The Solution of the Fractional Form of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No-Slip Boundaries by Analytical Techniques | ||||
Delta Journal of Science | ||||
Article 2, Volume 40, Issue 1, June 2019, Page 10-23 PDF (1.39 MB) | ||||
Document Type: Research and Reference | ||||
DOI: 10.21608/djs.2019.138918 | ||||
View on SCiNiTO | ||||
Authors | ||||
M. A. Abdeen ; I. A. Lairje | ||||
Department of Mathematics, Faculty of Science, Tanta University | ||||
Abstract | ||||
In this article, two powerful techniques called variational iteration and Adomian decomposition methods are proposed to solve analytically the fractional form of the fourth order nonlinear ordinary differential equation which reduced by similarity transformation from the basic system of nonlinear partial differential equations of motion of an unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates with slip and no-slip boundaries. The analysis of convergence of the proposed methods is discussed through the absolute residual errors for various Reynolds number and various values of the fractional order. Comparisons between the results obtained by the proposed methods with those obtained by the new iterative and Picard methods are made which confirm that the proposed methods are powerful methods and therefore suitable for solving this kind of problems. | ||||
Keywords | ||||
Squeezing flow; Axisymmetric flow; Variational iteration method; Adomian decomposition method; New iterative method; Picard method and Fractional Calculus | ||||
References | ||||
[1] M. J. Stefan, Versuch Über die scheinbare Adhäsion, Sitzungsber., Abt II, Öster. Akad. Wiss., Math.-Naturwiss. Kl., 69 (1874) 713- 721. [2] J. F. Thorpe, in W. A. Shaw, Developments in Theoretical and Applied Mechanics, Pergamon Press, Oxford, 1976. [3] P. S. Gupta and A. S. Gupta, Squeezing flow between parallel plates, wear, 45 (1997), 177- 185. [4] X. J. Ran, Q. Y. Zhu and Y. Li, An explicit series solution of the squeezing flow between two infinite plates by means of the homotopy analysis method, Comm. Nonlinear Sci. Numer. Simul., 14 (2009), 119-132. [5] M. M. Rashidi, A. M. Siddiqui and M. Asadi, Application of homotopy analysis method to the unsteady squeezing flow of a secondgrade fluid between circular plates, Math. Prob. Engin., vol. 2010, Article ID 706840, 18 pages, (2010). [6] D. Yao, V. L. Virupaksha and B. Kim, Study on squeezing flow during nonisothermal embossing of polymer microstructures, Polymer Engin. Sci., 45 (5) (2005), 625-660. [7] P. J. Leider and R. B. Bird, Squeezing flow between parallel disks, I. Theoretical Analysis, Ind. Eng. Chem. Fundam., 13 (1974), 336-341. [8] R. L. Verma, A numerical solution for squeezing flow between parallel channels, Wear, 72 (1981), 89-95. [9] P. Singh, V. Radhakrishnan and K. A. Narayan, Squeezing flow between parallel plates, Ingenieu-archives, 60 (1990), 274- 281. [10] A. A. Hemeda and E. E. Eladdad, Iterative methods for solving the fractional form of unsteady axisymmetric squeezing fluid flow with slip and no-slip boundaries. Advances of Mathematical Physics, Volume 2016, Article ID 6021462, 11 pages, DOI: 10.115/2016/6021462. [11] M. Qayyum, H. Khan, M. T. Rahim and I. Ullah, Analysis of unsteady axisymmetric squeezing fluid flow with slip and no-slip boundaries using OHAM, Math, Prob. Eng., 2015 (2015), 11 pages. | ||||
Statistics Article View: 98 PDF Download: 240 |
||||