Modares Mechanical Engineering

Modares Mechanical Engineering

Analytical and Semi-Analytical Investigation and Solutions for non-Newtonian Micropolar Fluid Flows in Three Different Cases

Authors
Ramin Ghorbani 1
Seyed Mostafa Hosseinalipoor 2
1 Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
2 School of Mechanical Engineering, Iran University of Science & Technology
Abstract
In this paper, the goal is to provide analytical solutions for the thin film flow of a non-Newtonian fluid in different geometries and boundary conditions. An analytical solution for the non-Newtonian fluids is one of the most important and challenging issues that helps in understanding the physics of these fluids. For this purpose, the theory of micropolar fluids has been used. Thin film in three specific geometries, including flow downward on an inclined surface, flow on a moving ribbon, and flow downward on a vertical cylinder is considered. In order to solve the governing equations and obtaining the velocity and rotational fields, in the first two geometries, an analytical methods and in the third geometry a combined analytic and numerical methods are used with respect to the complexity of the equations. The rotational and velocity fields are plotted for all three cases and the results are discussed for different values of the parameters of a micropolar fluid. Also, the effect of the concentration of microelements in the fluid has been studied. It was observed that with the increase of the micropolar fluid parameter, the magnitude of velocity and rotation decreases.
Keywords
Non-Newtonian Fluid
Thin Film
Analytical Solution
[1] F. Irgens, Rheology and non-newtonian fluids, Springer International PU, pp. 1-8, 2014.
[2] A. Eringen, Simple microfluids, International Journal of Engineering Science, Vol. 2, No. 2, pp. 205-217, 1964.
[3] A. Eringen, Theory of anisotropic micropolar fluids, International Journal of Engineering Science, Vol. 18, No. 1, pp. 5-17, 1980.
[4] D. Picchi, P. Poesio, A. Ullmann, N. Brauner, Characteristics of stratified flows of Newtonian/non-Newtonian shear-thinning fluids, International Journal of Multiphase Flow, Vol. 97, No. 4, pp. 109-133, 2017.
[5] M. Abou-zeid, Effects of thermal-diffusion and viscous dissipation on peristaltic flow of micropolar non-Newtonian nanofluid: Application of homotopy perturbation method, Results in Physics, Vol. 6, No. 6, pp. 481- 495, 2016.
[6] M. Sajid, Z. Abbas and T. Hayat, Homotopy analysis for boundary layer flow of a micropolar fluid through a porous channel, Applied Mathematical Modelling, Vol. 33, No. 11, pp. 4120-4125, 2009.
[7] J. Raza, A. Rohni, an Z. Omar, Rheology of micropolar fluid in a channel with changing walls: Investigation of multiple solutions, Journal of Molecular Liquids, Vol. 223, No. 2, pp. 890-902, 2016.
[8] A. Zaib, M. Sharif Uddin, K. Bhattacharyya, S. Shafie, Micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet, Propulsion and Power Research, Vol. 5, No. 4, pp. 310-317, 2016.
[9] N. Khan, S. Khan, A. Ara, Flow of micropolar fluid over an off centered rotating disk with modified Darcy's law, Propulsion and Power Research, Vol. 5, No. 7, pp. 423-432, 2017.
[10] A. R. Haghighi, A. Shadipour, M. Shahbazi Asl, Numerical simulation of micropolar fluid flow through an asymmetric tapered stenosis artery, Modares Mechanical Engineering, Vol. 17, No. 12, pp. 33-41, 2018. (in (فارسی Persian
[11] J. Kumar, J. Umavathi, A. Chamkha, I. Pop, Fully-developed free-convective flow of micropolar and viscous fluids in a vertical channel, Applied Mathematical Modelling, Vol. 34, No. 5, pp. 1175-1186, 2010.
[12] S. Xinhui, Z. Liancun, Z. Xinxin, S. Xinyi, Homotopy analysis method for the asymmetric laminar flow and heat transfer of viscous fluid between contracting rotating disks, Applied Mathematical Modelling, Vol. 36, No. 4, pp. 1806-1820, 2012.
[13] G. Ahmadi, Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate, International Journal of Engineering Science, Vol. 14, No. 7, pp. 639-646, 1976.
Modares Mechanical Engineering
Volume 18, Issue 2
April 2018
Pages 170-178