Flow of a second grade fluid with convective boundary conditions

Abstract

The flow and heat transfer in a second grade fluid over a stretching sheet subjected to convective boundary conditions are investegated. Similarity transformations have been used for the reduction of partial differential equation into the ordinary differential. Homotopy analysis method (HAM) has been utilized for the series solutions. Graphical results are displayed and analyzed. Computations for local Nusselt number have been carried out.

Dates

  • Submission Date2010-10-14
  • Revision Date2011-03-16
  • Acceptance Date2011-06-07

DOI Reference

10.2298/TSCI101014058H

References

  1. Crane, L.J., Flow past a stretching plate, Zeitschrift fur Angewandte Mathematik und Physik, 21 (1970) ,pp. 645-647.
  2. Ariel, P.D., Extended homotopy perturbation method and computation of flow past a stretching sheet, Computers & Mathematics with Applications, 58 (2009), pp. 2402-2409.
  3. Ishak, A., Nazar, R., Pop, I., Heat transfer over a stretching surface with variable heat flux in micropolar fluids, Physics Letters A, 372 (2008) ,pp. 559-561.
  4. Ishak, A., Nazar, R., Pop, I., Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder, Energy Conversion and Management, 49 (2008), pp. 3265-3269.
  5. Liao, S.J., On the analytic solution of magnetohydrodynamic flow of non-Newtonian fluid over a stretching sheet, Journal of Fluid Mechanics, 488 (2003) ,pp. 189-212.
  6. Hayat, T., Qasim, M., Abbas, Z., Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet, Zeitschrift fur Naturforschung A, 65a (2010) ,pp. 231- 239.
  7. Cortell, R., Similarity solution for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface, Journal of Materials Processing Technology, 203 (2008) ,pp. 176 -183.
  8. Hayat, T., Qasim, M., Mesloub, S., MHD flow and heat transfer over permeable stretching sheet with slip conditions, International Journal for Numerical Methods in Fluids, DOI: 10.1002/fld.2294.
  9. Singh, G. and Sharma, P. R., Effects of Ohmic heating and viscous dissipation on steady MHD flow near a stagnation point on an isothermal stretching sheet, Thermal Science, 13 (2009), 1, pp.5-12.
  10. Mushtaq, M., Asghar, S., Hossain, M.A., Mixed convection flow of second grade fluid along a vertical stretching surface with variable surface temperature, Heat and Mass Transfer, 43 (2007 ) ,pp. 1049-1061.
  11. Hussain, M., Hayat, T., Asghar, S., Fetecau, C., Oscillatory flows of second grade fluid in a porous space, Nonlinear Analysis: Real World Applications, 11 (2010), pp. 2403-2414.
  12. Hayat, T., Qasim, M., Radiation and magnetic field effects on the unsteady mixed convection flow of a second grade fluid over a vertical stretching sheet, International Journal for Numerical Methods in Fluids, DOI: 10.1002/fld.2285.
  13. Ariel, P.D., Axisymmetric flow of a second grade fluid past a stretching sheet, International Journal of Engineering Science, 39 (2001) ,pp. 529-553.
  14. Cortell, R., MHD flow and mass transfer of an electrically conducting fluid of a second grade in a porous medium over a stretching sheet with chemically reactive species, Chemical Engineering and Processing, 46 (2007 ) ,pp. 721- 728.
  15. Nazar, M., Fetecau, C., Vieru, D., Fetecau, C., New exact solutions corresponding to the second problem of Stokes for second grade fluids, Nonlinear Analysis: Real World Applications, 11 (2010) ,pp. 584-591.
  16. Tan, W. C., Masuoka, T., Stokes first problem for a second grade fluid in a porous half-space with heated boundary, International Journal of Non-Linear Mechanics, 40 (2005) ,pp. 515-522.
  17. Hayat, T., Naeem, I., Ayub, M., Asghar, S., Khalique, C.M., Exact solutions of second grade aligned MHD fluid with prescribed velocity, Nonlinear Analysis: Real World Applications, 10 (2009) ,pp. 2117-2126.
  18. Asghar, S., Hayat, T., Ariel, P.D., Unsteady Couette flows in a second grade fluid with variable material properties, Communications in Nonlinear Science and Numerical Simulation, 14 (2009) ,pp. 154 -159.
  19. Yao, S., Fang, T., Zhong, Y., Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions, Communications in Nonlinear Science and Numerical Simulation, 16 (2011) ,pp. 752-760.
  20. Liao, S.J., Notes on the homotopy analysis method: Some definitions and theorems, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 983-997.
  21. Liao, S.J., On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation, 147 (2004) ,pp. 499-513.
  22. Cheng, J., Liao, S.J., Mohapatra, R.N., Vajravelu, K., Series solutions of nano boundary layer flows by means of the homotopy analysis method, Journal of Mathematical Analysis and Applications, 343 (2008) ,pp. 233-245.
  23. Liao, S.J., Beyond Perturbation: Introduction to homotopy analysis method, Chapman and Hall, CRC Press, Boca Raton, (2003) .
  24. Liao, S.J., Series solution for unsteady boundary-layer flows over a stretching flat plate, Studies in Applied Mathematics, 117 (2006) ,pp. 239-263.
  25. Abbasbandy, S., Shivanian, E., Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation, 15 (2010), pp. 3830-3846.
  26. Abbasbandy, S., Magyari E., Shivanian, E., The homotopy analysis method for multiple solutions of nonlinear boundary value problems, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 3530-3536.
  27. Abbasbandy, S., Homotopy analysis method for the Kawahara equation, Nonlinear Analysis: Real World Applications, 11 (2010), pp. 307-312.
  28. Hashim, I., Abdulaziz, O., Momani, S., Homotopy analysis method for fractional IVPs, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 674-684.
  29. Bataineh, A.S., Noorani, M.S.M., Hashim, I., The homotopy analysis method for Cauchy reaction-diffusion problems, Physics Letters A, 372 (2008), pp. 613-618.
  30. Nadeem, S., Abbasbandy, S., Hussain, M., Series solutions of boundary layer flow of a micropolar fluid near the stagnation point towards a shrinking sheet, Zeitschrift fur Naturforschung A, 64a (2009), pp. 575-582.
  31. Hayat, T., Qasim, M., Abbas, Z., Magnetohydrodynamic flow and mass transfer of a Jeffery fluid over a nonlinear stretching surface, Zeitschrift fur Naturforschung A, 65a (2010), pp. 1111-1120..
  32. Hayat, T., Shehzad, S.A., Qasim, M., Mixed convection flow of a micropolar fluid with radiation and chemical reaction, International Journal for Numerical Methods in Fluids, In Press.
  33. Abdallah, I. A., Analytical solution of heat and mass transfer over a permeable stretching plate affected by a chemical reaction, internal heating, Dufour-Souret effect and hall effect, Thermal Science, 13 (2009), pp. 183-197.
  34. Hayat, T., 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 (2010) ,pp. 4780-4788.
  35. Nadeem, S., Hussain, M., Naz, M., MHD stagnation flow of a micropolar fluid through a porous medium, Meccanica, DOI: 10.1007/s11012-010-010-9297-9.
Volume 15, Issue 12, Pages253 -261