Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Constantin Fetecau, Dumitru Vieru, Tehseen Abbas and Rahmat Ellahi
Additional contact information
Constantin Fetecau: Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, Romania
Dumitru Vieru: Department of Theoretical Mechanics, Technical University of Iasi, 700050 Iasi, Romania
Tehseen Abbas: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Rahmat Ellahi: Department of Mathematics & Statistics, Faculty of Basic and Applied Sciences, International Islamic University, Islamabad 44000, Pakistan

Mathematics, 2021, vol. 9, issue 4, 1-22

Abstract: Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Keywords: analytical solutions; fluid mechanics; UCM fluids; pressure-dependent viscosity; shear stresses on the boundary; starting solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/4/334/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/4/334/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:4:p:334-:d:495290

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().