OPTIMALLY STAGGERED FINNED CIRCULAR AND ELLIPTIC TUBES IN FORCED CONVECTION - Matos, R. S.; Laursen, T. A.; Vargas, J. V. C.; Bejan, A. (Revista de Engenharia Térmica, 2003)
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.