Technical Briefs

Thin-Film Flow of a Power-Law Fluid Down an Inclined Plane

[+] Author and Article Information
A. Ganguly1

Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, Indiagangulyasish@rediffmail.com; aganguly@maths.iitkgp.ernet.in

M. Reza

Department of Mathematics, National Institute of Science and Technology, Berhampur, 761008, India

A. S. Gupta

Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India


Corresponding author.

J. Fluids Eng 134(4), 044502 (Apr 20, 2012) (5 pages) doi:10.1115/1.4006406 History: Received September 13, 2011; Revised March 19, 2012; Published April 20, 2012; Online April 20, 2012

An analysis is presented for two-dimensional flow of a thin layer of power-law fluid down an inclined plane. Integration of the equations of motion using lubrication approximations shows that for both pseudoplastic and dilatant fluids, the rate of advance of a blob of fluid of given volume decreases with increasing time. The analysis further reveals that for dimensionless time less than about 0.50, a blob of the fluid (of fixed volume) with given exponent n moves faster than a fluid of same volume with larger n. However, thereafter, a blob of the latter fluid moves faster than the former fluid.

Copyright © 2012 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 5

Variation of x¯N with power law exponent n as well as with dimensionless time t¯, computed from Eq. 44

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Figure 4

The advancement of the ‘nose’ of the blob is plotted for n=0.1,0.3,0.6,2.5 based on the numerical data obtained from the dimensionless formula (Eq. 44)

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Figure 3

Variation of x¯N with dimensionless time t¯ for n=0.1,1.5,2,2.5, computed from Eq. 44

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Figure 2

Advancement of the ‘nose’ of a blob of a Newtonian fluid (n=1) according to Eq. 42 in dimensionless form. The plot may be compared with the experimental plot in Fig. 20 of Ref. [5].

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Figure 1

Thin-film flow down an inclined plane (schematic diagram)




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