constructal optimization of the geometry of an array of micro-channels

this paper documents the geometric optimization of an array of circular and non-circular ducts. the optimization was carried out numerically using finite volume method. as optimal dimensions were independent of the array configuration, the numerical simulation was performed on a unit cell. numerical optimization for circular, square and isosceles right triangle cross-sections of channels was performed. based on the results of this investigation, some correlations were proposed to predict the optimal hydraulic diameter and dimensionless heat transfer per unit volume. in addition to examining the effect of pressure drop on these parameters, it was showed that among the different geometries of this study, square cross-section has the most efficiency for a given volume. the numerical results of the present study were compared with approximate results reported in the literature which a good agreement was observed.