Experimental and Numerical Investigation of Natural Convection Heat Transfer in Horizontal Elliptic Annuli

Abstract

Experimental and numerical studies for natural convection in two dimensional regions formed by a constant flux heat horizontal elliptic tube concentrically located in a larger, isothermally cooled horizontal cylinder were investigated. Both ends of the annulus are closed. Experiments were carried out for the Rayleigh number based on the equivalent annulus gap length ranges from 1.12x107 up to 4.92x107; the elliptic tube orientation angle varies from 0o to 90o and the hydraulic radius ratio, HRR, was 6.4. These experiments were carried out for the axis ratio of an elliptic tube (minor/major=b/c) of 1:3. The numerical simulation for the problem is carried out by using commercial CFD code. The effects of the orientation angle as well as other parameters such as elliptic cylinder axis ratio and hydraulic radius ratio on the flow and heat transfer characteristics are investigated numerically. The numerical simulations covered a range of elliptic tube axis ratios from 0.1 to 0.98 and for the hydraulic radius ratios from 1.5 to 6.4. The results showed that the average Nusselt number increases as the orientation angle of the elliptic cylinder increases from 0o (the major axis is horizontal) to 90o (the major axis is vertical) and with the Rayleigh number as well. Also, the average Nusselt number decreases with the increase of the hydraulic radius ratio. An increase up to 1.75 and further increases in the hydraulic radius ratio leads to an increase in the average Nusselt number. The axis ratio of the elliptic cylinder has an insignificant effect on the average Nusselt number. Both the average and local Nusselt number from the experimental results are compared with those obtained from the CFD code.Both the fluid flow and heat transfer characteristics for different operating and geometric conditions are illustrated velocity vectors and isotherm contours that were obtained from the CFD code. Also, two correlation equations that relate the average Nusslet number with the Rayleigh number, orientation angle, and hydraulic radius ratio and axis ratio are obtained.

Buoyancy driven flow within an inclined elliptic enclosure

“…The figure shows that for this particular case the thermal plume inclines to the right. The inclination of thermal plume has been observed in the work of [28].…”

“…On the other hand, the available studies on natural convection in case of UHF heating are those related to elliptic cylinders placed in infinite medium. The only attempts to investigate the case of asymmetric elliptic enclosure are those made by Schreiber and Singh [26], Mahfouz and Badr [27] and Sakr et al [28]. Schreiber and Singh [26] investigated natural convection in a horizontal elliptic enclosure placed at different orientations with respect to gravity vector using stream function vorticity formulation.…”

“…Mahfouz and Badr [27] numerically investigated unsteady natural convection in a horizontal isothermal elliptic enclosure placed at different orientations using Fourier spectral method without paying attention to the global flow circulation. While Sakr et al [28] experimentally investigated the natural convection from an elliptic tube placed at different orientations and subject to UHF heating within somehow large circular enclosure. The authors have also provided some numerical results using some commercial CFD software.…”

Effect of Opposed Lateral and Vertical Eccentricity on Free Convection in an Elliptical Annulus Enclosure in Blunt and Slender Orientations

“…Referring to figure (7,8,9,10); the opposed eccentricity results increases convective heat transfer. This is attributes to the heterogeneous temperature distribution on both outer surfaces of the inner elliptical cylinder and inner one of the outer one.…”

“…The heat transfer rates of the elliptical cylinder withslender orientation in porous med ia were found to be higher than those with blunt orientation. Experimental and numerical studies for natural convection in two dimensional region formed by a constant heat flu x horizontal elliptic tube concentrically located in a larger, isothermally cooled horizontal cylinder were investigated by Sakr [9]. Both ends of the annulus are closed.…”