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Research Papers: Heat and Mass Transfer

Thermocapillarity Effects on Power-Law Liquids Thin Film Over an Unsteady Stretching Sheet

[+] Author and Article Information
Tingting Liu, Liancun Zheng

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

Yiming Ding, Lin Liu

School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China;
School of Energy and
Environmental Engineering,
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 November 23, 2016; final manuscript received May 23, 2017; published online June 27, 2017. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 139(12), 122002 (Jun 27, 2017) (8 pages) Paper No: HT-16-1766; doi: 10.1115/1.4036872 History: Received November 23, 2016; Revised May 23, 2017

This paper investigates the effects of thermocapillarity on the flow and heat transfer in power-law liquid film over an unsteady stretching sheet. The surface tension is assumed to vary linearly with temperature, and the thermal conductivity of the fluid is assumed power-law-dependent on the velocity gradient with modified Fourier's law. The local similarity solutions are obtained numerically, and some interesting new phenomena are found. Results indicate that the thermally induced surface tension provides an opposite force in the direction of the stretching sheet which may cause the fluid adjacent to the free surface to flow in the opposite directions. The effect of thermocapillarity tends to decrease the thin film thickness and results in a smaller temperature distribution. With the increasing unsteadiness parameter, the thin film thickness has a local maximum, and thermal boundary layer is confined to the lower part of the thin film for bigger Prandtl number, while the temperature in the thin film remains equal to the slit temperature with Prandtl number close to 0.

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Figures

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Fig. 1

Schematic of the physical model

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Fig. 2

Variations of the velocity f′(η) with different values of M

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Fig. 3

Variations of the temperature θ(η) with the different values of M

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Fig. 4

The streamline of velocity for n=1.2, M=1.0, S=0.8, Pr=0.1, and t=0

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Fig. 5

Variations of the velocity f′(η) with the different values of n

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Fig. 6

Variations of the temperature θ(η) with the different values of n

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Fig. 7

Variations of the free surface velocity f′(β) with M for different values of n

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Fig. 8

Variations of the surface temperature θ(β) with M for different values of n

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Fig. 9

Variations of the film thickness β with S for different values of M

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Fig. 10

Variations of the film thickness β with S for different values of n

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Fig. 11

Variations of the temperature θ(η) with η for the different values of S

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Fig. 12

Variations of the temperature θ(η) with η for the different values of Pr

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