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Buoyant laminar flow of air in a long, square-section cavity aligned with the ambient temperature gradient

Published online by Cambridge University Press:  26 April 2006

G. S. H. Lock  and
J.-C. Han
G. S. H. Lock
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada
J.-C. Han
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada
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Abstract

Numerical solutions have been obtained for three-dimensional buoyant flow of air under laminar conditions in a slender, square-section cavity lying parallel to the gradient vector of the temperature field in which it is embedded. Velocity and temperature profiles in the cavity are presented in support of a flow model in which primary and secondary circulation are reconciled by an advective mechanism in the central region. The effect of the temperature gradient, represented by a Rayleigh number, is explored when the cavity is horizontal. The effect of inclining the cavity above and below this horizontal position is also explored. Comparisons are made with related work on cylindrical and two-dimensional rectangular cavities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 207 , October 1989 , pp. 489 - 504
Copyright
© 1989 Cambridge University Press

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References

Bayley, F. J. & Lock, G. S. H. 1965 Heat transfer characteristics of the closed thermosyphon. Trans. ASME C: J. Heat Transfer 87, 30–40.Google Scholar
Bejan, A., Al-Homoud, A. A. & Imberger, J. 1981 Experimental study of high-Rayleigh-number convection in a horizontal cavity with different end temperatures. J. Fluid Mech. 109, 283–299.Google Scholar
Bejan, A. & Tien, C. L. 1978a Laminar natural convection heat transfer in a horizontal cavity with different end temperatures. Trans. ASME C: J. Heat Transfer 100, 641–647.Google Scholar
Bejan, A. & Tien, C. L. 1978b Fully developed counterflow in a long horizontal pipe with different end temperatures. Intl J. Heat Mass Transfer 21, 701–708.Google Scholar
Blythe, P. A., Daniels, P. G. & Simpkins, P. G. 1983 Thermal convection in a cavity: the core structure near the horizontal boundaries. Proc. R. Soc. Lond. A 387, 367–388.Google Scholar
Bontoux, P., Roux, B., Schiroky, G. H., Markham, B. L. & Rosenberger, F. 1986a Convection in the vertical midplane of a horizontal cylinder. Comparison of two-dimensional approximations with three-dimensional results. Intl. J. Heat Mass Transfer 29, 227–239.Google Scholar
Bontoux, P., Smutek, C., Randriamampianina, A., Roux, B., Extremet, G. P., Hurford, A. C., Rosenberger, F. & Vahl De Davis, G. 1986b Numerical solutions and experimental results for three-dimensional buoyancy driven flows in tilted cylinders. Adv. Space Res. 6, 155–160.Google Scholar
Bontoux, P., Smutek, C., Roux, B. & LaCroix, J. M. 1986c Three-dimensional buoyancy-driven flows in cylindrical cavities with differentially heated endwalls. Part 1. Horizontal cylinders. J. Fluid Mech. 169, 211–227.Google Scholar
Cormack, D. E., Leal, L. G. & Imberger, J. 1974b Natural convection in a shallow cavity with differentially heated endwalls. Part 1. Asymptotic theory. J. Fluid Mech. 65, 209–229.Google Scholar
Cormack, D. E., Leal, L. G. & Seinfield, J. N. 1974b Natural convection in a shallow cavity with differentially heated endwalls. Part 2. Numerical solutions. J. Fluid Mech. 65, 231–246.Google Scholar
Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated endwalls. Part 3. Experimental results. J. Fluid Mech. 65, 2247–2260.Google Scholar
Japikse, D. & Winter, E. R. F. 1971 Heat transfer and fluid flow in the closed thermosyphon. Intl J. Heat Mass Transfer 14, 427–441.Google Scholar
Lighthill, M. J. 1953 Theoretical considerations on free convection in tubes. Q. J. Mech. Appl. Maths. 6, 398–439.Google Scholar
Lock, G. S. H. & Kirchner, J. D. 1988 Flow and heat transfer in an inclined, closed tube thermosyphon. In: Proc. 27th Natl H.T. Conf. ASME.
Mallinson, G. D. & Vahl De Davis, G. 1977 Three-dimensional natural convection in a box: a numerical study. J. Fluid Mech. 83, 1–31.Google Scholar
Menold, E. R. & Ostrach, S. 1965 Natural convection in a horizontal cylinder at large Prandtl numbers. Case Inst. of Technol. SFOSR Tech. Rep. 65–2239.
Ostrach, S. 1972 Natural convection in enclosures. Adv. Heat Transfer 8, 161–227.Google Scholar
Ostrach, S., Loka, R. R. & Kumar, A. 1980 Natural convection in low aspect ratio rectangular enclosures. In Natural Convection in Enclosures, HTD-8, pp. 1–10. ASME.
Patankar, S. V. 1981 A calculation procedure for two dimensional elliptic equations. Numer. Heat Transfer 4, 409–425.Google Scholar
Sabzevari, A. & Ostrach, S. 1966 Experimental studies of natural convection in a horizontal cylinder. Case Inst. of Technol. AFOSR Tech. Rep. 66–1401.
Schiroky, G. H. & Rosenberger, F. 1984 Free convection of gases in a horizontal cylinder with differentially heated endwalls. Intl. J. Heat Mass Transfer 27, 587–598.Google Scholar
Simpkins, P. G. & Chen, K. S. 1986 Convection in horizontal cavities. J. Fluid Mech. 166, 21–39.Google Scholar
Smutek, C., Bontoux, P., Roux, B., Schiroky, G. H., Hurford, A., Rosenberger, F. & Vahl De Davis, G. 1985 Three-dimensional convection in horizontal cylinders - numerical solutions and comparison with experimenta and analytical results. Numer. Heat Transfer 8, 613–631.Google Scholar
Van Doormaal, J. P. & Raithby, G. D. 1984 Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer. Heat Transfer 7, 147–163.Google Scholar