Axisymmetric Powell-Eyring fluid flow with convective boundary condition:optimal analysis

doi:10.1007/s10483-016-2093-9

Abstract

Abstract:

The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method (OHAM). The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.

Key words: optimal homotopy analysis method (OHAM) analysis, axisymmetric flow, convective boundary condition

2010 MSC Number:

80A20
70Kxx

T. HAYAT, S. MAKHDOOM, M. AWAIS, S. SALEEM, M. M. RASHIDI. Axisymmetric Powell-Eyring fluid flow with convective boundary condition:optimal analysis. Applied Mathematics and Mechanics (English Edition), 2016, 37(7): 919-928.

TrendMD

References

[1] Fetecau, C., Nazar, M., and Fetecau, C. Unsteady flow of an Oldroyd-B fluid generated by a constantly accelerating plate between two-side walls perpendicular to the plate. Internationl Journal of Nonlinear Mechanics, 44, 1039-1047(2009)
[2] Jamil, M. and Fetecau, C. Some exact solutions for rotating flows of a generalized Burgers' fluid in cylindrical domains. Journal of Non-Newtonian Fluid Mechanics, 165, 1700-1712(2010)
[3] Hussain, M., Hayat, T., Asghar, S., and Fetecau, C. Oscillatory flows of second grade fluid in a porous space. Nonlinear Analysis:Real World Applications, 11, 2403-2414(2010)
[4] Akbar, N. S. Influence of magnetic field on peristaltic flow of a Casson fluid in an asymmetric channel:application in crude oil refinement. Journal of Magnetism and Magnetic Materials, 378, 463-468(2015)
[5] Nadeem, S. and Saleem, S. Analytical study of third grade fluid over a rotating vertical cone in the presence of nanoparticles. Internationl Journal of Heat and Mass Transfer, 85, 1041-1048(2015)
[6] Alloui, Z. and Vasseur, P. Natural convection of Carreau-Yasuda non-Newtonian fluids in a vertical cavity heated from sides. Internationl Journal of Heat and Mass Transfer, 84, 912-924(2015)
[7] Sheikholeslami, M., Ganji, D. D., Javed, M. Y., and Ellahi, R. Effects of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two-phase model. Journal of Magnetism and Magnetic Materials, 374, 36-43(2015)
[8] Kang, J., Fu, C., and Tan, W. C. Thermal convective instability of viscoelastic fluids in a rotating porous layer heated from below. Journal of Non-Newtonian Fluid Mechanics, 166, 93-101(2011)
[9] Kang, J., Niu, J., Fu, C., and Tan, W. C. Coriolis effect on thermal convective instability of viscoelastic fluids in a rotating porous cylindrical annulus. Transport in Porous Media, 98, 349-362(2013)
[10] Kang, J., Zhou, F., Tan, W. C., and Xia, T. Thermal instability of a nonhomogeneous powerlaw nanofluid in a porous layer with horizontal through flow. Journal of Non-Newtonian Fluid Mechanics, 213, 50-56(2014)
[11] Kang, J., Liu, Y., and Xia, T. Unsteady flows of a generalized fractional Burgers' fluid between two-side walls perpendicular to a plate. Advances in Mathematics and Physics, 2015, 521069(2015)
[12] Ahmad, S., Ashraf, M., and Syed, K. S. Effects of thermal radiation on MHD axisymmetric stagnation point flow and heat transfer of a micropolar fluid over a shrinking sheet. World Applications Science Journal, 15, 835-848(2011)
[13] Sochi, T. The flow of power-law fluids in axisymmetric corrugated tubes. Journal of Peterolium and Science Engineering, 78, 582-585(2011)
[14] Khan, M. and Shahzad, A. On axisymmetric flow of Sisko fluid over a radially stretching sheet. International Journal of Nonlinear Mechanics, 47, 999-1007(2012)
[15] Hayat, T., Shafiq, A., Nawaz, M., and Alsaedi, A. MHD axisymmetric flow of third grade fluid between porous disks with heat transfer. Applied Mathematics and Mechanics (English Edition), 33(6), 749-764(2012) DOI 10.1007/s10483-012-1584-9
[16] Hosseini, Z., Sheikholeslami, M., and Ganji, D. D. Non-Newtonian fluid flow in an axisymmetric channel with porous wall. Propulsion and Power Research, 2, 254-262(2013)
[17] Mastroberardino, A. Series solutions of annular axisymmetric stagnation flow and heat transfer on moving cylinder. Applied Mathematics and Mechanics (English Edition), 34(9), 1043-1054(2013) DOI 10.1007/s10483-013-1726-7
[18] Hayat, T., Shafiq, A., Alsaedi, A., and Awais, M. MHD axisymmetric flow of third grade fluid between stretching sheets with heat transfer. Computors and Fluids, 86, 103-108(2013)
[19] Awais, M., Hayat, T., Nawaz, M., and Alsaedi, A. Newtonian heating, thermal-diffusion and diffusion-thermo effects in an axisymmetric flow of a Jeffrey fluid over a stretching sheet. Brazilien Journal of Chemical Enginerring, 32, 555-561(2015)
[20] Liao, S. J. An optimal homotopy analysis method approach for strongly nonlinear differential equation. Communication in Nonlinear Science and Numerical Simulations, 15, 2003-2016(2010)
[21] Rashidi, M. M. and Pour, S. A. M. Analytic approximate solutions for unsteady boundary-layer flow and heat transfer due to a stretching sheet by homotopy analysis method. Nonlinear Analysis:Modelling and Control, 15, 83-95(2010)
[22] Rashidi, M. M., Freidoonimehr, N., Hosseini, A., Beg, O. A., and Hung, T. K. Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration. Meccanica, 49, 469-482(2014)
[23] Abbasbandy, S. and Hayat, T. On series solution for unsteady boundary layer equations in a special third grade fluid. Communication in Nonlinear Science and Numerical Simulations, 16, 3140-3146(2011)
[24] Awais, M., Hayat, T., Irum, S., and Alsaedi, A. Heat generation/absorption effects in a boundary layer stretched flow of Maxwell nanofluid:analytic and numeric solutions. Plos One, 10, e0129814(2015)
[25] Hayat, T., Ali, S., Awais, M., and Alhuthali, M. S. Newtonian heating in stagnation point flow of Burgers fluid. Applied Mathematics and Mechanics (English Edition), 36(1), 61-68(2015) DOI 10.1007/s10483-015-1895-9
[26] Wang, C. Y. Natural convection on a vertical radially stretching sheet. Journal of Mathematical Analysis and Applications, 332, 877-883(2007)
[27] Asad, S., Alsaedi, A., and Hayat, T. Flow of couple stress fluid with variable thermal conductivity. Applied Mathematics and Mechanics (English Edition), 37(3), 315-324(2016) DOI 10.1007/s10483-016-2031-6