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Research Papers: Natural and Mixed Convection

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

[+] Author and Article Information
Jinhu Zhao

School of Energy and
Environmental Engineering,
University of Science and Technology Beijing,
Beijing 100083, China;
School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China

Liancun Zheng

School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China
e-mail: liancunzheng@ustb.edu.cn

Xinxin Zhang

School of Energy and
Environmental Engineering,
University of Science and Technology Beijing,
Beijing 100083, China

Fawang Liu

School of Mathematical Sciences,
Queensland University of Technology,
GPO Box 2434,
Brisbane, QLD 4001, Australia

Xuehui Chen

School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 26, 2016; final manuscript received August 22, 2016; published online September 13, 2016. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 139(1), 012501 (Sep 13, 2016) (8 pages) Paper No: HT-16-1231; doi: 10.1115/1.4034546 History: Received April 26, 2016; Revised August 22, 2016

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

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Figures

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Fig. 1

Coordinate system and schematic diagram of the problem

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Fig. 2

Grid independence comparisons

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Fig. 3

Velocity profiles for various values of ε

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Fig. 4

Temperature profiles for various values of ε

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Fig. 5

Velocity profiles for various values of Da

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Fig. 6

Temperature profiles for various values of Da

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Fig. 7

Velocity profiles for various values of α

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Fig. 8

Velocity profiles for various values of β

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Fig. 9

Velocity profiles for various values of Pr

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Fig. 10

Average Nusselt number for various values of Pr and ε

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