profiles of the longitudinal velocity, temperature, and Nusselt numbers at the upward and downward flows are obtained. An explanation is given for the peculiarities of these values under the influence of buoyancy force. All components of the hydraulic resistance coefficient for the upward and downward flows are analyzed. The influence of the Prandtl number and the velocity profile at the channel input on the hydrodynamic and thermal characteristics of the flow is considered.

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References

  1. E.P. Valueva, A.B. Garyaev, and A.V. Klimenko, Features of Hydrodynamics and Heat Transfer During Flow in Microchannel Technical Devices, MEI, Moscow, 2016.

    Google Scholar 

  2. R.C. Martinelli and L.M.K. Boelter, The analytical prediction of superposed free and forced viscous convection in vertical pipe, Univ. Calif. Publ. Engng, 1942, Vol. 5, No. 2, P. 23–58.

    Google Scholar 

  3. G.A. Ostroumov, Mathematical theory of the steady heat transfer in a circular vertical cavity with superposition of forced and free laminar convection, Techn. Phys., 1950, Vol. 20, Iss. 6, P. 750–757.

    MathSciNet  Google Scholar 

  4. G.A. Ostroumov, Free Convection under the Conditions of the Internal Problem, Gostekhteorizdat, Moscow, St. Petersburg, 1952.

    Google Scholar 

  5. B.S. Petukhov, Heat Transfer and Resistance in the Laminar Flow of Liquids in Tubes, Energiya, Moscow, 1967.

    Google Scholar 

  6. B. Gebhart, Y. Jaluria, R.L. Mahajan, and B. Sammakia, Buoyancy-induced Flows and Transport, Springer, 1988.

  7. T.M. Mallman, Combined forced and free-laminar heat transfer in vertical tubes with uniform internal heat generation, Trans. ASME. Ser. C, 1956, Vol. 78, P. 1831–1841.

    Google Scholar 

  8. L.N. Tao, Heat transfer of combined free and forced convection in circular and sector tubes, Appl. Sci. Res., 1960, Vol. A9, No. 5, P. 357–368.

    Article  MathSciNet  MATH  Google Scholar 

  9. A.F. Polyakov, Viscosity-gravitational flow in tubes with a small effect of thermogravitation, J. Appl. Mech. Techn. Phys., 1977, No. 1, P. 106–112.

  10. L.N. Tao, On combined free and forced convection on channels, Trans. ASME. Ser. C, 1960, Vol. 82, No. 3, P. 233–238.

    Article  Google Scholar 

  11. L.S. Yao, Free and forced convection in the entry region of a heated vertical channel, Intern. J. Heat Mass Transfer, 1983, Vol. 26, No. 1, P. 65–72.

    Article  MATH  Google Scholar 

  12. A.F. Polyakov, A steady viscous-thermogravitational flow of capillary liquid and heat transfer in a vertical cavity under asymmetric heat conditions, High Temp., 2014, Vol. 52, No. 1, P. 72–77

    Article  Google Scholar 

  13. A.F. Polyakov, Viscous-thermogravitational convection and heat transfer in a vertical cavity under various heat conditions, High Temp., 2015, Vol. 53, No. 5, C. 719–725.

    Article  Google Scholar 

  14. E.P. Valueva, Laminar mixed convection in a vertical flat channel with a constant wall heat flux, High Temp., 2019, Vol. 57, No. 3, P. 372–378.

    Article  Google Scholar 

  15. R.C. Martinelli, C.J. Southwell, G. Alves et al., Heat transfer and pressure drop for a fluid flowing in the viscous region through a vertical pipe, Trans. ASME, 1942, Vol. 38, No. 3, P. 493–530.

    Google Scholar 

  16. R.L. Pigford, Nonisothermal flow and heat transfer inside vertical tubes, Chem. Eng. Progr. Symp. Ser., 1955, Vol. 51, P. 79–92.

    Google Scholar 

  17. E.M. Rosen and T.J. Hanratty, Use of boundary layer theory to predict the effect of heat transfer on the laminar flow field in a vertical tube with a constant temperature wall, AIChE J., 1961, Vol. 7, No. 1, P. 112–123.

    Article  Google Scholar 

  18. W.J. Marner and H.K. McMillan, Combined free and forced laminar convection in a vertical tube with constant wall temperature, J. Heat Transfer, 1970, Vol. 92, No. 3, P. 559–562.

    Article  Google Scholar 

  19. B. Zeldin and F.W. Schmidt, Developing flow with combined forced-free convection in an isothermal vertical tube, J. Heat Transfer, 1972, Vol. 94, No. 2, P. 211–221.

    Article  Google Scholar 

  20. J. Quintiere and W.K. Mueller, An analysis of laminar free and forced convection between finite vertical parallel plates, J. Heat Transfer, 1973, Vol. 95, No. 1, P. 53–59.

    Article  Google Scholar 

  21. L.C. Chow, S.R. Husain, and A. Campo, Effects of free convection and axial conduction on forced-convection heat transfer inside a vertical channel at low Peclet number, J. Heat Transfer, 1984, Vol. 106, Is. 2, P. 297–303.

    Article  Google Scholar 

  22. W. Aung and G. Worku, Developing flow and flow reversal in a vertical channel with asymmetric wall temperature, J. Heat Transfer, 1986, Vol. 108, No. 2, P. 299–304.

    Article  Google Scholar 

  23. A. Steiner, On the reverse transition of a turbulent flow under the action of buoyancy forces, J. Fluid Mech., 1971, Vol. 47, P. 503–512.

    Article  ADS  Google Scholar 

  24. M.W. Collins, Heat transfer by laminar combined convection, in: Proc. 6th Inter. Heat Transfer Conf. Toronto, 1978, Vol. 1, P. 25–30.

  25. E.P. Valueva and M.S. Purdin, Heat exchange at laminar flow in rectangular channels, Thermophysics and Aeromechanics, 2016, Vol. 23, No. 6, P. 857–867.

    Article  ADS  Google Scholar 

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  1. Moscow Power Engineering Institute, Moscow, Russia

    E. P. Valueva

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  1. E. P. Valueva
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Correspondence to E. P. Valueva.

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Valueva, E.P. Laminar mixed convection in a vertical flat channel with constant wall temperature. Thermophys. Aeromech. 30, 445–458 (2023). https://doi.org/10.1134/S0869864323030058

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  • DOI: https://doi.org/10.1134/S0869864323030058

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