Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Constantin Fetecau, Dumitru Vieru, Abdul Rauf and Tahir Mushtaq Qureshi
Pages: [1] - [28]
Received Date: August 30, 2021
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122224
Two isothermal motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are investigated when gravity effects are taken into account. The fluid motion, between two infinite horizontal parallel plates, is generated by the lower plate that applies a time-dependent shear stress to the fluid. Exact expressions are established for the steady-state components of the dimensionless start-up velocity, shear stress, and normal stress. They are used to find the needed time to touch the steady-state and to provide corresponding solutions for the motion of the same fluids induced by an exponential shear stress on the boundary. This time is useful for experimentalists who want to eliminate transients from their experiments. It is higher for motions of ordinary fluids as compared to fluids with pressure-dependent viscosity. The variation of starting solutions (numerical solutions) in time and space is graphically represented and some characteristics of the fluid motion are brought to light.
steady-state solutions, Maxwell fluids, pressure-dependent viscosity, shear stress on the boundary.
