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Research Papers: Forced Convection

Coupling Effects of Viscous Sheet and Ambient Fluid on Boundary Layer Flow and Heat Transfer in Power-Law Fluids

[+] Author and Article Information
Xiaochuan Liu

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

Goong Chen

Department of Mathematics and Institute for
Quantum Science and Engineering,
Texas A&M University,
College Station, TX 77843

Lianxi Ma

Department of Physics,
Blinn College,
Bryan, TX 77805

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 27, 2018; final manuscript received January 26, 2019; published online April 17, 2019. Assoc. Editor: Yuwen Zhang.

J. Heat Transfer 141(6), 061701 (Apr 17, 2019) (7 pages) Paper No: HT-18-1057; doi: 10.1115/1.4042774 History: Received January 27, 2018; Revised January 26, 2019

This paper investigates the flow and heat transfer of power-law fluids over a stretching sheet where the coupling dynamics influence of viscous sheet and ambient fluid is taken into account via the stress balance. A modified Fourier's law is introduced in which the effects of viscous dissipation are taken into account by assuming that the thermal conductivity is to be shear-dependent on the velocity gradient. The conditions for both velocity and thermal boundary layers admitting similarity solutions are found, and numerical solutions are computed by a Bvp4c program. The results show that the viscous sheet and rheological properties of ambient fluids have significantly influences on both velocity and temperature fields characteristics. The formation of sheet varies with the viscosity of fluid and draw ratio, which then strongly affects the relations of the local skin friction coefficient, the local Nusselt number, and the generalized Reynolds number. Moreover, for specified parameters, the flow and heat transfer behaviors are discussed in detail.

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Figures

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Fig. 1

Physical schematic of boundary layer flow and heat transfer over a stretching sheet

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Fig. 2

The comparison of the numerical and exact solutions of the momentum self-similar equation with the condition m=1 and n=1

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Fig. 3

Velocity profiles for various values of fluid power-law index n with viscous sheet power-law index m=1.3

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Fig. 4

Velocity profiles for various values of viscous sheet power-law index m with fluid power-law index n=1.2

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Fig. 5

Temperature profiles for various values of fluid power-law index n with m=1.5 and NPr=2.0

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Fig. 6

Temperature profiles for various values of viscous sheet power-law index m with n=1.2 and NPr=2.0

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Fig. 7

Function relations between the local skin friction coefficient and the generalized Reynolds number of different power-law fluids for various draw ratio UL/U0 with m=1.2, L/h0=5

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Fig. 8

Function relations between the local skin friction coefficient and the generalized Reynolds number of different viscous sheet power-law index m for various draw ratio UL/U0 with n=0.9, L/h0=5

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Fig. 9

Function relations between the local Nusselt number and the generalized Reynolds number of different power-law fluids for various draw ratio UL/U0 with m=1.4, L/h0=5, NPr=1.0

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Fig. 10

Function relations between the local Nusselt number and the generalized Reynolds number of different viscous sheet power-law index m for various draw ratio UL/U0 with n=1.3, L/h0=5, NPr=1.0

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Fig. 11

Effects of various values of fluid power-law index and different draw ratio on the shape of the sheet with m=1

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Fig. 12

Effect of the generalized Prandtl number on the local Nusselt number with m=1.3, n=0.9, L/h0=5, UL/U0=2

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