Flow distribution uniformity in a comb-like microchannel network

  • Alan LugariniEmail author
  • Admilson T. Franco
  • Marcelo R. Errera
Research Paper


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.


Constructal design Flow access Microchannel network Vascularization Flow uniformity 

List of symbols


Network area (= Lli) (m2)


Constant (= 2νPo/π) (m2/s)


Constant (= π2A3/2/(16Vf2)) (m− 3)


Diameter (m)


Branch spacing


Branch length

Mass flow rate (kg/s)


Number of branches


Pressure (Pa)


Poiseuille number


Hydraulic resistance (= l/D4) (m− 3)


Reynolds number (= 4/πρνD)


Svelteness, Eq. (1)


Volume (m3)


Mass fraction (= i/in)


Mass fraction density, Eq. (23)

Greek symbols


Network aspect ratio (= ∑li/L)


factor (= (2n − i)(i − 1)/(2n))


Branch-to-manifold diameter ratio, Eq. (5)


Normalized branch spacing (= l/L)


Flow rate nonuniformity parameter, Eq. (15)


Kinematic viscosity (m2/s)


Density (kg/m3)



Constant quantity






Branch rank











Non-dimensional quantity



We thank the Brazilian Agency of Coordination for the Improvement of Higher Education Personnel (CAPES) for support at PPGEM/UTFPR and at PPGERHA/UFPR. This research was partially supported by CAPES/COFECUB through the Grant 854/15 and Grant ANEEL/COPEL PD 2866-0470-2017.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Research Center for Rheology and Non-Newtonian FluidsFederal University of Technology, ParanáCuritibaBrazil
  2. 2.Environmental Engineering DepartmentFederal University of ParanáCuritibaBrazil

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