Local Similarity Solutions for Laminar Boundary Layer Flow along a Moving Cylinder in a Parallel Stream

  • Anuar Ishak
  • Roslinda Nazar
  • Ioan Pop
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)


The present paper deals with a numerical method to analyze the axisymmetric boundary layer flow of a viscous and incompressible fluid along a static or moving cylinder, using local similarity approximation. Both parallel and reverse moving boundary to the free stream are considered. Local similarity solutions are obtained to show the effects of the velocity ratio parameter and the curvature parameter on the surface shear stress. The numerical results are comparable very well with the existing results available in the literature for some particular cases of the present problem. Moreover, the results indicate that dual solutions exist when the cylinder and the free stream move in opposite directions.


Boundary layer Dual solutions Local similarity solutions Moving cylinder Numerical solutions 


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  1. 1.
    Seban, R.A., Bond, R.: Skin Friction and Heat Transfer Characteristics of a Laminar Boundary Layer on a Cylinder in Axial Incompressible Flow. J. Aeronaut. Sci. 18, 671–675 (1951)zbMATHGoogle Scholar
  2. 2.
    Sakiadis, B.C.: Boundary Layer Behavior on Continuous Solid Surfaces: III. The Boundary Layer on a Continuous Cylindrical Surface. A.I.Ch.E. J. 7, 467–472 (1961)Google Scholar
  3. 3.
    Lin, H.-T., Shih, Y.-P.: Laminar Boundary Layer Heat Transfer along Static and Moving Cylinders. J. Chin. Ins. Eng. 3, 73–79 (1980)Google Scholar
  4. 4.
    Lin, H.-T., Shih, Y.-P.: Buoyancy Effects on the Laminar Boundary Layer Heat Transfer along Vertically Moving Cylinders. J. Chin. Ins. Eng. 4, 47–51 (1981)Google Scholar
  5. 5.
    Ishak, A., Nazar, R., Pop, I.: Uniform Suction/Blowing Effect on Flow and Heat Transfer due to a Stretching Cylinder. Appl. Math. Modell. 32, 2059–2066 (2008)CrossRefGoogle Scholar
  6. 6.
    Mahmood, T., Merkin, J.H.: Similarity Solutions in Axisymmetric Mixed-Convection Boundary-Layer Flow. J. Eng. Math. 22, 73–92 (1988)zbMATHCrossRefGoogle Scholar
  7. 7.
    Ishak, A., Nazar, R., Pop, I.: The Effects of Transpiration on the Boundary Layer Flow and Heat Transfer over a Vertical Slender Cylinder. Int. J. Non-Linear Mech. 42, 1010–1017 (2007)CrossRefGoogle Scholar
  8. 8.
    Lloyd, J.R., Sparrow, E.M.: Combined Forced and Free Convection Flow on Vertical Surfaces. Int. J. Heat Mass Transfer 13, 434–438 (1970)CrossRefGoogle Scholar
  9. 9.
    Narain, J.P., Uberoi, M.: Combined Forced and Free-Convection Heat Transfer from Vertical Thin Needles in a Uniform Stream. Phys. Fluid 15, 1879–1882 (1972)zbMATHCrossRefGoogle Scholar
  10. 10.
    Narain, J.P., Uberoi, M.: Combined Forced and Free-Convection over Thin Needles. Int. J. Heat Mass Transfer 16, 1505–1512 (1973)CrossRefGoogle Scholar
  11. 11.
    Na, T.Y.: Computational Methods in Engineering Boundary Value Problems. Academic Press, New York (1979)zbMATHGoogle Scholar
  12. 12.
    Cebeci, T., Bradshaw, P.: Physical and Computational Aspects of Convective Heat Transfer. Springer, New York (1988)zbMATHGoogle Scholar
  13. 13.
    Cebeci, T., Bradshaw, P.: Momentum Transfer in Boundary Layers. Hemisphere, Washington (1977)zbMATHGoogle Scholar
  14. 14.
    Cebeci, T., Chang, K.C., Bradshaw, P.: Solution of a Hyperbolic System of Turbulence-Model Equations by the “BOX” Scheme. Comp. Method Appl. Mech. Eng. 22, 213–227 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Schneider, W.: A Similarity Solution for Combined Forced and Free Convection Flow over a Horizontal Plate. Int. J. Heat Mass Transfer 22, 1401–1406 (1979)zbMATHCrossRefGoogle Scholar
  16. 16.
    Schneider, W., Wasel, M.G.: Breakdown of the Boundary-Layer Approximation for Mixed Convection above a Horizontal Plate. Int. J. Heat Mass Transfer 28, 2307–2313 (1985)zbMATHCrossRefGoogle Scholar
  17. 17.
    Ishak, A., Nazar, R., Pop, I.: The Schneider Problem for a Micropolar Fluid. Fluid Dyn. Res. 38, 489–502 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Sears, W.R., Teleonis, D.P.: Boundary-Layer Separation in Unsteady Flow. SIAM J. Appl. Math. 28, 215–235 (1975)zbMATHCrossRefGoogle Scholar
  19. 19.
    Ridha, A.: Aiding Flows Non-Unique Similarity Solutions of Mixed-Convection Boundary-Layer Equations. J. Appl. Math. Phys (ZAMP) 47, 341–352 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Ridha, A.: Three-Dimensional Mixed Convection Laminar Boundary-Layer near a Plane of Symmetry. Int. J. Eng. Sci. 34, 659–675 (1996)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Anuar Ishak
    • 1
  • Roslinda Nazar
    • 1
  • Ioan Pop
    • 2
  1. 1.School of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia, UKM BangiSelangorMalaysia
  2. 2.Faculty of MathematicsUniversity of ClujClujRomania

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