In this study, precise analytical formulas were obtained for dimensionless steady-state velocity and shear stress in modified Stokes flow scenarios involving fluids whose viscosity here varies exponentially with pressure, with magnetic effects and gravitational acceleration also taken into account.Actually, these are the first exact solutions for such motions of fluids with exponential dependence of viscosity on pressure in which magnetic effects are taken into consideration.They are important for experimental researchers who want to know the transition moment of a motion to the steady state.In addition, the exact solutions can be used to test numerical methods that are developed to study more complex motion problems.
For validation, different tokidoki hello kitty blind box limiting cases were explored, and several well-known results from previous studies were recovered.The impact of the magnetic field on steady-state behavior and fluid flow was visually represented and thoroughly examined.The findings demonstrated that fluids flowed more slowly and attained steady-state conditions more quickly when influenced by a magnetic field.