Flow distribution uniformity in a comb-like microchannel network

A comb-like network has a single manifold duct, which ramifies to several branches, all subject to a pressure reservoir. Applications for such networks include vascular systems such as microchannel heatsinks, in which a working fluid needs to be fed to a great number of small volume elements. A configuration with constant branches of diameter and spacing produces a non-uniform flow distribution: the first branch receives a large fraction of the inlet mass flow rate and the subsequent branches receive smaller and smaller fractions. To overcome this problem, two alternative configurations are proposed: variable diameters and variable spacings along the branches. The construction rules providing flow uniformity for both configurations are analytically determined by the method of constructal design and further validated numerically. It is shown that, when the system performance is evaluated at the most critical element, instead of the traditional global fluid flow resistance, the new configurations perform significantly better than the one with constant diameter and spacing. The importance of these results is elucidated under the view of constructal theory.