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, , 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. |
