Abstract
The aim of this paper is to compare the efficiency of various techniques for squeezing flow of an incompressible viscous fluid in a porous medium under the influence of a uniform magnetic field squeezed between two large parallel plates having slip boundary. Fourth-order nonlinear ordinary differential equation is obtained by transforming the Navier-Stokes equations. Resulting boundary value problem is solved using Differential Transform Method (DTM), Daftardar Jafari Method (DJM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and Optimal Homotopy Asymptotic Method (OHAM). The problem is also solved numerically using Mathematica solver NDSolve. The residuals of the problem are used to compare and analyze the efficiency and consistency of the abovementioned schemes.
Highlights
The study of squeezing flow started in 19th century and it continues to receive considerable attention due to its practical applications in physical and biophysical areas, namely, food industry, chemical engineering, polymer processing, compression, and injection modeling
Analysis of Newtonian fluid squeezed between two infinite planar plates is studied by Ran et al [2]
Squeezing flow under the influence of magnetic field is broadly applied to bearing with liquid-metal lubrication [4,5,6,7]
Summary
The study of squeezing flow started in 19th century and it continues to receive considerable attention due to its practical applications in physical and biophysical areas, namely, food industry, chemical engineering, polymer processing, compression, and injection modeling. Ullah et al studied the squeezing flow, in a porous medium, of a Newtonian fluid under the influence of imposed magnetic field [9]. High order nonlinear boundary value problems arise in the study of squeezing flow of Newtonian as well as nonNewtonian fluids. Marinca et al [12, 13] introduced OHAM for approximate solution of nonlinear problems of thin film flow of a fourth-grade fluid down a vertical cylinder and for Physics Research International the study of the behavior of nonlinear mechanical vibration of electrical machines. Ullah et al [17] investigated the squeezing fluid flow under the influence of magnetic field with slip boundary condition using DTM. The goal of this research paper is to solve the model of squeezing flow of a Newtonian fluid in a porous medium with MHD effect by using HPM, OHAM, DTM, ADM, NIM, and the Mathematica solver NDSolve. Preparation of the model and basic ideas of the mentioned techniques along with their applications are discussed in the respective sections
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