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Research Papers: Forced Convection

# Use of Optimal Homotopy Asymptotic Method and Galerkin’s Finite Element Formulation in the Study of Heat Transfer Flow of a Third Grade Fluid Between Parallel Plates

[+] Author and Article Information
S. Iqbal

Department of Computer Science, COMSATS Institute of Information Technology, Sahiwal Campus, Pakistan

A. R. Ansari1

Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait e-mail: ansari.a@gust.edu.kw

A. M. Siddiqui

Department of Mathematics, York Campus, Pennsylvania State University, York, PA 17403

A. Javed

Department of Engineering Management, CASE-Centre for Advanced Studies in Engineering, 19-Attaturk Avenue, G-5/1, Islamabad, Pakistan

1

Corresponding author.

J. Heat Transfer 133(9), 091702 (Jul 08, 2011) (13 pages) doi:10.1115/1.4003828 History: Received October 30, 2010; Accepted March 10, 2011; Revised March 10, 2011; Published July 08, 2011; Online July 08, 2011

## Abstract

We investigate the effectiveness of the optimal homotopy asymptotic method (OHAM) in solving nonlinear systems of differential equations. In particular we consider the heat transfer flow of a third grade fluid between two heated parallel plates separated by a finite distance. The method is successfully applied to study the constant viscosity models, namely plane Couette flow, plane Poiseuille flow, and plane Couette–Poiseuille flow for velocity fields and the temperature distributions. Numerical solutions of the systems are also obtained using a finite element method (FEM). A comparative analysis between the semianalytical solutions of OHAM and numerical solutions by FEM are presented. The semianalytical results are found to be in good agreement with numerical solutions. The results reveal that the OHAM is precise, effective, and easy to use for such systems of nonlinear differential equations.

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## Figures

Figure 1

Effect of different parameters on the temperature distribution by using OHAM and FEM for plane Couette flow; (a) Effect of β on temperature profile (OHAM); (b) Effect of β on temperature profile (FEM); (c) Effect of λ on temperature profile (OHAM); (d) Effect of λ on temperature profile (FEM)

Figure 2

Effect of different parameters on the velocity field using OHAM and FEM for plane Poiseuille flow; (a) Effect of β on velocity field (OHAM); (b) Effect of β on velocity field (FEM); (c) Effect of B on velocity field (OHAM); (d) Effect of B on velocity field (FEM)

Figure 3

Effect of different parameters on the velocity field using OHAM and FEM for plane Poiseuille flow; (a) Effect of β on temperature profile (OHAM); (b) Effect of β on temperature profile (FEM); (c) Effect of B on temperature profile (OHAM); (d) Effect of B on temperature profile (FEM); (e) Effect of λ on temperature profile (OHAM); (f) Effect of λ on temperature profile (FEM)

Figure 4

Effect of different parameters on the velocity field by using OHAM and FEM for plane Couette–Poiseuille flow; (a) Effect of β on velocity profile (OHAM); (b) Effect of β on velocity profile (FEM); (c) Effect of B on velocity profile (OHAM); (d) Effect of B on velocity profile (FEM)

Figure 5

Effect of different parameters on the temperature profile using OHAM and FEM for plane Couette–Poiseuille flow; (a) Effect of β on temperature profile (OHAM); (b) Effect of β on temperature profile (FEM); (c) Effect of B on temperature profile (OHAM); (d) Effect of B on temperature profile (FEM); (e) Effect of λ on temperature profile (OHAM); (f) Effect of λ on temperature profile (FEM)

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