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Steady-State Natural Convection in a Rectangular Cavity Filled with Low Prandtl Number Fluids

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Numerical Simulation of Oscillatory Convection on Low-Pr Fluids

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 27))

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Summary

Time-independent natural convection in a two-dimensional, rectangular cavity containing a low Prandtl fluid is solved numerically using a finite-difference method. The numerical results reported in the paper were obtained with the SIMPLER algorithm using the power law scheme for finite-differencing the advection terms in the transport equations. The results for steady-state thermal convection flow in a cavity, having an aspect ratio of four, were obtained with a nonuniform mesh of 101X31. The results show that the flow oscillates, and that the amplitude of the oscillation increases with the Grashof number for both Pr = 0 and 0.015, but the frequency remains the same.

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References

  1. KOSTER, J.N., MULLER, U., “Oscillatory convection in vertical slots”, J. Fluid Mech., 139 (1984) pp.363–390.

    Article  ADS  Google Scholar 

  2. IVEY, G.N., “Experiments on transient natural convection in cavity”, J. Fluid Mech., 144 (1984) pp.389–401.

    Article  ADS  Google Scholar 

  3. KESSLER, R., “Nonlinear transition in three-dimensional convection”, J. Fluid Mech., 174 (1987) pp.357–359.

    Article  ADS  MATH  Google Scholar 

  4. HURLE, D.T.J., JAKEMAN, E., JOHNSON, C.P., “Convective temperature oscillations in molten gallium”, J. Fluid Mech., 64 (1974) pp.565–576.

    Article  ADS  Google Scholar 

  5. GILL, A.E., “A theory of thermal oscillations in liquid metals,” J. Fluid Mech., 64 (1974) pp. 271–281.

    Article  Google Scholar 

  6. HART, J., “A note on the stability of Low-Prandtl-number Hadley Circulations”, J. Fluid Mech., 132 (1983) pp.271–281.

    Article  ADS  MATH  Google Scholar 

  7. PAMLIN, B.R., BOLT, G.H. “Temperature oscillations induced in a mercury bath by horizontal heat flow”, J. Phys., Section D, 9 (1976) pp.145–149.

    Google Scholar 

  8. KAMATONI, Y., SAHRAONI, T., “Oscillatory natural convection in rectangular enclosures filled with mercury”, in Proceedings of the 1987 ASME/JSME Thermal Engineering Joint Conference, P.J. Marto and I. Tanasawa, Editors, ASME/JSME, New York/Tokyo (1987), Vol.2, pp.241–245.

    Google Scholar 

  9. CROCHET, M.J., GEYLING, F.T., VAN SCHAFTINGEN, J.J., “Numerical simulation of the horizontal Bridgman growth of a gallium arsenide crystal”, J. Crystal Growth 65 (1983) pp.565–576.

    Google Scholar 

  10. CROCHET, M.J., GEYLING, F.T., VAN SCHAFTINGEN, J.J., “Numerical simulation of the horizontal Bridgman growth. Part I: Two-dimensional flow”, Int. J. Numer. Methods Fluids 7 (1987) pp.29–48.

    Article  ADS  MATH  Google Scholar 

  11. MATSUSHIMA, H., VISKANTA, R., “Effects of internal radiation on temperature distribution and natural convection in a vertical crystal growth configuration”, in Collected Papers in Heat Transfer 1988, K.T. Yang, Editor, ASME, New York (1988), pp.151–160.

    Google Scholar 

  12. PATANKAR, S.V., “Numerical heat transfer and fluid flow,” Hemisphere, Washington, DC (1980).

    MATH  Google Scholar 

  13. VISKANTA, R., KIM, D.M., GAU, C., “Three-dimensional natural convection and heat transfer of a liquid metal in a cavity”, Int. J. Heat Mass Transfer, 29 (1985) pp.475–485.

    Article  Google Scholar 

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© 1990 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

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Mohamad, A.A., Viskanta, R. (1990). Steady-State Natural Convection in a Rectangular Cavity Filled with Low Prandtl Number Fluids. In: Roux, B. (eds) Numerical Simulation of Oscillatory Convection on Low-Pr Fluids. Notes on Numerical Fluid Mechanics (NNFM), vol 27. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87877-9_12

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  • DOI: https://doi.org/10.1007/978-3-322-87877-9_12

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-07628-3

  • Online ISBN: 978-3-322-87877-9

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