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A New Algorithm on the Solutions of Forced Convective Heat Transfer in a Semi-Infinite Flat Plate

Published online by Cambridge University Press:  31 March 2011

P.-Y. Tsai  and
C.-K. Chen
P.-Y. Tsai
Affiliation:
Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
C.-K. Chen*
Affiliation:
Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
** Professor, corresponding author
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Abstract

In this paper, a new algorithm is proposed to solve the velocity and temperature fields in the thermal boundary layer flow over a semi-infinite flat plate. Both the flow and heat transfer solutions are calculated accurately by the Laplace Adomian decomposition method, Padé approximant and the optimal design concept. The Laplace Adomian decomposition method (LADM) is a combination of the numerical Laplace transform algorithm with the Adomian decomposition method (ADM). A hybrid method of the LADM combined with the Padé approximant, named the LADM-Padé approximant technique, is introduced to solve the thermal boundary layer problems directly without any small parameter assumptions, linearizatons or transformations of the boundary value problems to a pair of initial value problems. The LADM-Padé approximant solutions here in are given to show the accuracy in comparison with different method solutions.

Keywords

Adomian decomposition methodBoundary layer flowLaplace transformationPadé ap-proximant
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 1 , March 2011 , pp. 63 - 69
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

REFERENCES

1.Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston (1994).CrossRefGoogle Scholar
2.Khuri, S. A., “A Laplace Decomposition Algorithm Applied to a Class of Nonlinear Differential Equations,” Journal of Applied Mathematics, 1, pp. 141–155 (2001).CrossRefGoogle Scholar
3.Howarth, L., “On the Solution of the Laminar Boundary Layer Equations,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 164, pp. 547–579 (1938).Google Scholar
4.Liao, S.-J., “An Explict, Totally Analytic Approximante Solution for Blasius' Viscous Flow Problems,” International Journal of Non-Linear Mechanics, 34, pp. 759–778 (1999).CrossRefGoogle Scholar
5.Allan, F. M. and Syam, M. I., “On the Analytic Solutions of the Nonhomogeneous Blasius Problem,” Journal of Computational and Applied Mathematics, 182, pp. 362–371 (2005).CrossRefGoogle Scholar
6.He, J.-H., “Approximate Analytical Solution of Blasius' Equation,” Communications in Nolinear Science & Numerical Simulation, 3, pp. 260–263 (1998).CrossRefGoogle Scholar
7.Wazwaz, A.-M., “The Variational Iteration Method for Solving Two Forms of Blasius Equation on a Half-Infinite Domain,” Applied Mathematics and Computation, 188, pp. 485–491 (2007).CrossRefGoogle Scholar
8.He, J.-H., “A Simple Perturbation Approach to Blasius Equation,” Applied Mathematics and Computation, 140, pp. 217–222 (2003).CrossRefGoogle Scholar
9.Wazwaz, A.-M., “A Reliable Algorithm for Solving Boundary Value Problems for Higher-Order Integro-Differential Equations,” Applied Mathematics and Computation, 118, pp. 327–342 (2001).CrossRefGoogle Scholar
10.Wang, L., “A New Algorithm for Solving Classical Blasius Equation,” Applied Mathematics and Computation, 157, pp. 1–9 (2004).CrossRefGoogle Scholar
11.Abbasbandy, S., “A Numerical Solution of Blasius Equation by Adomian's Decomposition Method and Comparison with Homotopy Perturbation Method,” Chaos. Solitions & Fractals, 31, pp. 257–260 (2007).CrossRefGoogle Scholar
12.Ranasinghe, A. I., “Solution of Blasius Equation by Decomposition,” Applied Mathematical Sciences, 3, pp. 605–611 (2009).Google Scholar
13.Yu, L.-T. and Chen, C.-K., “The Solution of the Blasius Equation by the Differential Transformation Method,” Mathematical and Computer Modelling, 28, pp. 101–111 (1998).Google Scholar
14.Kuo, B.-L., “Application of the Differential Transformation Method to the Solutions of Falkner-Skan Wedge Flow,” Acta Mechanica, 165, pp. 161–174 (2003).CrossRefGoogle Scholar
15.Kuo, B.-L., “Thermal Boundary-Layer Problems in a Semi-Infinite Flat Plate by the Differential Transformation Method,” Applied Mathematics and Computation, 150, pp. 303–320 (2004).CrossRefGoogle Scholar
16.Cortell, R., “Numerical Solutions of the Classical Blasius Flat-Plate Problem,” Applied Mathematics and Computation, 170, pp. 706–710 (2005).CrossRefGoogle Scholar
17.Bejan, A., Convection Heat Transfer, John Wiley & Sons, New Jersey (2004).Google Scholar