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R. S. Matos, T. A. Laursen, J. V. C. Vargas, A. Bejan


This work presents a three-dimensional (3-D) numerical and experimental geometric
optimization study to maximize the total heat transfer rate between a bundle of finned
tubes in a given volume and a given external flow both for circular and elliptic
arrangements, for general staggered configurations. The optimization procedure started
by recognizing the design limited space availability as a fixed volume constraint. The
experimental results were obtained for circular and elliptic configurations with a fixed
number of tubes (12), starting with an equilateral triangle configuration, which fitted
uniformly into the fixed volume with a resulting maximum dimensionless tube-to-tube
spacing S/2b = 1.5, where S is the actual spacing and b is the smaller ellipse semi-axis.
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 other two geometric degrees of
freedom, i.e., tube eccentricity and fin-to-fin spacing. The results are reported for air as
the external fluid in the laminar regime, for 125 and 100 Re 2b , where 2b is the
ellipses smaller axis length. Circular and elliptic arrangements with the same flow
obstruction cross-sectional area were compared on the basis of maximum total heat
transfer. This criterion allows one to quantify the heat transfer gain in the most isolated
way possible, by studying arrangements with equivalent total pressure drops
independently of the tube cross section shape. This paper reports three-dimensional (3-
D) numerical optimization results for finned circular and elliptic tubes arrangements,
which are validated by direct comparison with experimental measurements with good
agreement. Global optima with respect to tube-to-tube spacing, eccentricity and fin-tofin
spacing ( 0.5 e 0.5, S/2b and 06 . 0 f for 125 and 100 Re 2b ,
respectively) were found and reported in general dimensionless variables. 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 one, show the elliptical arrangement has the potential for a considerably
better overall performance and lower cost than the traditional circular geometry.

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