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.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

On Spectral Relaxation Approach to Radiating Powell-Eyring Fluid Flow over a Stretching Disk with Newtonian Heating

2018 ◽  
Vol 387 ◽  
pp. 461-473 ◽  
Author(s):  
K. Gangadhar ◽  
D. Vijaya Kumar ◽  
S. Mohammed Ibrahim ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Newtonian Heating ◽  
Nonlinear Boundary Value Problems ◽  
Local Skin ◽  
Boundary Layer Equations ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

In this study we use a new spectral relaxation method to investigate an axisymmetric law laminar boundary layer flow of a viscous incompressible non-Newtonian Eyring-Powell fluid and heat transfer over a heated disk with thermal radiation and Newtonian heating. The transformed boundary layer equations are solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significantly improved by using method in conjunction with the successive over-relaxation method. It is observed that CPU time is reduced in SOR method compare with SRM method.

scholarly journals Nonclassical Symmetry Analysis of Boundary Layer Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Rehana Naz ◽  
Mohammad Danish Khan ◽  
Imran Naeem
Keyword(s):  
Boundary Layer ◽  
Exact Solutions ◽  
Similarity Solution ◽  
Symmetry Analysis ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Nonclassical Symmetry ◽  
Nonclassical Symmetries

The nonclassical symmetries of boundary layer equations for two-dimensional and radial flows are considered. A number of exact solutions for problems under consideration were found in the literature, and here we find new similarity solution by implementing the SADE package for finding nonclassical symmetries.

scholarly journals Solving Boundary-Layer Problems by Residual-Power-Series Method

2016 ◽  
Vol 8 (3) ◽  
pp. 68
Author(s):  
Mohd Taib Shatnawi
Keyword(s):  
Boundary Layer ◽  
Power Series ◽  
Nonlinear Boundary ◽  
Power Series Method ◽  
Boundary Layer Equations ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Linear And Nonlinear ◽  
Boundary Layer Problems ◽  
Residual Power

<p><span lang="EN-US">In this paper, the so-called residual-power-series (RPS) method is presented for solving nonlinear boundary-layer equations. The RPS method provides a single unified treatment for the linear and nonlinear terms in the equations. The accuracy and efficiency of the RPS method is demonstrated for both a single and a system of two coupled boundary-layer equations on an unbounded domain.</span></p>

Homotopy perturbation method for MHD non-Newtonian Williamson fluid over exponentially stretching sheet with viscous dissipation and convective boundary condition

2019 ◽  
Vol 30 (11) ◽  
pp. 1950088 ◽  
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Perturbation Method ◽  
Numerical Method ◽  
Homotopy Perturbation Method ◽  
Stretching Sheet ◽  
Fluid Temperature ◽  
Williamson Fluid ◽  
Homotopy Perturbation ◽  
Exponential Stretching ◽  
Special Cases

This research is aimed at presenting the two-dimensional steady fluid flow, represented by Williamson constitutive model past a nonlinear exponential stretching sheet theoretically. The system of ODEs describing the physical problem is successfully solved numerically with the help of the homotopy perturbation method (HPM). Special attention is given to study the convergence analysis of the proposed method. The influences of the physical governing parameters acting on the fluid velocity and the fluid temperature are explained with the help of the figures and tables. Further, the presented numerical method is employed to calculate both the rate of heat transfer and the drag force for the Williamson fluid flow. In particular, it is observed that both the Eckert number and the dimensionless convective parameter have the effect of enhancing the temperature of the stretching surface, while the inverse was noted for the dimensionless mixed convection parameter. Finally, the comparison with previous numerical investigations of other authors at some special cases which is reported here proves that the results obtained via homotopy perturbation method are accurate and the numerical method is reliable.

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