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Laminar boundary layer flow of power-law fluids over wavy surfaces

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Summary

The results of a study of forced flow of a power-law fluid over a wavy wall are presented. The boundary layer regime is considered where the generalized Reynolds number is very large and assumed that the waves of the surface haveO(1) amplitude and wavelength. The non-similarity boundary layer equation is solved numerically by means of a modern finite-difference scheme for several values of the sinusoidal wavy wall amplitude and power-law index. A discussion is provided for the effect of the sinusoidal waves and power-law index on the velocity field and on the skin friction coefficient.

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Abbreviations

a :

amplitude of the wavy surface

C f :

skin friction coefficient

f :

reduced stream function

J :

second invariant of the strain-rate tensor

K :

consistency index of the power-law fluid

L :

half-wavelength, or lengthscale, of the surface undulations

n :

power-law index

p :

pressure

Re:

generalized Reynolds number

Rex :

generalized local Reynolds number

S(x):

surface profile

u, v :

velocity components along (x, y)-axes

x, y :

streamwise and cross-streamwise coordinates

ξ, η:

non-similarity variables

σ:

notation, Eq. (15)

τ:

shear stress

ϱ:

density

ψ:

stream function

w :

wall condition

∞:

free stream condition

−:

dimensional variables

^:

boundary layer variables

':

partial differentiation with respect to η

References

  1. Irvine, Jr., T. F., Karni, J.: Non-Newtonian fluid flow and heat transfer. In: Handbook of single-phase convective heat transfer (Kakac, S., Shah, R. K., Aung, W., eds.), pp. 20.1–20.57. New York: Wiley 1987.

    Google Scholar 

  2. Andersson, H. I., Toften, T. H.: Numerical solution of the laminar boundary layer equations for power-law fluids. J. Non-Newtonian Fluid Mech.32, 175–195 (1989).

    Google Scholar 

  3. Kim, H. W., Jeng, D. R., DeWitt, K. J.: Momentum and heat transfer in power-law fluid flow over two-dimensional or axisymmetrical bodies. Int. J. Heat Mass Transfer26, 245–249 (1983).

    Google Scholar 

  4. Nakayama, A., Shenoy, A. V., Koyama, H.: An analysis for forced convection heat transfer from external surfaces to non-Newtonian fluids. Wärme-Stoffübertr.20, 219–227 (1986).

    Google Scholar 

  5. Benjamin, T. Br.: Shearing flow over a wavy boundary. J. Fluid Mech.6, 161–205 (1959).

    Google Scholar 

  6. Shankar, P. N., Sinha, U. N.: The Rayleigh problem for a wavy wall. J. Fluid Mech.77, 243–256 (1976).

    Google Scholar 

  7. Bordner, G. L.: Nonlinear analysis of laminar boundary layer flow over a periodic wave surface. Phys. Fluids21, 1471–1474 (1978).

    Google Scholar 

  8. Caponi, E. A., Fornberg, B., Knight, D. D., McLean, J. W., Saffman, P. G., Yuen, H. C.: Calculation of laminar viscous flow over a moving wavy surface. J. Fluid Mech.124, 347–362 (1984).

    Google Scholar 

  9. Tsangaris, S., Potamitis, D.: On laminar small Reynolds-number flow over wavy walls. Acta Mech.61, 109–115 (1986).

    Google Scholar 

  10. Pop, I., Gorla, R. S.: Second-order boundary layer solution for a continuous moving surface in a non-Newtonian fluid. Int. J. Eng. Sci.28, 313–322 (1990).

    Google Scholar 

  11. Rees, D. A. S., Pop, I.: A note on free convection along a vertical wavy surface in a porous medium. J. Heat Transfer116, 505–508 (1994).

    Google Scholar 

  12. Rees, D. A. S., Pop, I.: Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium. J. Heat Transfer117 (1995).

  13. Nakamura, S.: Applied numerical method in C. New Jersey:Prentice-Hall 1992.

    Google Scholar 

  14. Nakamura, S., Gorla, R. S. R., Pop, I.: Free convection similarity solutions of a non-Newtonian fluid on a horizontal surface. Math. Modell. Sci. Comput.2, 1243–1248 (1993).

    Google Scholar 

  15. Gorla, R. S. R., Lee, J. K., Nakamura, S., Pop, I.: Effects of transverse magnetic field on mixed convection in wall plume of power-law fluids. Int. J. Eng. Sci.31, 1035–1045 (1993).

    Google Scholar 

  16. Lee, J. K., Gorla, R. S. R., Nakamura, S., Pop, I.: Mixed convection in wall plume of power-law fluids. Acta Mech.102, 47–58 (1994).

    Google Scholar 

  17. Nakamura, S.: Iterative finite difference schemes for similarity and nonsimilarity boundary layer equations. Adv. Eng. Softwave (in press).

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Author notes

  1. I. Pop

    Present address: Faculty of Mathematics, University of Cluj, CP 253, R-3400, Cluj, Romania

  2. S. Nakamura

    Present address: Department of Mechanical Engineering, The Ohio State University, 43210, Columbus, OH, USA

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    1. I. Pop
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    2. S. Nakamura
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    Pop, I., Nakamura, S. Laminar boundary layer flow of power-law fluids over wavy surfaces. Acta Mechanica 115, 55–65 (1996). https://doi.org/10.1007/BF01187428

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