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Objectives: To study the unsteady magneto-hydro-dynamic (MHD) thin layer flow of a fourth-order fluid through a moving and oscillating belt. Methods: The well-known analytical technique, namely Adomian decomposition method (ADM) is used to solve the non-linear partial differential equation for governing equations of velocity profile with subjects to initial and boundary conditions for both lift and drainage problems. Findings and novelty/ improvements: The solution is found in excellent agreement. The basic purpose to study the effect of MHD on velocity field and understand the behavior of this physical problem and the effects of different non-dimensional parameters the graphical results are provided.

Analysis of Unsteady MHD Thin Layer Flow of Fourth-Order Fluid Through a Vertical Belt