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Flow and heat transfer over hyperbolic stretching sheets

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Abstract

The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numerical results are obtained by a series expansion method and a local non-similarity (LNS) method, respectively. The analytical and numerical results for the skin friction and the Nusselt number are calculated and compared with each other. The significant observation is that the momentum and the thermal boundary layer thickness decrease as the distance from the leading edge increases. The well-known solution of linear stretching is found as the leading order solution for the hyperbolic stretching.

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References

  1. Altan, T., Oh, S. I., and Gegel, H. L. Metal Forming: Fundamentals and Applications, American Society for Metals, Metals Park, Ohio, 85 (1983)

    Google Scholar 

  2. Fisher, E. G. Extrusion of Plastics, John Wiley and Son, New York, 14–140 (1976)

    Google Scholar 

  3. Sakiadis, B. C. Boundary layer behavior on continuous solid surfaces. American Institute of Chemical Engineers Journal, 7(1), 26–28 (1961)

    Article  Google Scholar 

  4. Crane, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik, 21(4), 645–647 (1970)

    Article  Google Scholar 

  5. Dandapat, B. S. and Singh, S. K. Thin film flow over a heated nonlinear stretching sheet in presence of uniform transverse magnetic field. International Communications in Heat and Mass Transfer, 38, 324–328 (2011)

    Article  Google Scholar 

  6. Labropulu, F., Li, D., and Pop, I. Non-orthogonal stagnation-point flow towards a stretching surface in a non-Newtonian fluid with heat transfer. International Journal of Thermal Sciences, 49, 1042–1050 (2010)

    Article  Google Scholar 

  7. Fang, T. G., Zhang, J., and Yao, S. S. New family of unsteady boundary layers over a stretching surface. Applied Mathematics and Computation, 217(8), 3747–3755 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Yao, S. S., Fang, T. G., and Zhong, Y. F. Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Communications in Nonlinear Science and Numerical Simulation, 16, 752–760 (2010)

    Article  Google Scholar 

  9. Nadeem, S. and Hussain, A. MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method. Applied Mathematics and Mechanics (English Edition), 30(12), 1569–1578 (2009) DOI 10.1007/s10483-009-1208-6

    Article  MathSciNet  MATH  Google Scholar 

  10. Ali, F. M., Nazar, R., Arifin, N. M., and Pop, I. MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field. Applied Mathematics and Mechanics (English Edition), 32(4), 409–418 (2011) DOI 10.1007/s10483-011-1426-6

    Article  MathSciNet  MATH  Google Scholar 

  11. Kechil, S. A. and Hashim, I. Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field. Physics Letters A, 372, 2258–2263 (2008)

    Article  MATH  Google Scholar 

  12. Hayat, T., Qasim, M., and Abbas, Z. Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space. Communications in Nonlinear Science and Numerical Simulation, 15, 2375–2387 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hayat, T. and Qasim, M. Influence of thermal radiation and Joule heating on MHD flow of a Maxwell fluid in the presence of thermophoresis. International Journal of Heat and Mass Transfer, 53, 4780–4788 (2010)

    Article  MATH  Google Scholar 

  14. Ishak, A. MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malaysiana, 40(4), 391–395 (2011)

    MathSciNet  Google Scholar 

  15. Patrick, D. W. and Magyari, E. Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities. Acta Mechanica, 209, 353–362 (2010)

    Article  MATH  Google Scholar 

  16. Bognár, G. Analytic solutions to the boundary layer problem over a stretching wall. Computers and Mathematics with Applications, 61(8), 2256–2261 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen, C. K. and Char, M. I. Heat transfer of a continuous stretching surface with suction and blowing. Journal of Mathematical Analysis and Applications, 135, 568–580 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fang, T. and Zhang, J. Note on the heat transfer of flows over a stretching wall in porous media: exact solutions. Transport in Porous Media, 86, 609–614 (2011)

    Article  Google Scholar 

  19. Sparrow, E. M. and Yu, H. S. Local non-similarity thermal boundary layer solution. ASME Journal of Heat Transfer, 93, 328–334 (1971)

    Article  Google Scholar 

  20. Sparrow, E. M., Quack, H., and Boerner, C. J. Local non-similarity boundary layer solution. AIAA Journal, 8, 1936–1942 (1970)

    Article  MATH  Google Scholar 

  21. Mahmood, M., Asghar, S., and Hossain, M. A. Squeezed flow and heat transfer over a porous surface for viscous fluid. Heat and Mass Transfer, 44, 165–173 (2007)

    Article  Google Scholar 

  22. Mushtaq, M., Asghar, S., and Hossain, M. A. Mixed convection flow of second grade fluid along a vertical stretching flat surface with variable surface temperature. Heat and Mass Transfer, 43, 1049–1061 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. COMSATS Institute of Information Technology, Islamabad, Pakistan

    A. Ahmad & S. Asghar

  2. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    S. Asghar

Authors
  1. A. Ahmad
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  2. S. Asghar
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Corresponding author

Correspondence to A. Ahmad.

Additional information

Project supported by the CIIT Research Grant Program of COMSATS Institute of Information Technology of Pakistan (No. 16-69/CRGP/CIIT/IBD/10/711)

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Ahmad, A., Asghar, S. Flow and heat transfer over hyperbolic stretching sheets. Appl. Math. Mech.-Engl. Ed. 33, 445–454 (2012). https://doi.org/10.1007/s10483-012-1562-6

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  • DOI: https://doi.org/10.1007/s10483-012-1562-6

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2010 Mathematics Subject Classification

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