MELTING HEAT TRANSFER IN THE STAGNATION-POINT FLOW OF THIRD GRADE FLUID PAST A STRETCHING SHEET WITH VISCOUS DISSIPATION

Abstract

An analysis has been carried out for the characteristics of melting heat transfer in the boundary layer flow of third grade fluid in a region of stagnation point past a stretching sheet. The relevant partial differential equations are reduced into ordinary differential system by suitable transformations. The series solutions are developed by homotopy analysis method (HAM). It is revealed that an increase in the melting parameter (M ) decreases the velocity and the temperature (θ ). An increase in the third grade parameter (φ ) increases the velocity and the boundary layer thickness. The present results are also compared with the previous studies.

Dates

  • Submission Date2011-04-05
  • Revision Date2011-08-22
  • Acceptance Date2011-08-24

DOI Reference

10.2298/TSCI110405119H

References

  1. Sajid, M., Hayat, T., Non-simliar series solution for boundary layer flow of a third-order fluid over a stretching sheet, Appl. Math. Comput., 189 (2007), 2, pp. 1576-1585.
  2. Sajid, M., Hayat, T., Asghar, S., Non-similar analytic solution for MHD flow and heat transfer in a third order fluid over a stretching sheet, Int. J. Heat Mass Transfer, 50, 9-10, (2007) 1723-1736.
  3. Hayat, T., Mustafa, M., Asghar, S., Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction, Nonlinear Anal : RWA, 11 (2010), 4, 3186-3197.
  4. Sahoo, B., Heimenz flow and heat transfer of a third grade fluid, Comm. Nonlinear Sci. Num. Simul., 14 (2009) 811-826.
  5. Sahoo, B., Do, Y., Effects of slip on sheet driven flow and heat transfer of a third grade fluid pasta stretching sheet, Int. Comm. Heat Mass Transfer, 37 (2010), 3, 1064-1071.
  6. Hiemenz, K., Die Grenzschicht an einem in den gleichfÄormigen FlÄussigkeitsstrom eingetauchten geraden Kreiszylinder, Dinglers Polytech. J., 326 (1911) 321-324.
  7. Crane, L. J., Flow past a stretching plate, Z. Angew. Math. Phys., 21 (1970) , 4, 645 − 647 . H. Kumar, Heat transfer over a stretching porous sheet subjected to power law heat flux in presence of heat source, Therm. Sci. doi: 10.2298/TSCI100331074K
  8. Chiam, T. C., Stagnation-point flow towards a stretching plate, J. Phys. Soc. Jpn., 63 (1994) 2443 − 2444.
  9. Mahapatra, T. R., Nandy, S. K., Gupta, A. S., Magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface, Int. J. Nonlinear. Mech., 44 (2009) , 2, 124 −129 .
  10. Labropulu, F., Li, D., Stagnation-point flow of a second grade fluid with slip, Int. J. Nonlinear Mech., 43 (2008) , 9, 941− 947 .
  11. Hayat, T., Abbas, Z., Sajid, M., MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface, Chaos Solitons & Fractals, 39 (2009) , 2, 840 − 848.
  12. Hayat, T., Nawaz, M., Unsteady stagnation point flow of viscous fluid caused by an impulsively rotating disk, J. Taiwan Inst. Chem. Eng., 42 (2011) , 1, 41− 49 .
  13. Epstein, M., Cho, D. H., Melting heat transfer in steady laminar flow over a flat plate, J. Heat transfer, 98 (1976) , 3, 531− 533 .
  14. Ishak, A., Nazar, R., Bachok, N., Pop, I., Melting heat transfer in steady laminar flow over a moving surface, Heat Mass Transfer, 46 (2010) , 4, 463 − 468.
  15. Bachok, N., Ishak, A., Pop, I., Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet, Phys. Lett. A., 374 (2010) , 40, 4075 − 4079 .
  16. Liao, S., Notes on the homotopy analysis method: Some definitions and theorems, Comm. Nonlinear Sci. Num. Simul., 14 (2009) , 4, 983 − 997 .
  17. Liao, S. J., On the relationship between the homotopy analysis method and Euler transform, Comm. Nonlinear Sci. Numer. Simul., 15 (2010), 6, 1421−1431.
  18. Kousar, N., Liao, S. J., Series solution of non-similarity boundary-layer flows over a porous wedge, Transport in Porous Media, 83 (2010) , 2, 397 − 412.
  19. Abbasbandy, S., Shivanian, E., Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method, Comm. Nonlinear Sci. Num. Simul., 15 (2010) , 12, 3830 − 3846.
  20. Abbasbandy, S., Shirzadi, A., A new application of the homotopy analysis method: Solving the Sturm-Liouville problems, Comm. Nonlinear Sci. Num. Simul., 16 (2011) , 1, 112 −126 .
  21. Hashim, I., Abdulaziz, O., Momani, S., Homotopy analysis method for fractional IVPs, Comm. Nonlinear Sci. Num. Simul., 14 (2009) , 3, 674 − 684.
  22. Bataineh, A. S., Noorani, M. S. M., Hashim, I., On a new reliable modification of homotopy analysis method, Comm. Nonlinear Sci. Num. Simul., 14 (2009) , 2, 409 − 423 .
  23. Bataineh, A. S., Noorani, M. S. M., Hashim, I., Homotopy analysis method for singular IVPs of Emden--Fowler type, Comm. Nonlinear Sci. Num. Simul., 14 (2009) , 4, 1121−1131.
  24. Hayat, T., Qasim, M., Abbas, Z., Homotopy solution for unsteady three-dimensional MHD flow and mass transfer in a porous space, Comm. Nonlinear. Sci. Num. Simul., 15 (2010) , 9, 2375 − 2387.
  25. Hayat, T., Mustafa, M., Mesloub, S., Mixed convection boundary layer flow over a stretching surface filled with a Maxwell fluid in presence of Soret and Dufour effects, Z. Naturforsch., 65a (2010) , 1, 401− 410 .
  26. Hayat, T., Mustafa, M., Influence of thermal radiation on the unsteady mixed convection flow of a Jeffrey fluid over a stretching sheet, Z. Naturforsch., 65a (2010) , 711− 719 . Hayat, T., Awais, M., Sajid, M., Similar solutions of stretching flow with mass transfer, Int. J. Num. Meth. Fluids, 64 (2010) , 8, 908 − 921.
  27. Khan, M., Farooq, J., On heat transfer analysis of a magneto-hydrodynamic Sisko fluid through a porous medium, J. Porous Media, 13 (2010), 3, 287-294
  28. Khan, M., Munawar, S., Abbasbandy, S., Steady flow and heat transfer of a Sisko fluid in annular pipe, Int. J. Heat Mass Transfer, 53 (2010), 7-8, 1290-1297.
  29. Khan, M., Qurrat-ul-Ain, Sajid, M., Heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to a suddenly moved plate, Comm. Nonlinear Sci. Num. Simul., 16 (2011), 3, 1347-1355.
  30. Hayat, T., Shehzad, S. A., Qasim, M., Obaidat, S., Flow of second grade fluid with convective boundary conditions, Therm. Sci. doi: 10.2298/TSCI101014058H.
  31. Ahmad, I., Ahmed, M., Abbas, Z., Sajid, M., Hydromagnetic flow and heat transfer over a bidirectional stretching surface in a porous medium, Therm. Sci. doi:10.2298/TSCI100926006A
  32. Ishak, A., Nazar, R., Amin, N., Filip, D., Pop, I., Mixed convection in the stagnation point flow towards a stretching vertical permeable sheet, Malaysian. J. Math. Sci. 2 (2007) , 2, 217 − 226
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