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

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