Optimization study and heat transfer comparison of staggered circular and elliptic tubes in forced convection

In this study, a two-dimensional (2-D) heat transfer analysis was performed in circular and elliptic tube heat exchangers. The finite element method w as used to discretize the fluid flow and heat transfer governing equations and a 2-D isoparametric, four-noded, linear element was implemented for the finite element analysis program, FEAP (O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, vol. 1, McGraw-Hill, London, 1989, Chapter 15). The numerical results for the equilateral triangle staggering configuration, ob tained with the new element were then validated qualitatively by means of d irect comparison to previously published experimental results for circular tubes heat exchangers (G. Stanescu, A.J. Fowler, A. Bejan, Int. J. Heat Mas s Transfer 39 (2) (1996) 311-317). Next, a numerical geometric optimization was conducted to maximize the total heat transfer rate between the given v olume and the given external flow both for circular and elliptic arrangemen ts, for general staggering configurations. The results are reported for air in the range 300 less than or equal to Re-L less than or equal to 800, whe re L is the swept length of the fixed volume. Circular and elliptical arran gements with the same flow obstruction cross-sectional area were compared o n the basis of maximum total heat transfer. The effect of ellipses eccentri city was also investigated. A relative heat transfer gain of up to 13% is o bserved in the optimal elliptical arrangement, as compared to the optimal c ircular one. The heat transfer gain, combined with the relative pressure dr op reduction of up to 25% observed in previous studies (H. Brauer, Chem. Pr ocess Eng., August (1964) 451-460; S.N. Bordalo, F.E.M. Saboya, Determinaca o experimental dos coeficientes de perda de carga em trocadores de calor de tubos circulares e elipticos aletados, in: Proceedings of the 13th COBEM, Congresso Brasileiro de Engenharia Mecanica (in Portuguese), Belo Horizonte , Brasil, 1995) show that the elliptical arrangement has the potential for a considerably better overall performance than the traditional circular one . (C) 2001 Published by Elsevier Science Ltd.