Natural heat convection within an annular annulus bounded by two horizontal vertically eccentric long cylinders has been investigated. The annulus inner wall has been heated and maintained at either constant wall temperature CWT or constant heat flux CHF while the outer wall is cooled and maintained at constant temperature. The induced buoyancy driven flow and the associated heat convection are predicted through solving numerically the full conservation equations for mass, momentum, and energy using Fourier spectral method. Beside Rayleigh and Prandtl numbers, the heat convection process in the annulus depends on the annulus radius ratio and eccentricity (normalized by the radius difference). The study considered a moderate range of Rayleigh numbers up to 10^{5} while Prandtl number is fixed at 0.7. The radius ratio is considered up to 3.2 while the eccentricity is varied between − 0.65 and + 0.65. The study has revealed that at certain radius ratio for a given Rayleigh number and eccentricity, the heat transfer is minimum in case of CWT and the mean inner wall temperature is maximum in case of CHF. The study has also shown, in the range considered for controlling parameters, that multiple convection cells only exist in case of CWT and only for positive eccentricity. Moreover, the study has shown that the present numerical solution of the pure conduction problem is almost identical with the newly presented analytical solution which confirms the high accuracy of the numerical solution.

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August 2012

Natural And Mixed Convection

# Heat Convection Within an Eccentric Annulus Heated at Either Constant Wall Temperature or Constant Heat Flux

F. M. Mahfouz

F. M. Mahfouz

Department of Mechanical Power,Faculty of Engineering,

fmahfouz64@hotmail.com
Menoufia University

, P.O. 32511, Egypt

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F. M. Mahfouz

Department of Mechanical Power,Faculty of Engineering,

Menoufia University

, P.O. 32511, Egypt

fmahfouz64@hotmail.com

*J. Heat Transfer*. Aug 2012, 134(8): 082502 (9 pages)

**Published Online:**June 5, 2012

Article history

Received:

September 29, 2011

Revised:

January 25, 2012

Online:

June 5, 2012

Published:

June 5, 2012

Citation

Mahfouz, F. M. (June 5, 2012). "Heat Convection Within an Eccentric Annulus Heated at Either Constant Wall Temperature or Constant Heat Flux." ASME. *J. Heat Transfer*. August 2012; 134(8): 082502. https://doi.org/10.1115/1.4006170

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