Application of the theory of micropolar continuum on the flow suspension in a cylindrical channel

Abstract

This paper presents an analytical solution of a mathematical model which treats fluid flow suspension in a cylindrical channel. The model is the application of the theory of micropolar continuum on the flow of suspension and it consists of coupled linear differential equations with variable coefficients. The cylindrical channel consists of two cylinders: the internal cylinder was still and the external one rotated with constant velocity. This model enabled us to analyze the motion of a suspension, as heterogeneous mixture of a liquid with solid particles. The solution was found in the form of special Bessel's functions of the zero and the first order. The results were shown on diagrams for some characteristic values, and the good agreement was achieved between the calculated and expected results.

Micropolar fluid between two coaxial cylinders (numerical approach)

“…In the end, it should be mentioned that the results presented here are in complete accordance with the results presented in papers [8,19]. Differences in the values of 𝑣(𝑟) and 𝑤(𝑟) between the analytical and numerical solutions are negligible, i.e.…”

“…In order to obtain the values of the velocity of suspension 𝑣 and the velocity of microrotation 𝑤, the coefficients that consist of Bessel's functions must be calculated first. That is why the numerical solutions have a more practical application, although it showed good agreement with the results of the analytical procedure [8,19]. Furthermore, Agarwal and Dhanpal [2] obtained a numerical solution for the micropolar fluid flow with heat transfer between two coaxial porous circular cylinders.…”

“…Finally, it should be mentioned that the problem was solved in the analytical form [8,19]. The disadvantage of these analytical solutions is their complexity.…”