Heat Transfer for MHD Second Grade Fluid Flow over a Porous Nonlinear Radially Stretching Sheet

Asif MUNIR; Azeem SHAHZAD; Masood KHAN

Authors

Asif MUNIR Department of Mathematics, Quaid-i-Azam University, Islamabad
Azeem SHAHZAD Department of Basic Science, University of Engineering & Technology, Taxila
Masood KHAN Department of Mathematics, Quaid-i-Azam University, Islamabad

Keywords:

Heat transfer, second grade fluid, radially stretching sheet

Abstract

The heat transfer for the steady axisymmetric flow of a second grade fluid over an isothermal radially stretching porous sheet is investigated. A power law stretching of sheet is assumed, while the fluid is electrically conducting in the presence of a transverse magnetic field. Appropriate similarity transformations are introduced to reduce the resulting highly non-linear partial differential equations into ordinary differential equations, which are then solved analytically by the homotopy analysis method (HAM) and numerically by the shooting method using the adaptive Runge Kutta method with Broyden's method. The developed analytical expressions for the temperature field are graphically presented and the influence of pertinent parameters on the thermal boundary layer is discussed in detail. To check the reliability of the HAM results, a comparison is made with numerical results. An excellent agreement is observed between the 2 sets of results. In addition, the local Nusselt number is tabulated for several influential parameters.

doi:10.14456/WJST.2015.58

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References

P Carragher and LJ Crane. Heat transfer on a continuous stretching sheet. Z. Angew. Math. Mech. 1982; 62, 564-73.

R Cortell. Viscous flow and heat transfer over a nonlinearly stretching sheet. Appl. Math. Comput. 2007; 184, 864-73.

J Alinejad and S Samarbakhsh. Viscous flow over nonlinearly stretching sheet with effects of viscous dissipation. J. Appl. Math. 2012; 2012, Article ID 587834.

PD Ariel. A numerical algorithm for computing the stagnation point flow of a second grade fluid with/without suction. J. Comput. Appl. Math. 1995; 59, 9-24.

C Liu. Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field. Int. J. Heat Mass Tran. 2004; 47, 4427-37.

V Singh and S Agarwal. Heat transfer in a second grade fluid over an exponentially stretching sheet through porous medium with thermal radiation and ellastic deformation under the effects of magnetic field. Int. J. Appl. Math. Mech. 2012; 8, 41-63.

T Hayat, SA Shehzad, M Qasim and S Obaidat. Flow of a second grade fluid with convective boundary conditions. Therm. Sci. 2011; 15, 253-61.

T Hayat, Z Iqbal and M Mustafa. Flow of a second grade fluid over a stretching surface with Newtonian heating. J. Mech. 2012; 28, 209-16.

T Hayat and M Sajid. Analytic solution for axisymmetric flow and heat transfer of second grade fluid past a stretching sheet. Int. J. Heat Mass Tran. 2007; 50, 75-84.

B Sahoo. Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet. Appl. Math. Mech. 2010; 31, 159-73.

I Ahmad, M Sajid and T Hayat. Heat transfer in unsteady axisymmetric second grade fluid. Appl. Math. Comput. 2009; 215, 1685-95.

PS Gupta and AS Gupta. Heat and mass transfer on a stretching sheet with suction or blowing. Can. J. Chem. Eng. 1977; 55, 744-6.

A Shahzad, R Ali and M Khan. On the exact solution for axisymetric flow and heat transfer over a nonlinear radially stretching sheet. Chin. Phys. Lett. 2012; 29, Article ID 084705.

RS Rivlin and JL Ericksen. Stress deformation relations for isotropic materials. J. Rat. Mech. Anal. 1955; 4, 323-425.

S Liao. Homotopy Analysis Method in Nonlinear Differential Equations. Springer, New York, 2012, p. 1-119.