# UFR 3-07 References

# Natural and mixed convection boundary layers on

vertical heated walls (B)

Underlying Flow Regime 3-07 © copyright ERCOFTAC 2004

## References

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Brown, C.K. and Gauvin, W.H. (1965), “Combined free and forced convection, II. Heat transfer in opposing flow”,* The Canadian J. Chem. Eng.,* Dec 1965, pp. 313-318.

Brown, C.K. and Gauvin, W.H. (1966), “Temperature profiles and fluctuations in combined free and forced convection flows”, *Chem. Eng. Science*, Vol. 21, pp. 961-970.

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Cotton, M.A. and Jackson, J.D. (1987), “Comparison between theory and experiment for turbulent flow of air in a vertical tube with interaction between free and forced convection”, *Mixed Convection Heat Transfer &emdash; 1987* (eds. V. Prasad, I. Catton and P. Cheng), ASME publication HTD-84, 1987, pp. 43-50.

Craft, T.J., Gerasimov, A.V., Iacovides, H. and Launder, B.E. (2002), “Progress in the generalisation of wall function treatments”, *Int. J. Heat and Fluid Flow*, 23, No. 2, pp. 148-160.

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Gerasimov, A.V. (2002), “CFD Quality and Trust, Development and Validation of an analytical wall function strategy for modelling forced, mixed and natural convection flows”, IMC report number PM/GNSR/5106.

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Jackson, J.D. and Hall, W.B. (1979), “Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions”, *Turbulent Forced Convection in Channels and Bundles, Theory and Applications to Heat Exchangers and Nuclear Reactors*, Vol. 2, (eds. Kakac, S. and Spalding, D.B.), Advanced Study Institute Book, pp. 613-640.

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Jackson, J.D, He, S., Xu, Z., and Wu, T. (2000), “CFD Quality and Trust — generic studies of thermal convection”, Technical report HTH/GNSR/5029, School of Engineering, University of Manchester.

Khosla, J., Hoffman, T.W. and Pollock, K.G. (1974), “Combined forced and natural convective heat transfer to air in a vertical tube”, *Proc. 5 ^{th} Int. Heat Transfer Conference*, Tokyo, Paper NC4.4.

Launder, B.E. and Sharma, B.I. (1974), “Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc”, *Lett. Heat Mass Transfer*, Vol. 1, pp. 131-138.

Leschziner, M.A. (1982), “An introduction and guide to the computer code PASSABLE”, Report, University of Manchester Institute of Science and Technology.

Li, J.K. (1994), “Studies of buoyancy influenced convective heat transfer to air in a vertical tube”, Ph. D.Thesis, University of Manchester.

Perkins, K.R. and McEligot, D.M. (1975), “Mean temperature profiles in heated laminarizing air flows”, *Trans. ASME C., J. Heat Transfer*, November 1975.

Petukhov, B.S. and Nolde, L.D. (1959), “Heat transfer to water in a vertical heated tube for upward and downward flow”, *Teploenergetika*, Vol. 6, pp. 72-80.

Petukhov, B.S. and Strigin, B.K. (1968), “Experimental investigation of heat transfer with viscous inertial-gravitational flow of a liquid in vertical tubes”, *Teplofizika Vysokikh temperatur*, Vol. 6, No. 5, pp. 933-937.

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Vilemas, J.V., Poskas, P.S. and Kaupas, V.E. (1992), “Local heat transfer in a vertical gas-cooled tube with turbulent mixed convection and different heat fluxes”, *Int. J. Heat Mass* *Transfer,* Vol. 35, No. 10, pp. 2421-2428.

Yu, L.S.L. (1991), “A computational study of turbulent mixed convection in vertical tubes”, Ph. D. Thesis, Unversity of Manchester.

LIST OF FIGURES

**Figure 1** Downward flow of air in a heated tube, inlet Re=14815, Gr=3.812x10^{7}, Bo=0.0499, T_{w}=83.3°C, T_{a}=23.1°C, outlet T_{w}=212.0°C, T_{a}=137.1°C. Also shown are predictions for a different set of conditions. CFD predictions by Gerasimov (2002).

**Figure 2** Downward flow of air in a heated tube, inlet Re=7044, Gr=8.010x10^{7}, Bo=0.5573, T_{w}=58.3°C, T_{a}=20.5°C, outlet T_{w}=147.9°C, T_{a}=105.0°C. Also shown are predictions for a different set of conditions, inlet Re=5016, Gr=8.003x10^{7}, Bo=1.7816, T_{w}=72.7°C, T_{a}=20.9°C, outlet T_{w}=195.3°C, T_{a}=143.9°C. CFD predictions by Gerasimov (2002).

**Figure 3** Downward flow of air in a heated tube, inlet Re=4097, Gr=6.800x10^{7}, Bo=3.0268, T_{w}=71.8°C, T_{a}=20.1°C, outlet T_{w}=194.4°C, T_{a}=147.7°C. CFD predictions by Gerasimov (2002).

**Figure 4** Upward flow of air in a heated tube, inlet Re=15023, Gr=2.163x10^{8}, Bo=0.1124, T_{w}=74.0°C, T_{a}=19.1°C, outlet T_{w}=222.4°C, T_{a}=130.4°C. Also shown are predictions for a different set of parameters. CFD predictions by Gerasimov (2002).

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© copyright ERCOFTAC 2004

Contributors: Mike Rabbitt - British Energy