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.

Unsteady Boundary Layer Flow and Heat Transfer Over a Stretching Sheet

2008 ◽  
Author(s):  
Cornelia Revnic ◽  
Teodor Grosan ◽  
Ioan Pop ◽  
Theodore E. Simos ◽  
George Maroulis ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Unsteady Boundary Layer ◽  
Flow And Heat Transfer ◽  
Layer Flow

scholarly journals An efficient spectral solution for unsteady boundary-layer flow and heat transfer due to a stretching sheet

2017 ◽  
Vol 21 (5) ◽  
pp. 2167-2176 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohamad Rashidi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Legendre Polynomials ◽  
Stretching Sheet ◽  
Unsteady Boundary Layer ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Layer Flow

In this paper, an efficient spectral collocation method based on the shifted Legendre polynomials is applied to study the unsteady boundary-layer flow and heat transfer due to a stretching sheet. A similarity transformation is used to reduce the governing unsteady boundary-layer equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an analytical approximate solution of this system of non-linear ordinary differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed spectral collocation method and those of previously published ones.

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.

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