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PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: B.H.V. Topping and Z. Bittnar
Numerical Simulation of Steady and Unsteady Mixed Convection from Tubes of Elliptic Cross-section
H.M. Badr and E.H. Ahmed
Mechanical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
H.M. Badr, E.H. Ahmed, "Numerical Simulation of Steady and Unsteady Mixed Convection from Tubes of Elliptic Cross-section", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Third International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 27, 2002. doi:10.4203/ccp.76.27
Keywords: heat transfer, mixed convection, elliptic tube, fluctuating flow.
The paper deals with the problem of two-dimensional convective heat transfer from a tube of elliptic cross-section. Heat transfer from tubes of various shapes has been the subject of many theoretical and experimental studies because of its direct relevance to engineering practice. Tubes of elliptic cross-section have been used in compact heat exchangers not only to increase heat transfer rates but also to reduce the pressure drop across the heat exchanger. Moreover, the elliptic tube geometry is flexible enough to represent a circular tube or a very thin two- dimensional fin depending on the axis ratio. The rate of heat transfer from an elliptic tube depends on its geometry, the fluid properties, the approaching flow conditions and the tube surface temperature. Various modes of heat transfer may take place ranging from forced convection dominated regime to free convection dominated one. Studying fluctuating flows is of theoretical interest as being a prototypical model for studying important aspects of unsteady flow separation and its effect on heat transfer.
The literature on convection about a circular cylinder in an unbounded medium is rich , however, most of the studies on the elliptic cylinder focused on the fluid flow problem [2,3,4,5,6]. Published research on convective heat transfer from elliptic cylinders includes the early measurement of the local heat transfer coefficient reported in 1953  as well as a number of recent experimental investigations [8,9,10]. On the other hand, theoretical studies on convective heat transfer from elliptic cylinders are not only very few but also based on the solution of the boundary layer equations [10,12] are mainly boundary-layer analyses of the forced convection case. According to the boundary-layer approximations their results are only applicable in the neighborhood of the leading edge where the boundary layer thickness is small.
In this work, the problem of mixed convection from a tube of elliptic cross- section placed in a fluctuating free stream has been numerically simulated based on the solution of the conservation equations of mass, momentum and energy. The effects of amplitude and frequency of free stream fluctuations, Reynolds and Grashof numbers on the main features of the flow and heat transfer processes are obtained. The numerical scheme is developed in a way to cover the special cases of steady and unsteady flows, parallel and counter flows, forced convection as well as mixed convection flows. The study revealed that the effect of fluctuations on the time-average Nusselt number becomes more pronounced with increasing Reynolds number. It also revealed that the rate of heat transfer increases with the increase of the amplitude of fluctuations but decreases with the increase of frequency. The details of flow and thermal fields will be presented in the form of local and average Nusselt number variations as well as streamline and temperature contours for some selected cases.
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