Skip to main content
SpringerLink
Log in

Nonlinear Radiative Heat Transfer in Blasius and Sakiadis Flows Over a Curved Surface

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

This study investigates the heat transfer characteristics for Blasius and Sakiadis flows over a curved surface coiled in a circle of radius R having constant curvature. Effects of thermal radiation are also analyzed for nonlinear Rosseland approximation which is valid for all values of the temperature difference between the fluid and the surface. The considered physical situation is represented by a mathematical model using curvilinear coordinates. Similar solutions of the developed partial differential equations are evaluated numerically using a shooting algorithm. Fluid velocity, skin-friction coefficient, temperature and local Nusselt number are the quantities of interest interpreted for the influence of pertinent parameters. A comparison of the present and the published data for a flat surface validates the obtained numerical solution for the curved geometry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. T. Altan, S. Oh, H. Gegel, Metal Forming Fundamental and Applications (American Society of Metals, Metals Park, 1979)

    Google Scholar 

  2. E.G. Fisher, Extrusion of Plastics (Wiley, New York, 1976)

    Google Scholar 

  3. Z. Tadmor, I. Klein, Engineering Principles of Plasticating Extrusion. Polymer Science and Engineering Series (Van Nostrand Reinhold, New York, 1970)

    Google Scholar 

  4. R.M. Griffith, Velocity temperature and concentration distribution during the fiber spinning. Ind. Eng. Chem. Fund. 3, 245–250 (1964)

    Article  Google Scholar 

  5. M.V. Karwe, Y. Jaluria, Numerical simulation of thermal transport associated with a continuous moving flat sheet in materials processing. ASME Heat Transf. 113, 612–619 (1991)

    Article  Google Scholar 

  6. H. Blasius, Grenzschicten in Flussigkeitenmitkleinerreibung. Z. Math. Phys. 56, 1–37 (1908)

    Google Scholar 

  7. A.M.M. Abussita, A note on a certain boundary-layer equation. Appl. Math. Comput. 64, 73–77 (1994)

    MathSciNet  Google Scholar 

  8. A. Asaithambi, A finite-difference method for the Falkner–Skan equation. Appl. Math. Comput. 92, 135–141 (1998)

    Article  MathSciNet  Google Scholar 

  9. L. Wang, A new algorithm for solving classical Blasius equation. Appl. Math. Comput. 157, 1–9 (2004)

    MathSciNet  MATH  Google Scholar 

  10. R.C. Battaler, Numerical solutions of the classical Blasius flat-plate problem. Appl. Math. Comput. 170, 706–710 (2005)

    MathSciNet  Google Scholar 

  11. T. Fang, F. Guo, C.F. Lee, A note on the extended Blasius equation. Appl. Math. Lett. 19, 613–617 (2006)

    Article  MathSciNet  Google Scholar 

  12. T. Fang, C.F.F. Lee, A new solution branch for the Blasius equation: a shrinking sheet problem. Comput. Math. Appl. 56, 3088–3095 (2008)

    Article  MathSciNet  Google Scholar 

  13. J.H. He, A simple perturbation approach to Blasius equation. Appl. Math. Comput. 140, 217–222 (2003)

    MathSciNet  MATH  Google Scholar 

  14. J. Zhang, B. Chen, An iterative method for solving the Falkner–Skan equation. Appl. Math. Comput. 210, 215–222 (2009)

    MathSciNet  MATH  Google Scholar 

  15. M. Naveed, Z. Abbas, M. Sajid, Thermophoresis and Brownian effects on the Blasius flow of a nanofluid due to curved surface with thermal radiation. Eur. Phy. J. Plus 131, 214 (2016)

    Article  Google Scholar 

  16. B.C. Sakiadis, Boundary layer behavior on continuous solid surface: I. The boundary layer on a continuous flat surface. AICHE J. 7, 26–28 (1961)

    Article  Google Scholar 

  17. K. Tsou, E. Sparrow, R.J. Goldstein, Flow and heat transfer in the boundary layer on a continuous moving surface. Int. J. Heat Mass Transf. 10, 219–235 (1967)

    Article  Google Scholar 

  18. E. Magyari, The moving plate thermometer. Int. J. Therm. Sci. 47, 1436–1441 (2008)

    Article  Google Scholar 

  19. A. Pantokratoras, The Blasius and Sakiadis flow with variable fluid properties. Heat Mass Transf. 44, 1187–1198 (2008)

    Article  ADS  Google Scholar 

  20. A. Pantokratoras, Asymptotic profiles for the Blasius and Sakiadis flows in a Darcy-Brinckman isotropic porous medium either with uniform suction or with zero transverse velocity. Transp. Porous Med. (2008). doi:10.1007/s11242-008-9255-3

  21. R.C. Bataller, Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition. Appl. Maths. Comput. 206, 832–840 (2008)

    Article  MathSciNet  Google Scholar 

  22. R.C. Bataller, Numerical comparison of Blasius and Sakiadis flows. Mathematika 26, 187–196 (2010)

    MathSciNet  Google Scholar 

  23. P.O. Olanrewaju, J.A. Gbadeyan, O.O. Agboola, S.O. Abah, Radiation and viscous dissipation effects for the Blasius and Sakiadis flows with a convective surface boundary condition. Int. J. Adv. Sci. Technol. 2, 102–115 (2011)

    Google Scholar 

  24. A. Ishak, R. Nazar, I. Pop, Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature. Non-linear Anal. Real World Appl. 10, 2909–2913 (2009)

    Article  MathSciNet  Google Scholar 

  25. K. Bhattacharyya, S. Mukhopadhyay, G.C. Layek, Unsteady MHD boundary layer flow with diffusion and first-order chemical reaction over a permeable stretching sheet with suction or blowing. Chem. Eng. Commun. 200, 379–397 (2013)

    Article  Google Scholar 

  26. A.J. Chamkha, I. Pop, H.S. Takhar, Marangoni mixed convection boundary layer flow. Meccanica 41, 219–232 (2006)

    Article  MathSciNet  Google Scholar 

  27. M.M. Rashidi, S.A. Mohimanian, S. Abbasbandy, Analytic approximation solutions for heat transfer of a micropolar fluid through a porous medium with radiation. Commun. Non-Linear Sci. Numer. Simul. 16, 1874–1889 (2011)

    Article  ADS  Google Scholar 

  28. O.D. Makinde, Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition. Int. J. Phy. Sci. 5, 700–710 (2010)

    Google Scholar 

  29. M. Sheikholeslami, S. Soleimani, D.D. Ganji, Effect of electric field on hydrothermal behavior of nanofluid in a complex geometry. J. Mol. Liq. 213, 153–161 (2016)

    Article  Google Scholar 

  30. M. Sheikholeslami, M.M. Rashidi, D.D. Ganji, Numerical investigation of magnetic nanofluid forced convective heat transfer in existence of variable magnetic field using two phase method. J. Mol. Liq. 212, 117–126 (2015)

    Article  Google Scholar 

  31. M. Sheikholeslami, H.R. Ashorynejad, P. Rana, Lattice Boltzmann simulation of nanofluid heat transfer enhancement and entropy generation. J. Mol. Liq. 214, 86–95 (2016)

    Article  Google Scholar 

  32. M. Sheikholeslami, T. Hayat, A. Alsaedi, MHD free convection of \(Al_2 O_3 \)- water nanofluid considering thermal radiation: A numerical study. Int. J. Heat Mass Transf. 96, 513–524 (2016)

    Article  Google Scholar 

  33. M. Sheikholeslami, K. Vajravelu, M.M. Rashidi, Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field. Int. J. Heat Mass Transf. 92, 339–348 (2016)

    Article  Google Scholar 

  34. A. Raptis, C. Perdikis, H.S. Takhar, Effect of thermal radiation on MHD flow. Appl. Math. Comput. 153, 645–649 (2004)

    MathSciNet  MATH  Google Scholar 

  35. R.C. Battaler, Radiation effects in the Blasius flow. Appl. Math. Comput. 198, 333–338 (2008)

    MathSciNet  Google Scholar 

  36. R.C. Battaler, A numerical tackling on Sakiadis flow with thermal radiation. Chin. Phys. Lett. 25, 1340–1342 (2008)

    Article  Google Scholar 

  37. A. Pantokratoras, T. Fang, Sakiadis flow with nonlinear Rosseland thermal radiation. Phys. Scr. 87, 015703 (2013)

    Article  ADS  Google Scholar 

  38. A. Pantokratoras, T. Fang, Blasius flow with nonlinear Rosseland thermal radiation. Meccanica 49, 1539–1545 (2014)

    Article  MathSciNet  Google Scholar 

  39. A. Mushtaq, M. Mustafa, T. Hayat, A. Alsaedi, Nonlinear radiative heat transfer in the flow of nanofluid due to solar energy: a numerical study. J. Taiwan Inst. Chem. Eng. 45, 1176–1183 (2014)

    Article  Google Scholar 

  40. M. Naveed, Z. Abbas, M. Sajid, Flow and heat transfer in a semi porous curved channel with radiation and porosity effects. J. Porous Med. 19, 1–11 (2016)

    Article  Google Scholar 

  41. Z. Abbas, M. Naveed, M. Sajid, Nonlinear radiative heat transfer and Hall effects on a viscous fluid in a semi-porous curved channel. AIP Adv. 5, 107124 (2015)

    Article  ADS  Google Scholar 

  42. M. Sajid, N. Ali, T. Javed, Z. Abbas, Stretching a curved surface in a viscous fluid. Chin. Phys. Lett. 27, 024703 (2010)

    Article  ADS  Google Scholar 

  43. Z. Abbas, M. Naveed, M. Sajid, Heat transfer analysis for stretching flow over curved surface with magnetic field. J. Eng. Therm. Phys. 22, 337–345 (2013)

    Article  Google Scholar 

  44. M. Naveed, Z. Abbas, M. Sajid, MHD flow of micropolar fluid due to a curved stretching sheet with thermal radiation. J. Appl. Fluid Mech. 9, 131–138 (2016)

    Article  Google Scholar 

  45. N.C. Rosca, I. Pop, Unsteady boundary layer flow over a permeable curved stretching/shrinking surface. Euro. J. Mech. B/Fluids 51, 61–67 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  46. M. Naveed, Z. Abbas, M. Sajid, Hydromagnetic flow over an unsteady curved stretching surface. Eng. Sci. Technol. Int. J. 19, 841–845 (2016)

    Article  Google Scholar 

  47. Z. Abbas, M. Naveed, M. Sajid, Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation. J. Mol. Liq. 215, 756–762 (2016)

    Article  Google Scholar 

  48. S. Rosseland, Astrophysik und atom-theoretischeGrundlagen (Springer, Berlin, 1931)

    MATH  Google Scholar 

Download references

Acknowledgements

We are thankful to the honorable reviewers for their constructive suggestions.

Author information

Authors and Affiliations

  1. Department of Computer Science, Comsats Institute of Information Technology Vehari, Vehari, 61100, Pakistan

    M. Naveed

  2. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Z. Abbas

  3. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    M. Sajid

Authors
  1. M. Naveed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. Abbas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Sajid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Naveed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Naveed, M., Abbas, Z. & Sajid, M. Nonlinear Radiative Heat Transfer in Blasius and Sakiadis Flows Over a Curved Surface. Int J Thermophys 38, 14 (2017). https://doi.org/10.1007/s10765-016-2154-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10765-016-2154-x

Keywords

Search

Navigation