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Analytical solution of the low Reynolds third-grade non-newtonian fluids flow inside rough circular pipes

Acta Mechanica Sinica 2020年第5期36卷 1018-1030,I0001页

作者： Zohreh Sheidaei Pooria Akbarzadeh Faculty of Mechanical and Mechatronics Engineering Shahrood University of TechnologyShahroodIran

The present paper focuses on finding an analytical solution for fully developed third-grade non-newtonian fluids flows inside rough circular pipes at low Reynolds numbers(Stokes flows).The wall roughness is modeled by two different periodic morphologies based on sinusoidal and triangular *** this study,the relative roughness(ratio of the roughness amplitude to the pipe hydraulic diameter)is selected to be a small value,which is appropriate for the perturbation *** governing parameters including the axial and radial velocity profiles,stream function,wall shear stress,pressure gradient,and friction factor are expressed in analytical formulas and they are compared to the smooth *** effect of the relative roughness,the wall wave number,and the non-newtonian parameter on the governing parameters are *** results show that modeling the roughness by triangular geometry has a better prediction of pressure drop regarding the basic solution of the smooth pipe.

关键词： Relative roughness third-grade non-newtonian fluid Perturbation method Low Reynolds number

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Investigation of third-grade non-newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

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Applied Mathematics and Mechanics(English Edition) 2015年第11期36卷 1449-1458页

作者： M.HATAMI S.E.GHASEMI S.A.R.SAHEBI S.MOSAYEBIDORCHEH D.D.GANJI J.HATAMI Department of Mechanical Engineering Esfarayen University of Technology Young Researchers and Elite Club Islamic Azad University Deptartment of Mechanical Engineering Islamic Azad University Department of Mechanical Engineering Babol University of Technology Garmsar Health & Care Center Semnan University of Medical Sciences

In this paper, a non-newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the third- grade non-newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method （Hybrid-Ms- DTM） and the Crank-Nicholson method （CNM） are used to solve the partial differential equation （PDE）, and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, 9, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when Ag increases.

关键词： pulsatile blood third-grade non-newtonian fluid differential transforma-tion method (DTM) femoral artery coronary artery

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