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On the Exact Solutions of Couple Stress Fluids

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Abstract:

Exact solutions of the momentum equations of couple stress fluid are investigated. Making use of stream function, the two-dimensional flow equations are transformed into non-linear compatibility equation, and then it is linearized by vorticity function. Stream functions and velocity distributions are discussed for various flow situations.

Info:

Periodical:
Advanced Trends in Mathematics (Volume 1)
Pages:
27-32
Citation:
W. Khan and F. Yousafzai, "On the Exact Solutions of Couple Stress Fluids", Advanced Trends in Mathematics, Vol. 1, pp. 27-32, 2014
Online since:
December 2014
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References:

V. K. Stokes, Couple Stresses in fluid, The physics of fluids., 9, 1709-1715, (1966).

G. Ramanaiah, Squeeze films between finite plates lubricated by fluids with couple-stresses, Wear., 54, 315-320, (1979).

P. Sinha and C. Singh, Couple stress in the lubrication of rolling contact bearings considering cavitations, Wear., 67, 85-91, (1981).

Li-Wang, Qin-Zhu and Zhu-Wen, On the performance of dynamically loaded journal bearings with couple stress fluids, Tribology Int., 35, 185-191, (2002).

S. Islam and C. Y. Zhou, Exact solutions for two dimensional flows of couple stress fluids., ZAMP, 58, 1035-1048, (2007).

S. Islam, C. Y. Zhou, X. J. Ran, Exact solutions for different vorticity functions of couple stress fluids., J Zhejiang Univ Sci A, 9(5), 672-680, (2008).

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[1] S. Joseph, Numerical Heat Transfer and Fluid Flow, p. 527, 2019

DOI: https://doi.org/10.1007/978-981-13-1903-7_61

[2] I. Barna, L. Mátyás, M. Pocsai, "Self-similar analysis of a viscous heated Oberbeck–Boussinesq flow system", Fluid Dynamics Research, Vol. 52, p. 015515, 2020

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[3] M. Nazeer, F. Hussain, S. Iftikhar, M. Ijaz Khan, K. Ramesh, N. Shehzad, A. Baig, S. Kadry, Y. Chu, " Mathematical modeling of bio‐magnetic fluid bounded within ciliated walls of wavy channel ", Numerical Methods for Partial Differential Equations, 2021

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[4] M. Dhlamini, H. Mondal, P. Sibanda, S. Motsa, "Numerical Analysis of Couple Stress Nanofluid in Temperature Dependent Viscosity and Thermal Conductivity", International Journal of Applied and Computational Mathematics, Vol. 7, 2021

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[5] T. Anusha, U. Mahabaleshwar, Y. Sheikhnejad, "An MHD of Nanofluid Flow Over a Porous Stretching/Shrinking Plate with Mass Transpiration and Brinkman Ratio", Transport in Porous Media, 2021

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[6] M. Bilal, A. Saeed, T. Gul, M. Rehman, A. Khan, "Thin-film flow of Carreau fluid over a stretching surface including the couple stress and uniform magnetic field", Partial Differential Equations in Applied Mathematics, p. 100162, 2021

DOI: https://doi.org/10.1016/j.padiff.2021.100162

[7] M. Bilal, A. Saeed, T. Gul, M. Rehman, A. Khan, "Thin-film flow of Carreau fluid over a stretching surface including the couple stress and uniform magnetic field", Partial Differential Equations in Applied Mathematics, Vol. 4, p. 100162, 2021

DOI: https://doi.org/10.1016/j.padiff.2021.100162

[8] T. Anusha, U. Mahabaleshwar, Y. Sheikhnejad, "An MHD of Nanofluid Flow Over a Porous Stretching/Shrinking Plate with Mass Transpiration and Brinkman Ratio", Transport in Porous Media, Vol. 142, p. 333, 2022

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