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Numerical Study for the Flow and Heat Transfer in a Thin Liquid Film Over an Unsteady Stretching Sheet with Variable Fluid Properties in the Presence of Thermal Radiation

Published online by Cambridge University Press:  08 May 2012

I-C. Liu  and
A. M. Megahed
I-C. Liu*
Affiliation:
Department of Civil Engineering, National Chi Nan University, Nantou, Taiwan 54561, R.O.C
A. M. Megahed
Affiliation:
Department of Mathematics, Faculty of Science, Benha University, Benha, Al Qalyobia 13518, Egypt
*
*Corresponding author (icliu@ncnu.edu.tw)
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Abstract

In this paper, the effect of thermal radiation, variable viscosity and variable thermal conductivity on the flow and heat transfer of a thin liquid film over an unsteady stretching sheet is analyzed. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations, are reduced to a set of two non-linear ordinary differential equations, before being solved numerically. Results for the skin-friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. It is found that increasing the viscosity parameter leads to a rise in the velocity near the surface of the sheet and a fall in the temperature. Furthermore, it is shown that the temperature increases due to an increase in the values of the thermal conductivity parameter and the thermal radiation parameter, while it decreases with an increase of the Prandtl number.

Keywords

Liquid filmUnsteady stretching sheetThermal radiationVariable fluid propertiesSimilarity transformation
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 2 , June 2012 , pp. 291 - 297
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1. Crane, L. J., “Flow Past a Stretching Plane,” Zeitschrift für Angewandte Mathematik und Physik, 21, pp. 645–647 (1970).CrossRefGoogle Scholar
2. Wang, C. Y., “Liquid Film on an Unsteady Stretching Surface,” Quarterly of Applied Mathematics, 48, pp. 601–610 (1990).Google Scholar
3. Usha, R. and Sridharan, R., “The Axisymmetric Motion of a Liquid Film on an Unsteady Stretching Surface,” ASME Fluids Engineering, 117, pp. 81–85 (1995).CrossRefGoogle Scholar
4. Andersson, H. I., Aarseh, J. B. and Dandapat, B. S., “Heat Transfer in a Liquid Film on an Unsteady Stretching Surface,” International Journal of Heat and Mass Transfer, 43, pp. 69–74 (2000).CrossRefGoogle Scholar
5. Dandapat, B. S., Santra, B. and Anderson, H. I., “Thermocapillarity in a Liquid Film on Unsteady Stretching Surface,” International Journal of Heat and Mass Transfer, 46, pp. 3009–3015 (2003).CrossRefGoogle Scholar
6. Wang, C., “Analytic Solutions for a Liquid Thin Film on an Unsteady Stretching Surface,” Heat and Mass Transfer, 42, pp. 759–766 (2006).CrossRefGoogle Scholar
7. Santra, B. and Dandapat, B. S., “Unsteady Thin-Film Flow over a Heated Stretching Sheet,” International Journal of Heat and Mass Transfer, 52, pp. 1965–1970 (2009).CrossRefGoogle Scholar
8. Subhas Abel, M., Mahesha, N. and Tawade, J., “Heat Transfer in a Liquid Film over an Unsteady Stretching Surface with Viscous Dissipation in the Presence of External Magnetic Field,” Applied Mathematical Modelling, 33, pp. 3430–3441 (2009).CrossRefGoogle Scholar
9. Noor, N. F. M. and Hashim, I., “Thermocapillarity and Magnetic Field Effects in a Thin Liquid Film on an Unsteady Stretching Surface,” International Journal of Heat and Mass Transfer, 53, pp. 2044–2051 (2010).CrossRefGoogle Scholar
10. Andersson, H. I., Aarseth, J. B., Braud, N. and Dandapat, B. S., “Flow of a Power-Law Fluid on an Unsteady Stretching Surface,” Journal of Non-Newtonian Fluid Mechanics, 62, pp. 1–8 (1996).Google Scholar
11. Chen, C.-H., “Heat Transfer in a Power-Law Fluid Film over a Unsteady Stretching Sheet,” Heat and Mass Transfer, 39, pp. 791–796 (2003).CrossRefGoogle Scholar
12. Wang, C. and Pop, I., “Analysis of the Flow of a Power-Law Fluid Film on an Unsteady Stretching Surface by Means of Homotopy Analysis Method,” Journal of Non-Newtonian Fluid Mechanics, 138, pp. 161–172 (2006).CrossRefGoogle Scholar
13. Chen, C.-H., “Effect of Viscous Dissipation on Heat Transfer in a Non-Newtonian Liquid Film Over an Unsteady Stretching Sheet,” Journal of Non-Newtonian Fluid Mechanics, 135, pp. 128–135 (2006).CrossRefGoogle Scholar
14. Siddiqui, A. M., Ahmed, M. and Ghori, Q. K., “Thin Film Flow of Non-Newtonian Fluids on a Moving Belt,” Chaos, Solitons and Fractals, 33, pp. 1006–1016 (2007).CrossRefGoogle Scholar
15. Hayat, T., Saif, S. and Abbas, Z., “The Influence of Heat Transfer in an MHD Second Grade Fluid Film over an Unsteady Stretching Sheet,” Physical Letters A, 372, pp. 5037–5045 (2008).CrossRefGoogle Scholar
16. Siddiqui, A. M., Mahmood, R. and Ghori, Q. K., “Homotopy Perturbation Method for Thin Film Flow of a Third Grade Fluid down an Inclined Plane,” Chaos, Solitons and Fractals, 35, pp. 140–147 (2008).CrossRefGoogle Scholar
17. Hayat, T., Ellahi, R. and Mahomed, F. M., “Exact Solutions for Thin Film Flow of a Third Grade Fluid down an Inclined Plane,” Chaos, Solitions and Fractals, 38, pp. 1336–1341 (2008).CrossRefGoogle Scholar
18. Massoudi, M. and Phuoc, T. X., “Flow of a Generalized Second Grade Non-Newtonian Fluid with Variable Viscosity,” Continuum Mechanics and Thermodynamics, 16, pp. 529–538 (2004).CrossRefGoogle Scholar
19. Mahmoud, M. A. A., “Thermal Radiation Effect on Unsteady MHD Free Convection Flow Past a Vertical Plate with Temperature-Dependent Viscosity,” The Canadian Journal of Chemical Engineering, 87, pp. 47–52 (2009).CrossRefGoogle Scholar
20. Chiam, T. C., “Heat Transfer with Variable Conductivity in a Stagnation-Point Flow Towards a Stretching Sheet,” International Communications in Heat and Mass Transfer, 23, pp. 239–248 (1996).CrossRefGoogle Scholar
21. Chiam, T. C., “Heat Transfer in a Fluid with Variable Thermal Conductivity over a Linearly Stretching Sheet,” Acta Mechanica, 129, pp. 63–72 (1998).CrossRefGoogle Scholar
22. Mahmoud, M. A. A., “Thermal Radiation Effects on MHD Flow of a Micropolar Fluid over a Stretching Surface with Variable Thermal Conductivity,” Physica A, 375, pp. 401–401 (2007).Google Scholar
23. Dandapat, B. S., Santra, B. and Vajravelu, K., “The Effects of Variable Fluid Properties and Thermocapillarity on the Flow of a Thin Film on an Unsteady Stretching Sheet,” International Journal of Heat and Mass Transfer, 50, pp. 991–996 (2007).CrossRefGoogle Scholar
24. Mahmoud, M. A. A. and Megahed, A. M., “MHD Flow and Heat Transfer in a Non-Newtonian Liquid Film over an Unsteady Stretching Sheet with Variable Fluid Properties,” The Canadian Journal of Physics, 87, pp. 1065–1071 (2009).CrossRefGoogle Scholar
25. Raptis, A., “Flow of a Micropolar Fluid Past a Continuously Moving Plate by the Presence of Radiation,” International Journal of Heat and Mass Transfer, 41, pp. 2865–2866(1998).CrossRefGoogle Scholar
26. Raptis, A., “Radiation and Viscoelastic Flow,” International Communications in Heat and Mass Transfer, 26, pp. 889–895 (1999).CrossRefGoogle Scholar