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 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.

Analytical Approach of Unsteady Boundary-Layer Flows Over a Semi-Infinite Plate for All Strouhal Numbers

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Mohamed Bachiri ◽  
Ahcene Bouabdallah
Keyword(s):  
Boundary Layer ◽  
Strouhal Number ◽  
Boundary Layer Flow ◽  
Ad Hoc ◽  
Infinite Plate ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Flows ◽  
Local Skin ◽  
Analytic Expressions ◽  
Layer Flow

In this paper, the unsteady boundary-layer flow over a semi-infinite flat plate is solved by means of an analytic approach. Via an ad hoc technique based on the boundary-layer flow evolution, an analytic expression of the velocity profile is proposed. The proposed formula verifies well the results given by Rayleigh, Blasius, and Williams–Rhyne for all time, thus for all Strouhal number values, which is the characteristic of the studied problem. As the main results, the local skin friction depending on a Strouhal number is given in an aim to show an explanation on the flow evolutions from the initial solution to the steady solution in the whole spatial region. This approach permits us to take many applications in engineering technology when the analytic expressions of the velocity, temperature, and matter are looked for.

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.

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