scholarly journals Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Saeed Dinarvand ◽  
Abed Moradi
Keyword(s):  
Shooting Method ◽  
Homotopy Perturbation Method ◽  
Viscous Incompressible Fluid ◽  
Axisymmetric Flow ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Homotopy Perturbation ◽  
Two Dimensional Flow ◽  
Squeeze Number ◽  
Flow Case

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). Graphical results are presented to investigate the influence of the squeeze number on the velocity, skin friction, and pressure gradient. The validity of our solutions is verified by the numerical results obtained by shooting method, coupled with Runge-Kutta scheme.

A New Reliable Approach for Two-Dimensional and Axisymmetric Unsteady Flows Between Parallel Plates

2013 ◽  
Vol 68 (10-11) ◽  
pp. 629-634 ◽  
Author(s):  
◽  
Jagdev Singh ◽  
Yadvendra S. Shishodia
Keyword(s):  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Unsteady Flows ◽  
Solution Procedure ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Homotopy Perturbation ◽  
Roundoff Errors ◽  
Sumudu Transform

The main aim of this work is to present a new reliable approach to compute an approximate solution of the system of nonlinear differential equations governing the problem of two-dimensional and axisymmetric unsteady flows due to normally expanding or contracting parallel plates by the homotopy perturbation method, and the Sumudu transform is adopted in the solution procedure. The method finds the solution without any discretization or restrictive assumptions and avoids the roundoff errors. The numerical solutions obtained by the proposed technique indicate that the approach is easy to implement and computationally very attractive.

THE INFLUENCE OF A MAGNETIC FIELD ON A LAMINAR VISCOUS FLOW IN A SEMI-POROUS CHANNEL

2010 ◽  
Vol 24 (04) ◽  
pp. 497-513
Author(s):  
A. A. RANJBAR ◽  
G. DOMAIRRY ◽  
M. S. JAVADEIN
Keyword(s):  
Magnetic Field ◽  
Homotopy Perturbation Method ◽  
Viscous Incompressible Fluid ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Transverse Magnetic ◽  
Porous Channel ◽  
Two Dimensional ◽  
System Of Differential Equations ◽  
Homotopy Perturbation

In this article, the steady two-dimensional laminar flow of a viscous incompressible fluid in a semi-porous channel in the presence of a transverse magnetic field is considered. The homotopy perturbation method (HPM) and variational iteration method (VIM) are employed to compute an approximation to the solution of the system of differential equations governing on the problem. Velocity profiles, streamlines, and the other parameters of flow are determined. Comparisons are made between the numerical method (NM) and the results of our methods. The results reveal that these methods are very effective, simple, and can be applied to other nonlinear problems.

scholarly journals Radiation Effects on Two-Dimensional MHD Falkner-Skan Wedge Flow

2015 ◽  
Vol 773-774 ◽  
pp. 368-372 ◽  
Author(s):  
M. Abdulhameed ◽  
Habibi Saleh ◽  
Ishak Hashim ◽  
Rozaini Roslan
Keyword(s):  
Boundary Layer ◽  
Radiation Effects ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Fluid Temperature ◽  
Two Dimensional ◽  
Wedge Flow ◽  
Boundary Layer Equations ◽  
Homotopy Perturbation ◽  
The Magnetic Field

Radiation effects on two-dimensional MHD Falkner-Skan boundary layer wedge have been studied. Analytical solution of nonlinear boundary-layer equations is obtained by modified homotopy perturbation method. It is observed that the magnetic field tends to decelerate fluid flow whereas radiations and thermal diffusion tend to increase fluid temperature.

Heat Transfer Analysis on Squeezing Unsteady MHD Nanofluid Flow Between Two Parallel Plates Considering Thermal Radiation, Magnetic and Viscous Dissipations Effects a Solution by Using Homotopy Perturbation Method

2020 ◽  
Vol 18 (2) ◽  
pp. 113-121
Author(s):  
A. El Harfouf ◽  
A. Wakif ◽  
S. Hayani Mounir
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Heat Transfer Analysis ◽  
Nonlinear Ordinary Differential Equations ◽  
Parallel Plates ◽  
Homotopy Perturbation

In this current work, the heat transfer analysis for the unsteady squeezing magnetohydrodynamic flow of a viscous nanofluid between two parallel plates in the presence of thermal radiation, viscous and magnetic dissipations impacts, considering Fourier heat flux model have been explored. The partial differential equations representing flow model are reduced to nonlinear ordinary differential equations by introducing a similarity transformation. The dimensionless and nonlinear ordinary differential equations of the velocity and temperatures functions obtained are solved by employing the homotopy perturbation method. The effects of different parameters on the velocity and temperature profiles are examined graphically, and numerical calculations for the skin friction coefficient and local Nusselt number are tabulated. It is found an excellent agreement in the comparative study with literature results. This present numerical exploration has great relevance, consequently a better understanding of the squeezing flow phenomena in the hydraulic lifts, power transmission, nano gastric tubes, reactor fluidization areas.

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