scholarly journals Approximate Analytical Expressions of Non-Linear Boundary Value problem for a Boundary Layer Flow using the Homotopy Analysis Method

2019 ◽  
Vol 1 (2) ◽  
pp. 34-39
Author(s):  
V Ananthaswamy ◽  
M Subha ◽  
A Mohamed Fathima
Keyword(s):  
Boundary Layer ◽  
Boundary Value Problem ◽  
Homotopy Analysis Method ◽  
Boundary Layer Flow ◽  
Linear Boundary ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Analytical Expressions ◽  
Linear Boundary Value Problem

scholarly journals Analytic approximate solutions for unsteady boundary-layer flow and heat transfer due to a stretching sheet by homotopy analysis method

2010 ◽  
Vol 15 (1) ◽  
pp. 83-95 ◽  
Author(s):  
M. M. Rashidi ◽  
S. A. Mohimanian Pour
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Analysis Method ◽  
Unsteady Boundary Layer ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Layer Flow

In this work, the homotopy analysis method is applied to study the unsteady boundary-layer flow and heat transfer due to a stretching sheet. The analytic solutions of the system of nonlinear ordinary differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. The velocity and temperature profiles are shown and the influence of non-dimensional parameter on the heat transfer is discussed in detail. The validity of our solutions is verified by the numerical results.

scholarly journals On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
S. S. Motsa
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Boundary Layer Flow ◽  
Analysis Method ◽  
Unsteady Boundary Layer ◽  
Local Skin ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Spectral Homotopy Analysis Method

This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. The applicability and effectiveness of the expanded SHAM approach are tested on a non-linear PDE that models the problem of unsteady boundary layer flow caused by an impulsively stretching plate. Numerical simulations are conducted to generate results for the important flow properties such as the local skin friction. The accuracy of the present results is validated against existing results from the literature and against results generated using the Keller-box method. The preliminary results from the proposed study indicate that the present method is more accurate and computationally efficient than more traditional methods used for solving PDEs that describe nonsimilar boundary layer flow.

scholarly journals Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet

2019 ◽  
pp. 1-7
Author(s):  
S. Alao ◽  
R. A. Oderinu ◽  
F. O. Akinpelu ◽  
E. I. Akinola
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Analysis Method ◽  
Viscous Boundary Layer ◽  
New Approach ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Viscous Boundary ◽  
Adomian Polynomial

This paper investigates a new approach called Homotopy Analysis Decomposition Method (HADM) for solving nonlinear differential equations, the method was developed by incorporating Adomian polynomial into Homotopy Analysis Method. The Adomian polynomial was used to decompose the nonlinear term in the equation then apply the scheme of homotopy analysis method. The accuracy and efficiency of the proposed method was validated by considering algebraically decaying viscous boundary layer  flow due to a moving sheet. Diagonal Pade approximation was used to get the skin friction. The obtained results were presented along with other methods in the literature in tabular form to show the computational efficiency of the new approach. The results were found to agree with those in literature. Owing to its small size of computation, the method is not aected by discretization error as the results are presented in form of polynomials.

scholarly journals Homotopy Analysis Method to determine Magneto Hydrodynamics flow of compressible fluid in a channel with porous walls

2016 ◽  
Vol 34 (1) ◽  
pp. 173-186
Author(s):  
Reza Mohammadyari ◽  
J. Rahimipetroudi ◽  
Iman Rahimipetroudi ◽  
Mazaher Rahimi Esboee
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Compressible Fluid ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Analysis Method ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Porous Walls ◽  
Layer Flow

In this article magnetohydrodynamics (MHD) boundary layer flow of compressible fluid in a channel with porous walls is researched. In this study it is shown that the nonlinear Navier-Stokes equations can be reduced to an ordinary differential equation, using the similarity transformations and boundary layer approximations. Analytical solution of the developed nonlinear equation is carried out by the Homotopy Analysis Method (HAM). In addition to applying HAM into the obtained equation, the result of the mentioned method is compared with a type of numerical analysis as Boundary Value Problem method (BVP) and a good agreement is seen. The effects of the Reynolds number and Hartman number are investigated.

Approximate Analytical Solution of Magnetohydrodynamics Compressible Boundary Layer flow with Pressure Gradient and suction/injection

2014 ◽  
Vol 6 (3) ◽  
pp. 1216-1226
Author(s):  
Sathyanarayana. S. B
Keyword(s):  
Boundary Layer ◽  
Analytical Solution ◽  
Pressure Gradient ◽  
Boundary Layer Flow ◽  
Exact Analytical Solution ◽  
Adverse Pressure Gradient ◽  
Compressible Boundary Layer ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Layer Flow

The aim of this work is to obtain exact analytical solution to the two dimensional laminar compressible boundary layer flow with an adverse pressure gradient in the presence of heat and mass transfer with MHD. The method applied is homotopy analysis method. It is shown that this solution agrees very well with numerical solution which is obtained by Runge-Kutta Merson method and results are shown graphically for different magnetic parameters.

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