Magnetohydrodynamic squeezing flow of casson nanofluid between two parallel plates in a porous medium using method of matched asymptotic expansion

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.

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HOMOTOPY ANALYSIS OF TRANSIENT MAGNETO-BIO-FLUID DYNAMICS OF MICROPOLAR SQUEEZE FILM IN A POROUS MEDIUM: A MODEL FOR MAGNETO-BIO-RHEOLOGICAL LUBRICATION

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519411004642 ◽

2012 ◽

Vol 12 (03) ◽

pp. 1250051 ◽

Cited By ~ 32

Author(s):

O. ANWAR BÉG ◽

M. M. RASHIDI ◽

T. A. BÉG ◽

M. ASADI

Keyword(s):

Magnetic Field ◽

Porous Medium ◽

Angular Velocity ◽

Differential Equations ◽

Darcy Number ◽

Squeeze Film ◽

Squeezing Flow ◽

Parallel Plates ◽

Viscosity Parameter ◽

Homotopy Analysis

The transient squeezing flow of a magneto-micropolar biofluid in a noncompressible porous medium intercalated between two parallel plates in the presence of a uniform strength transverse magnetic field is investigated. The partial differential equations describing the two-dimensional flow regime are transformed into nondimensional, nonlinear coupled ordinary differential equations for linear and angular momentum (micro-inertia). These equations are solved using the robust Homotopy Analysis Method (HAM) and also numerical shooting quadrature. Excellent correlation is achieved. The influence of magnetic field parameter (Ha) , micropolar spin gradient viscosity parameter (Γ) and unsteadiness parameter (S) on linear and angular velocity (micro-rotation) are presented graphically, for specified values of the micropolar vortex viscosity parameter (R), Darcy number (Da i.e. permeability parameter) and medium porosity parameter (ε). Increasing magnetic field (Ha) serves to decelerate both the linear and angular velocity i.e. enhances lubrication. The excellent potential of HAM in bio-lubrication flows is highlighted.

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Application of Daftardar Jafari Method to First Grade MHD Squeezing Fluid Flow in a Porous Medium with Slip Boundary Condition

Abstract and Applied Analysis ◽

10.1155/2014/479136 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Inayat Ullah ◽

M. T. Rahim ◽

Hamid Khan

Keyword(s):

Boundary Condition ◽

Porous Medium ◽

Velocity Profile ◽

Nonlinear Boundary ◽

Slip Boundary Condition ◽

First Grade ◽

Squeezing Flow ◽

Parallel Plates ◽

Governing Equations ◽

Slip Boundary

In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.

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