TY - JOUR

T1 - Analytical expression for velocity profiles and flow resistance in channels with a general class of noncircular cross sections

AU - Navardi, Shahin

AU - Bhattacharya, Sukalyan

AU - Azese, Martin

PY - 2015/9

Y1 - 2015/9

N2 - This article discusses how to derive a closed-form analytical solution describing the profile of unidirectional
flow through a class of noncircular tubes. The cross sections of the conduits are a slightly distorted version
of regular shapes, like triangles or trapeziums or rectangles, that are commonly seen in microfluidic or heat pipe
applications. Hence, the study leads to approximate but useful expression for velocity profiles as well as resistivity
for the aforementioned channels. Moreover, the paper shows how to extend the fundamental idea to other arbitrary
geometries, providing simple expressions for flow fields that can be used subsequently in various hydrodynamic
calculations. The analysis also gives an estimate of error in such a mathematical treatment that is found to be
adequately accurate. Thus, the findings will be especially relevant in a number of fields, including microfluidic
separation, heat pipe design, and capillary transport optimization.

AB - This article discusses how to derive a closed-form analytical solution describing the profile of unidirectional
flow through a class of noncircular tubes. The cross sections of the conduits are a slightly distorted version
of regular shapes, like triangles or trapeziums or rectangles, that are commonly seen in microfluidic or heat pipe
applications. Hence, the study leads to approximate but useful expression for velocity profiles as well as resistivity
for the aforementioned channels. Moreover, the paper shows how to extend the fundamental idea to other arbitrary
geometries, providing simple expressions for flow fields that can be used subsequently in various hydrodynamic
calculations. The analysis also gives an estimate of error in such a mathematical treatment that is found to be
adequately accurate. Thus, the findings will be especially relevant in a number of fields, including microfluidic
separation, heat pipe design, and capillary transport optimization.

U2 - 10.1007/s10665-015-9823-9

DO - 10.1007/s10665-015-9823-9

M3 - Article

JO - J Eng Math

JF - J Eng Math

ER -