@Article{AAMM-1-5,
author = {Mahfouz, M., F. and M., H., Badr},
title = {Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2009},
volume = {1},
number = {5},
pages = {639--663},
abstract = {<p style="text-align: justify;">In this paper, transient and steady natural convection heat transfer 
in an elliptical annulus has been investigated. The annulus occupies
the space between two horizontal concentric tubes of elliptic
cross-section. The resulting velocity and thermal fields are
predicted at different annulus orientations assuming isothermal
surfaces. The full governing equations of mass, momentum and energy
are solved numerically using the Fourier Spectral method. The heat
convection process between the two tubes depends on Rayleigh number,
Prandtl number, angle of inclination of tube axes and the geometry
and dimensions of both tubes. The Prandtl number and inner tube axis
ratio are fixed at 0.7 and 0.5, respectively. The problem is solved
for the two Rayleigh numbers of $10^4$ and $10^5$ considering a
ratio between the two major axes up to 3 while the angle of
orientation of the minor axes varies from <span style="text-align: justify;">$0^\circ$</span> to $90^\circ$. The
results for local and average Nusselt numbers are obtained and
discussed together with the details of both flow and thermal fields.
For isothermal heating conditions, the study has shown an optimum
value for major axes ratio that minimizes the rate of heat transfer
between the two tubes. Another important aspect of this paper is to
prove the successful use of the Fourier Spectral Method in solving
confined flow and heat convection problems.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.09-m0930},
url = {https://global-sci.com/article/73706/heat-convection-between-two-confocal-elliptic-tubes-placed-at-different-orientations}
}