Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, transient and steady natural convection heat transfer in an elliptical annulus has been investigated. The annulus occupiesthe space between two horizontal concentric tubes of ellipticcross-section. The resulting velocity and thermal fields arepredicted at different annulus orientations assuming isothermalsurfaces. The full governing equations of mass, momentum and energyare solved numerically using the Fourier Spectral method. The heatconvection process between the two tubes depends on Rayleigh number,Prandtl number, angle of inclination of tube axes and the geometryand dimensions of both tubes. The Prandtl number and inner tube axisratio are fixed at 0.7 and 0.5, respectively. The problem is solvedfor the two Rayleigh numbers of $10^4$ and $10^5$ considering aratio between the two major axes up to 3 while the angle oforientation of the minor axes varies from $0^°$ to $90^°$. Theresults for local and average Nusselt numbers are obtained anddiscussed together with the details of both flow and thermal fields.For isothermal heating conditions, the study has shown an optimumvalue for major axes ratio that minimizes the rate of heat transferbetween the two tubes. Another important aspect of this paper is toprove the successful use of the Fourier Spectral Method in solvingconfined flow and heat convection problems.