×

Unsteady flow and heat transfer in a thin film of Ostwald-de Waele liquid over a stretching surface. (English) Zbl 1316.76013

Summary: In this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald-de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of nonlinear ordinary differential equations. The resulting five parameter problem is solved by the Keller-Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.

MSC:

76A20 Thin fluid films
80A20 Heat and mass transfer, heat flow (MSC2010)
76A05 Non-Newtonian fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Crane, L. J., Flow past a stretching plate, ZAMP, 21, 645-647 (1970)
[2] Siddappa, B.; Subhas Abel, M., Non-Newtonian flow past a stretching plate, ZAMP, 36, 890-892 (1985) · Zbl 0591.76011
[3] Dandapat, B. S.; Gupta, A. S., Flow and heat transfer in a visco-elastic fluid over a stretching sheet, Int J Non-Linear Mech, 24, 215-219 (1989) · Zbl 0693.76015
[4] Cortell, R., Similarity solutions for flow and heat transfer of a viscoelastic fluid over a stretching sheet, Int J Non-Linear Mech, 29, 155-161 (1994) · Zbl 0795.76010
[5] Hassanien, I. A.; Abdullah, A. A.; Gorla, R. S.R., Flow and heat transfer in a power-law fluid over a non isothermal stretching sheet, Math Comput Model, 28, 105-116 (1998) · Zbl 1098.76531
[6] Ali, M. E., On the thermal boundary layer on a power law stretched surface with suction or injection, Int J Heat Fluid Flow, 16, 280-290 (1995)
[7] Wang, C. Y., Liquid film on an unsteady stretching surface, Quart Appl Math, 48, 601-610 (1990) · Zbl 0714.76036
[8] Usha, R.; Sridharan, R., On the motion of a liquid film on an unsteady stretching surface, ASME Fluids Eng, 150, 43-48 (1993)
[9] Dandapat, B. S.; Santra, B.; Vajravelu, K., The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet, Int J Heat Mass Transfer, 50, 991-996 (2007) · Zbl 1124.80317
[10] Liu, I. C.; Andersson, H. I., Heat transfer on an unsteady stretching sheet, Int J Therm Sci, 47, 766-772 (2008)
[11] Abel, M. S.; Mahesha, N.; Tawade, J., Heat transfer in a liquid film on an unsteady stretching surface with viscous dissipation in the presence of external magnetic field, Appl Math Model, 33, 3430-3441 (2009) · Zbl 1205.76040
[12] Nadeem, S.; Awais, M., Thin film flow of an unsteady shrinking sheet, through medium with variable viscosity, Phys Lett A, 372, 4695-4972 (2008) · Zbl 1221.76233
[13] Aziz, R. C.; Hasim, I.; Almari, A. K., Thin film flow and heat transfer on an unsteady stretching sheet with internal heating, Meccanica, 46, 349-357 (2011) · Zbl 1271.76025
[14] Andersson, H. I.; Aaresh, J. B.; Braud, N.; Dandapat, B. S., Flow of a power law fluid on an unsteady stretching surface, J Non-Newtonian Fluid Mech, 62, 1-8 (1996)
[15] Savvas, T. A.; Markatos, N. C.; Papaspyrides, C. D., On the flow of non-Newtonian polymer solutions, Appl Math Model, 18, 14-22 (1994) · Zbl 0800.76039
[16] Chaim, T. C., Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet, Acta Mech, 129, 63-72 (1998) · Zbl 0914.76026
[17] Prasad, K. V.; Pal, Dulal; Datti, P. S., MHD flow and heat transfer in the flow of a power law fluid over a non-isothermal stretching sheet, CNSNS, 14, 2178-2189 (2009)
[18] Cebeci, T.; Bradshaw, P., Physical and computational aspects of convective heat transfer (1984), Springer-Verlag: Springer-Verlag New York · Zbl 0545.76090
[19] Keller, H. B., Numerical methods for two-point boundary value problems (1992), Dover Publ: Dover Publ New York · Zbl 1409.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.