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Exact analytical expressions are derived for the long time components of the dimensionless velocities and shear stresses corresponding to the modified Stokes problems for incompressible upper-convected Maxwell fluids whose viscosity exponentially depends on pressure.The influence of magnetic field and of the gravitational acceleration is taken into account and some known results from the literature are recovered as limiting cases.Obtained solutions can be used as tests for numerical methods that are developed for more complex flow problems and to find the required time to reach the steady state.Graphical representations showed that the fluids with pressure dependent viscosity flow more quickly in comparison with ordinary fluids.
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Constantin Fetecau (2025) studied this question.
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