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A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

Part of: Generalities, axiomatics, foundations of continuum mechanics of solids Numerical methods

Published online by Cambridge University Press:  20 July 2016

Botong Li ,
Liancun Zheng ,
Ping Lin ,
Zhaohui Wang  and
Mingjie Liao
Botong Li*
Affiliation:
College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China International Center for Applied Mechanics, State Key Laboratory for the Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, 710049, China
Liancun Zheng*
Affiliation:
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing, 100083, China
Ping Lin*
Affiliation:
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing, 100083, China Department of Mathematics, University of Dundee, Dundee, DD1 4HNUK
Zhaohui Wang*
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh NC 27695-8205, USA
Mingjie Liao*
Affiliation:
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing, 100083, China
*
*Corresponding author. Email addresses:plin@maths.dundee.ac.uk (P. Lin), leedonlion408@163.com (B.-T. Li), liancunzheng@ustb.edu.cn (L.-C. Zheng), zwang24@ncsu.edu (Z.-H. Wang), mliao@xs.ustb.edu.cn (M.-J. Liao)
*Corresponding author. Email addresses:plin@maths.dundee.ac.uk (P. Lin), leedonlion408@163.com (B.-T. Li), liancunzheng@ustb.edu.cn (L.-C. Zheng), zwang24@ncsu.edu (Z.-H. Wang), mliao@xs.ustb.edu.cn (M.-J. Liao)
*Corresponding author. Email addresses:plin@maths.dundee.ac.uk (P. Lin), leedonlion408@163.com (B.-T. Li), liancunzheng@ustb.edu.cn (L.-C. Zheng), zwang24@ncsu.edu (Z.-H. Wang), mliao@xs.ustb.edu.cn (M.-J. Liao)
*Corresponding author. Email addresses:plin@maths.dundee.ac.uk (P. Lin), leedonlion408@163.com (B.-T. Li), liancunzheng@ustb.edu.cn (L.-C. Zheng), zwang24@ncsu.edu (Z.-H. Wang), mliao@xs.ustb.edu.cn (M.-J. Liao)
*Corresponding author. Email addresses:plin@maths.dundee.ac.uk (P. Lin), leedonlion408@163.com (B.-T. Li), liancunzheng@ustb.edu.cn (L.-C. Zheng), zwang24@ncsu.edu (Z.-H. Wang), mliao@xs.ustb.edu.cn (M.-J. Liao)
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Abstract

This paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudosimilarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.

Keywords

Boundary layerthermal diffusivityparallel computation

MSC classification

Secondary: 74A15: Thermodynamics 74S05: Finite element methods 74S30: Other numerical methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 3 , August 2016 , pp. 315 - 336
Copyright
Copyright © Global-Science Press 2016 

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