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Research Papers

Heat Transfer in a Liquid Film Due to an Unsteady Stretching Surface With Variable Heat Flux

[+] Author and Article Information
I.-Chung Liu

Department of Civil Engineering,
National Chi Nan University,
1 University Road, Puli, Nantou,
Taiwan 565, R. O. C.
e-mail: icliu@ncnu.edu.tw

Ahmed M. Megahed

Faculty of Science,
Department of Mathematics,
Benha University,
Benha, 13518Egypt

Hung-Hsun Wang

Department of Civil Engineering,
National Chi Nan University,
1 University Road, Puli, Nantou,
Taiwan 565, R. O. C.

1Corresponding author.

Manuscript received June 19, 2011; final manuscript received October 18, 2012; accepted manuscript posted October 30, 2012; published online May 16, 2013. Assoc. Editor: Nesreen Ghaddar.

J. Appl. Mech 80(4), 041003 (May 16, 2013) (7 pages) Paper No: JAM-11-1196; doi: 10.1115/1.4007966 History: Received June 19, 2011; Revised October 18, 2012; Accepted October 30, 2012

The heat transfer characteristics of a viscous liquid film flow over an unsteady stretching sheet subject to variable heat flux are investigated numerically. The effect of thermal radiation applying to an optically thick medium is also considered. The governing boundary layer equations are transformed into a set of nonlinear ordinary differential equations using an efficient fifth-order step-adapted Runge–Kutta integration scheme together with Newton–Raphson method. The dimensionless temperature is plotted for various governing parameters; say, unsteadiness parameter, effective Prandtl number, distance index, as well as time index. It is found that the heat transfer aspects are strongly influenced by the relevant parameters.

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References

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Figures

Grahic Jump Location
Fig. 1

Schematic representation of the problem

Grahic Jump Location
Fig. 2

(a) Velocity distribution for various values of S. (b) Temperature distribution for various values of S.

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Fig. 3

(a) Temperature distribution for various values of Peff. (b) Temperature distribution for various values of Nr.

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Fig. 4

(a) Temperature distribution for various values of r with S = 0.8. (b) Temperature distribution for various values of r with S = 1.2.

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Fig. 5

(a) Temperature distribution for various values of m with S = 0.8. (b) Temperature distribution for various values of m with S = 1.2.

Grahic Jump Location
Fig. 6

(a) Variation of θ(0) versus S for various values of r. (b) Variation of θ(β) versus S for various values of r.

Grahic Jump Location
Fig. 7

(a) Variation of θ(0) versus S for various values of m. (b) Variation of θ(β) versus S for various values of m.

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