Open AccessSteady-state solutions for modified Stokes’ second problem of Maxwell fluids with power-law dependence of viscosity on the pressure
Author(s) -
Constantin Fetecău,
Dumitru Vieru
Publication year - 2022
Publication title -
open journal of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 2616-4906
pISSN - 2523-0212
DOI - 10.30538/oms2022.0175
Subject(s) - couette flow , compressibility , newtonian fluid , viscosity , power law , mechanics , physics , classical mechanics , power law fluid , non newtonian fluid , flow (mathematics) , fluid dynamics , mathematics , thermodynamics , statistics
Analytical expressions for the steady-state solutions of modified Stokes’ second problem of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are determined when the gravity effects are considered. Fluid motion is generated by a flat plate that oscillates in its plane. We discuss similar solutions for the simple Couette flow of the same fluids. Obtained results can be used by the experimentalists who want to know the required time to reach the steady or permanent state. Furthermore, we discuss the accuracy of results by graphical comparisons between the solutions corresponding to the motion due to cosine oscillations of the plate and simple Couette flow. Similar solutions for incompressible Newtonian fluids with power-law dependence of viscosity on the pressure performing the same motions and some known solutions from the literature are obtained as limiting cases of the present results. The influence of pertinent parameters on fluid motion is graphically underlined and discussed.