Investigation of Power-Law Fluid Flow through a Two-Dimensional Microchannel Based on a Couple Stress Theory-Calculation of Characteristic Length

Document Type : Research Article

Authors

1 PHD student, Shahrekord University

2 Mechanical Engineering Department, Shahrekord University, Shahrekord

3 Shahrekord University

Abstract

The present paper aims to investigate the developed flow of Newtonian and non Newtonian fluids in a two-dimensional microchannel based on the completely consistent couple stress theory and the characteristic length of the fluids. First, the velocity and volumetric flow rate profiles of Newtonian and power-law non-Newtonian fluids in the microchannel were obtained via analytical methods. After that, the characteristic material lengths of water as a Newtonian fluid and blood as a non-Newtonian fluid were obtained and then the results were compared with the experimental data of other papers. Comparing the characteristic lengths of water and blood indicated the dependence of characteristic material length scale on the fluid material. Calculating the characteristic length produced the blood velocity profile of the couple stress theory in microchannel which was in turn compared to the results of classical Navier-Stokes theory. According to the results, increasing the volumetric flow rate of the fluid also increases the difference between the results of couple stress theory and classical theory, indicating the increased influence of length on microchannel flow properties. Further, the velocity profile of water in the microchannel was compared with the experimental results, revealing a good consistency between them and the couple stress theory.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 7
October 2020
Pages 1707-1714

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