Abstract
We investigate properties of solutions for a squeezing flow problem governed by a fourth-order nonlinear ODE. The findings obtained reveal significant mathematical features with crucial physical implications. Those findings are obtained via the use of appropriate mathematical equations and approximations, as well as very careful mathematical analysis and derivations, which lead to mathematical formulas for relevant parameters, and results that enable us achieve a new understanding for the physical problem. The derived formulas for the parameters are compared with computations obtained using MATLAB built-in integrators to illustrate the accuracy of those derived formulas. In addition to doing the computations and generating the tabulated results, the MATLAB software is used to generate the figures and illustrations which highlight the main results and conclusions. Existence of solutions is discussed, and some special case solutions are obtained. Properties of parameters and their interdependence are determined, where relevant relations are derived.
Similar content being viewed by others
References
Stefan, J.: Versuch Uber die scheinbare adhasion: Sitzungsberichte der kaiserlichen Akademie der Wissenschaften. Mathematisch Naturwissenschaftliche Classe 69, 713–735 (1874)
Reynolds, O.: On the theory of lubrication. Philos. Trans. R. Soc. 177, 157–235 (1886)
Wolfe, W.A.: Squeeze film pressures. Appl. Sci. Res. 14, 77–90 (1965)
Kuzma, D.C.: Fluid inertia effects in squeeze films. Appl. Sci. Res. 18, 15–20 (1967)
Tichy, J.; Winner, W.O.: Inertial considerations in parallel circular squeeze film bearings. Trans. ASME J. Lub. Technol. 92, 588–592 (1970)
Ishizawa, S.: Squeezing flows of Newtonian liquid films an analysis include the fluid Inertia. Appl. Sci. Res. 32, 149–166 (1976)
Grimm, R.J.: Squeezing flows of Newtonian liquid films an analysis include the fluid inertia. Appl. Sci. Res. 32, 146–149 (1976)
Wang, C.Y.; Watson, L.T.: Squeezing of a viscous fluid between elliptic plates. Appl. Sci. Res. 35, 195–207 (1979)
Usha, R.; Sridharan, R.: Arbitrary squeezing of a viscous fluid between elliptic plates. Fluid Dyn. Res. 18, 35–51 (1996)
Laun, H.M.; Rady, M.: Hassager: analytical solutions for squeeze flow with partial wall slip. J. Non-Newton. Fluid Mech. 81, 1–15 (1999)
Hamdan, M.H.; Baron, R.M.: Squeeze flow of dusty fluids. Appl. Sci. Res. 49, 345–354 (1992)
Nhan, P.T.: Squeeze flow of a viscoelastic solid. J. Non-Newton. Fluid Mech. 95, 343–362 (2000)
Ran, X.J.; Zhu, Q.Y.; Li, Y.: An explicit series solution of the squeezing flow between two infinite plates by means of the homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 14, 119–132 (2009)
Filobello-Nino, U.; Vazquez-Leal, H.; Cervantes-Perez, J.; Benhammouda, B.; Perez-Sesma, A.; Hernandez-Martinez, L.; Jimenez-Fernandez, V.M.; Herrera-May, A.L.; Pereyra-Diaz, D.; Marin-Hernandez, A.; Chua, J.H.: A handy approximate solution for a squeezing flow between two infinite plates by using of Laplace transform-homotopy perturbation method. Springer Plus 3, 421 (2014)
Inc, M.; Akgul, A.: Approximate solutions for MHD a squeezing fluid flow by a novel method. Bound. Value Probl. 1, 18 (2014)
Shamshuddin, Md; Mishra, S.R.; Anwar Beg, O.; Kadir, A.: Viscous dissipation and joule heating effects in non-Fourier MHD squeezing flow. Arab. J. Sci. Eng. 44, 8053–8066 (2019)
Celik, I.: Squeezing flow of nanofluids of CU-water and kerosene between two parallel plates by Gegenbauer collocation method. Eng. Comput. (2019). https://doi.org/10.1007/s00366-019-00821-1
Criffiths, P.T.: Flow of generalised Newtonian fluid due to a rotating disk. J. Non-Newton. Fluid Mech. 221, 9–17 (2015)
Acknowledgements
This research was supported by the Deanship of Scientific Research, Al Imam Mohammad Ibn Saud Islamic University, Saudi Arabia, Grant No. (18-11-12-008).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Al-Ashhab, S. Properties of Solutions in a Fourth-Order Equation of Squeezing Flows. Arab J Sci Eng 45, 7551–7559 (2020). https://doi.org/10.1007/s13369-020-04585-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-020-04585-5