**Papers Published**

- Matos, R.S. and Laursen, T.A. and Vargas, J.V.C. and Bejan, A.,
*Three-dimensional optimization of staggered finned circular and elliptic tubes in forced convection*, International Journal of Thermal Sciences, vol. 43 no. 5 (2004), pp. 477 - 487 [003] .

(last updated on 2007/04/06)**Abstract:**

This paper presents a three-dimensional numerical and experimental geometric optimization study to maximize the total heat transfer rate between a bundle of finned tubes in a given volume and external flow, for staggered arrangements of circular and elliptic tubes. Experimental results were obtained for circular and elliptic configurations with twelve tubes, starting with an equilateral triangle configuration, which fitted uniformly into the fixed volume with a resulting optimal dimensionless tube-to-tube spacing of S/2b=1.5, where S is the actual spacing and b is the smaller semi-axis of the ellipse. Several experimental configurations were built by reducing the tube-to-tube spacings, identifying the optimal spacing for maximum heat transfer. Similarly, it was possible to investigate the existence of optima with respect to two other geometric degrees of freedom, such as tube eccentricity and fin-to-fin spacing. The results are reported for air as the external fluid in the laminar regime, for Re_{L}=852 and 1065, where L is the swept length of the fixed volume. Circular and elliptic arrangements with the same flow obstruction cross-sectional area were compared on the basis of maximizing the total heat transfer. This criterion allows one to isolate and quantify the heat transfer gain, by studying arrangements with equivalent total pressure drops independently of the tube cross-section shape. This paper continues with three-dimensional numerical optimization results for finned circular and elliptic tubes arrangements, which are validated by direct comparison with experimental measurements. Global optima with respect to tube-to-tube spacing, eccentricity and fin-to-fin spacing (S/2b [approximately equal to] 0.5, e [approximately equal to] 0.5, φ_{f}[approximately equal to] 0.06 for Re_{L}=852 and 1065) were found and reported in dimensionless terms. A relative heat transfer gain of up to 19% is observed in the optimal elliptic arrangement, as compared to the optimal circular one. The heat transfer gain, combined with the relative material mass reduction of up to 32% observed in the optimal elliptic arrangement in comparison to the circular, show that the elliptical tubes arrangement has better overall performance and lower cost than the traditional circular tubes geometry. © 2003 Elsevier SAS. All rights reserved.**Keywords:**

Tubes (components);Laminar flow;Heat exchangers;Temperature distribution;Reynolds number;Optimization;Geometry;Mathematical models;