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Natural convection in tilted cylindrical cavities embedded in rocks
Phys. Rev. E 71, 066308 – Published 27 June, 2005
DOI: https://doi.org/10.1103/PhysRevE.71.066308
Abstract
This paper presents a theoretical investigation of the low Rayleigh number conjugate natural convection in a slender tilted cylindrical cavity which is embedded in a solid that is subject to a uniform vertical temperature gradient. Two cases have been analyzed; a fluid-filled cavity and a cavity filled with a fluid-saturated porous medium. The temperature of the solid and the velocity, temperature, and pressure in the cavity have been determined by analytically solving the coupled problems within and around the cavity. The effect of the ratio of the thermal conductivity of the material in the cavity to the thermal conductivity of the solid on the structure of the convection flow is discussed. The theoretical results for convection in the fluid-filled cavity are shown to be in good agreement with experimental PIV measurements.
Article Text
References (17)
- E. J. Shaughnessy and J. W. Van Gilder, Numer. Heat Transfer, Part A 28, 389 (1995).
- M. Nagata and F. H. Busse, J. Fluid Mech. 135, 1 (1983).
- O. M. Phillips, Flow and Reactions in Permeable Rocks (Cambridge University Press, Cambridge, England, 1991).
- S. H. Davies, S. Rosenblat, J. R. Wood, and T. A. Hewett, Am. J. Sci. 285, 207 (1985).
- A. W. Woods and S. J. Linz, J. Fluid Mech. 241, 59 (1992).
- S. J. Linz and A. W. Woods, Phys. Rev. A 46, 4869 (1992).
- E. Luna, J. A. Córdova, A. Medina, and F. J. Higuera, Phys. Lett. A 300, 449 (2002).
- A. Medina, E. Luna, C. Pérez-Rosales, and F. J. Higuera, J. Phys.: Condens. Matter 14, 2467 (2002).
- L. W. Lake, Enhanced Oil Recovery (Prentice Hall, Englewood Cliffs, NJ, 1989).
- R. A. Lake and E. L. Lewis, J. Geophys. Res. 75, 583 (1970).
- W. O. Criminale and M-P. Lelong, J. Geophys. Res. B 89, 3581 (1984).
- G. Z. Gershuni and E. M. Zhukhovitskii, Convective Stability of Incompressible Fluids (Keter, Jerusalem, 1996).
- A. Jerschow, J. Magn. Reson. 145, 125 (2000).
- H. H. Bau and K. E. Torrance, Trans. ASME 104, 166 (1982).
- K. B. Haugen and P. A. Tyvand, Phys. Fluids 15, 2661 (2003).
- L. Storesletten and M. Tveitereid, Int. J. Heat Mass Transfer 34, 1959 (1991).
- S. Kimura and A. Bejan, Int. J. Heat Mass Transfer 23, 1117 (1980).