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research-article

Fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness

[+] Author and Article Information
Lin Liu

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaBeijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, Beijing 100083, China
liulin1020@126.com

Liancun Zheng

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaBeijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, Beijing 100083, China
liancunzheng@163.com

Yanping Chen

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
yanpingch@126.com

Fawang Liu

School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland 4001, Australia
f.liu@qut.edu.au

1Corresponding author.

ASME doi:10.1115/1.4039765 History: Received August 26, 2017; Revised January 11, 2018

Abstract

The paper gives a comprehensive study on the space fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness, and the variable magnetic field is applied. Novel governing equations with left and right Riemann-Liouville fractional derivatives subject to irregular region are formulated. Solutions of the governing equations are obtained using numerical method by introducing new variables to change the boundary as a regular one, and meanwhile, the shifted Grünwald formulae are applied. By introducing new source items, the exact solutions are constructed and the comparisons between the numerical solutions and the exact ones are presented. Dynamic characteristics with the effects of fractional parameter, magnetic parameter, exponent parameter and weight coefficient on the velocity and temperature distributions are shown and discussed by graphical illustrations.

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