scholarly journals Homotopy perturbation method for three-dimensional problem of condensation film on inclined rotating disk

2012 ◽  
Vol 19 (3) ◽  
pp. 437-442 ◽  
Author(s):  
M. Sheikholeslami ◽  
H.R. Ashorynejad ◽  
D.D. Ganji ◽  
A. Yıldırım
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Dimensional Problem ◽  
Homotopy Perturbation

scholarly journals Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Saeed Dinarvand
Keyword(s):  
Perturbation Method ◽  
Series Solution ◽  
Homotopy Perturbation Method ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Homotopy Perturbation ◽  
Spinning Disk ◽  
Through Flow

The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.

NEW ANALYTICAL SOLUTION OF THE THREE-DIMENSIONAL NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 23 (26) ◽  
pp. 3147-3155 ◽  
Author(s):  
MOHAMMAD MEHDI RASHIDI ◽  
GANJI DOMAIRRY
Keyword(s):  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Differential Transform ◽  
Conditions At Infinity

The purpose of this study is to implement a new analytical method (the DTM-Padé technique, which is a combination of the differential transform method (DTM) and the Padé approximation) for solving Navier–Stokes equations. In this letter, we will consider the DTM, the homotopy perturbation method (HPM) and the Padé approximant for finding analytical solutions of the three-dimensional viscous flow near an infinite rotating disk. The solutions are compared with the numerical (fourth-order Runge–Kutta) solution. The results illustrate that the application of the Padé approximants in the DTM and HPM is an appropriate method in solving the Navier–Stokes equations with the boundary conditions at infinity. On the other hand, the convergence of the obtained series from DTM-Padé is greater than HPM-Padé.

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. 

Sign in / Sign up

Export Citation Format

Share Document