Here we illustrate the free search for the optimal geometry of flow channel cross-sections that meet two objectives simultaneously: reduced resistances to heat transfer and fluid flow. The element cross section and the wall material are fixed, while the shape of the fluid flow opening, or the wetted perimeter is free to vary. Two element cross sections are considered, square and equilateral triangular. We find that the two objectives are best met when the solid wall thickness is uniform, i.e., when the wetted perimeters are square and triangular, respectively. We also consider arrays of square elements and triangular elements, on the basis of equal mass flow rate per unit of array cross sectional area. The conclusion is that the array of triangular elements meets the two objectives better than the array of square elements. (C) 2016 Elsevier Ltd. All rights reserved.