Volume 1, Issue 5
Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations

Adv. Appl. Math. Mech., 1 (2009), pp. 639-663.

Published online: 2009-01

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• Abstract

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 $0^\circ$ 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.

80A20, 35Q80

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@Article{AAMM-1-639, author = {Mahfouz , F. M. and Badr , H. M.}, 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 = {

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 $0^\circ$ 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0930}, url = {http://global-sci.org/intro/article_detail/aamm/8389.html} }
TY - JOUR T1 - Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations AU - Mahfouz , F. M. AU - Badr , H. M. JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 639 EP - 663 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/10.4208/aamm.09-m0930 UR - https://global-sci.org/intro/article_detail/aamm/8389.html KW - Heat convection, Elliptic tubes, Fourier spectral methods, Rayleigh number, Prandtle number. AB -

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 $0^\circ$ 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.

F. M. Mahfouz & H. M. Badr. (1970). Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations. Advances in Applied Mathematics and Mechanics. 1 (5). 639-663. doi:10.4208/aamm.09-m0930
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