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Journal of Porous Media
IF: 1.752 5-Year IF: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v15.i6.50
pages 567-584

NATURAL CONVECTION HEAT TRANSFER IN A HORIZONTAL CONCENTRIC ELLIPTIC ANNULUS CONTAINING SATURATED POROUS MEDIA

Ramadan Y. Sakr
Department of Mechanical Engineering, Faculty of Engineering, Benha University, 108 Shoubra Street, 11689, Cairo, Egypt
Nabil S. Berbish
Department of Mechanical Engineering, Faculty of Engineering, Benha University, 108 Shoubra Street, 11689, Cairo, Egypt

ABSTRACT

Natural convection heat transfer in a horizontal elliptic annulus filled with saturated porous media is investigated experimentally and numerically. The inner horizontal elliptic tube is heated under constant heat flux conditions and is located concentrically in a larger isothermally cooled horizontal cylinder. Both ends of the water-saturated porous annulus are closed. The heated elliptic tube was made of copper material and has an axis ratio (AR = a/b) of 3.0. The porous media used in the experiments were made of sandstone and glass materials with different solid thermal conductivities and particle diameters. The elliptic tube orientation angle is varied from 0° to 90°, and the hydraulic radius ratio, HRR = Ro/Ri, is 6.85. The numerical solution scheme is based on a two-dimensional model, which is governed by Darcy-Boussinseq equations. The inner elliptic cylinder is heated isothermally, while the outer circular cylinder is also cooled isothermally. Discretization of the governing equations is achieved using a finite element scheme based on Galerkin method of weighted residuals. The effect of pertinent parameters such as modified Rayleigh number, Ra (Rayleigh-Darcy), orientation angle of the elliptic cylinder, δ, and the axis ratio of the elliptic cylinder, AR, is investigated. The numerical results obtained from the present model are compared with the available published results and with the present experimental results, and good agreement is found. The variation of the average Nusselt number with the investigated parameters is presented. It is concluded that the effect of modified Rayleigh number, which includes the effect of fluid properties, porous medium properties, and operating conditions on the average Nusselt number, is more significant than the effect of the geometric parameters such as the elliptic cylinder orientation angle and the elliptic cylinder axis ratio. The results showed that the average Nusselt number increases with the increase of the modified Rayleigh number. Also, the flow and heat transfer characteristics are illustrated via stream function and isotherms contours. Moreover, an empirical correlation for the average Nusselt number is obtained as a function of Rayleigh number, elliptic cylinder orientation angle, and elliptic cylinder axis ratio.


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