EFFECT OF VARIABLE VISCOSITY AND SUCTION/INJECTION ON THERMAL BOUNDARY LAYER OF A NON-NEWTONIAN POWER-LAW FLUIDS PAST A POWER-LAW STRETCHED SURFACE

Abstract

The analysis of laminar boundary layer flow and heat transfer of non-Newtonian fluids over a continuous stretched surface with suction or injection has been presented.The velocity and temperature of the sheet were assumed to vary in a power-law form, that is u = U0xm, and Tw(x) = T+ Cxb. The viscosity of the fluid is assumed to be inverse linear function of temperature. The resulting governing boundary-layer equations are highly non-linear and coupled form of partial differential equations and they have been solved numerically by using the Runge-Kutta method and Shooting technique. Velocity and temperature distributions as well as the Nusselt number where studied for two thermal boundary conditions: uniform surface temperature (b = 0) and cooled surface temperature (b = -1), for different parameters: variable viscosity parameter qr, temperature exponent b, blowing parameter d and Prandtl number. The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters.

Dates

  • Submission Date2009-07-13
  • Revision Date2009-07-24
  • Acceptance Date2009-11-19

DOI Reference

10.2298/TSCI10041111S

References

  1. Crane, L. J., Flow Pas a Stretching Plate, Z. Angew, Math. Phys., 21 (1970), pp. 645-647
  2. Gupta, P. S., Gupta, A. S., Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing, Can. J. Eng., 55 (1977), 6, pp. 744-746
  3. Chen, C. K., Char, M. I., Heat Transfer of a Continuous Stretching Surface with Suction or Blowing, J. Math. Anal Appl., 135 (1988), 2, pp. 568-580
  4. Mcleod, B., Rajagopal, K. R., On the Uniqueness of the Flow of a Navier Stokes Fluid due to Stretching Boundary, Arch. Ration. Mech. Annal., 98 (1987), 4, pp. 385-493
  5. Chaim, T. C., Heat Transfer in a Fluid with Variable Thermal Conductivity over a Linearly Stretching Sheet, Acta Mechanica, 129 (1998), 1-2, pp. 63-72
  6. Seddeek, M. A., Abdelmeguid, M. S., Effects of Radiation and Thermal Diffusivity on Heat Transfer over a Stretching Surface with Variable Heat Flux, Physics Letter A., 348 (2006), 3-4, pp. 172-179
  7. Chabra, R. P., Bubbles, Drops, and Particles in Non-Newtonian Fluids, CRC Press, Boca Raton, Fla., USA, 1993
  8. Altan, T., Oh, S. I., Gegel, H. L., Metal Forming Fundamentals and Applications, American Society of Metals, Metals Park, O., USA, 1983
  9. Fisherr, E. G., Extrusion of Plastics, John Wiley and Sons, New York, USA, 1979
  10. Hassanien, I. A., Abdullah, A. A., Gorla, R. S., Heat Transfer in a Power Law Fluid over a Non-Isothermal Stretching Sheet, Mathl. Comput. Modellin, 28, (1997), 9, pp. 105-116
  11. Abo-Eldahab, E. M., Salem, A. M., MHD Free-Convection Flow of a Non-Newtonian Power-Law Fluid at a Stretching Surface with a Uniform Free-Stream, Applied Mathematics and Computation, 169 (2005), 2, pp. 806-818
  12. Seddeek, M. A., Finite Element Method for the Effect of Various Injection Parameter on Heat Transfer for Power-Law Non-Newtonian Fluid over a Continuous Stretched Surface with Thermal Radiation, Computational Material Science, 37 (2006), 4, pp. 624-627
  13. Gary, J., et al., The Effect of Significant Viscosity Variation on Convective Heat Transport in Wate-Saturated Porous Media, J. Fluid Mech., 117 (1982), pp. 233-249
  14. Hossain, M. A., Munir, M. S., Takhar, H. S., Natural Convection Flow of a Fluid about a Truncated Cone with Temperature Dependent Viscosity, Acta Mechanica, 140 (2000), 3-4, pp. 171-181
  15. Ling, J. X., Dybbs, A., The Effect of Variable Viscosity on Forced Convection over a Flat Plate Submersed in a Porous Medium, ASME J. Heat Transfer, 114 (1992), pp. 1063-1065
  16. Seddeek, M. A. Salama, F. A., The Effects of Temperature Dependent Viscosity and Thermal Conductivity on Unsteady MHD Convective Heat Transfer past a Semi-Infinite Vertical Porous Moving Plate with Variable Suction, Computational Material Science, 48 (2007), 2, pp. 186-192
  17. Ghaly, A. Y., Seddeek, M. A., Chebyshev Finite Difference Method for Effects of Chemical Reaction, Heat and Mass Transfer on Laminar Flow along a Semi Infinite Horizontal Plate with Temperature Dependent Viscosity, Chaos Solitons and Fractals, 19 (2004), 1, pp. 61-70
  18. Salem, A. M., The Influence of Thermal Conductivity and Variable Viscosity on the Flow of a Micropolar Fluid Past a Continuously Semi-Infinite Moving Plate with Suction or Injection, Il Nuovo Cimento B, 121 (2006), 1, pp. 35-42
  19. Ali, M. E., On Thermal Boundary Layer on a Power-Law Stretched Surface with Suction of Injection, Int. J. Heat and Fluid Flow, 16 (1995), 4, pp. 280-290
  20. Eldabe, N. T. M., et al., Mixed Convective Heat and Mass Transfer in a Non-Newtonian Fluid at a Peristaltic Surface with Temperature-Dependent Viscosity, Archive of Appl. Mechanics, 78 (2008), 8, pp. 599-624
  21. Bird, R. B., Stewart, W. E., Lightfood, E. N., Transport Phenomena, John Wiley and Sons, New York, USA, 1960
  22. Lai, F. C., Kulacki, L. A. The Effect of Variable Viscosity on Convective Heat and Mass Transfer along a Vertical Surface in Saturated Porous Media, Int. J. Heat Mass Transfer, 33 (1990), 5, pp. 1028-1031
  23. Elbashbeshy, E. M. A., Bazid, M. A. A., The Effect of Temperature-Dependent Viscosity o Heat Transfer over a Continuous Moving Surface with Variable Internal Heat Generation, Appl. Math. Comm. Commput, 153 (2004), 3, pp. 721-731
  24. Conte, S. D., De Bor, C., Elementary Numerical Analysis, McGraw-Hill, New York, USA, 1972
  25. Cebeci, T., Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, USA, 1984
Volume 14, Issue 4, Pages1111 -1120