Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Constantin Fetecau, Abdul Rauf and Tahir Mushtaq
Pages: [17] - [39]
Received Date: January 17, 2023; Revised February 24, 2023
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122273
Two isothermal unsteady motions of the incompressible Burgers fluids between infinite horizontal parallel plates are analytically and numerically investigated when a differential expression of the shear stress is prescribed on the lower plate. Closed-form expressions are established for the dimensionless permanent velocity fields and the corresponding shear stresses. They seem to be the first exact solutions for such motions of Burgers fluids. The corresponding permanent solutions for Oldroyd-B, Maxwell, second grade and Newtonian fluids performing similar motions can immediately be obtained as limiting cases of general solutions. The obtained velocity fields are used to determine the needed time to reach the steady state for the respective motions. It was found that the steady state for such isothermal motions of the incompressible non-Newtonian fluids is earlier obtained for the Burgers fluids in comparison with Oldroyd-B or Maxwell fluids.
permanent solutions, Burgers fluids, parallel plates, mixed initial-boundary value problems.
