Abstract
This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.
Highlights
In recent time, non-Newtonian fluids have become quite prevalent in industry and engineering
The governing partial differential equations for velocity are analytically solved by using Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM) methods
And 2, we calculated the numerical comparisons of OHAM and HPM
Summary
Non-Newtonian fluids have become quite prevalent in industry and engineering. They are known as (i) the differential type, (ii) the rate type, and (iii) the integral type. We will study the second model, the rate type fluid and consider its subclass known as Oldroyd-B fluid. The Oldroyd-B fluid model, on the other hand, has a measurable retardation time and can relate the viscoelastic manners of dilute polymeric solutions under general flow conditions. Fetecau et al [1] obtained exact solutions in their study on constantly accelerating flow over a flat plate for Oldroyd-B fluid. Fetecau et al [2] studied the transient oscillating motion of an Oldroyd-B fluids in cylindrical domains and obtained the exact solutions. Haitao and Mingyu [3] studied the series solution for the plane Poiseuille flow
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