A Cosserat Continuum Mechanical Approach to Turbulent Channel Pressure Driven Flow of Isotropic Fluid

Abstract

In this study the theory of the micropolar fluid based on a Cosserat continuum is explained briefly and the governing equations of first degree Cosserat continua are achieved from a new method. Then they are used to analyze the fully developed steady channel flow. This system of differential equations requires additional boundary conditions in comparison with Navier-Stokes equations. This problem is closed in this study in two ways: (a) The addition to no-slip boundary conditions, a new boundary condition are utilized to find the velocity profile. This profile is too close to exact solution of classical Navier-Stokes for laminar channel flow. (b) Whole points of an experimental study of turbulent channel flow are considered and by means of a least square algorithm constants are determined. This result is consistent with the experimental data and semi-empirical relation for turbulent channel flow for Reynolds number from 4 × 10³ to 3.24 × 10⁶.

Keywords:

• Channel flow
• Cosserat continua
• higher-order continuum mechanics
• micropolar fluid