Effects of Thermal Radiation and Magnetic Field on Unsteady Stretching Permeable Sheet in Presence of Free Stream Velocity

The aim of this paper is to investigate twodimensional unsteady flow of a viscous incompressible fluid about stagnation point on permeable stretching sheet in presence of time dependent free stream velocity. Fluid is considered in the influence of transverse magnetic field in the presence of radiation effect. Rosseland approximation is use to model the radiative heat transfer. Using time-dependent stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by using Runge-Kutta Fehlberg method with the help of Newton-Raphson shooting technique. In the present work the effect of unsteadiness parameter, magnetic field parameter, radiation parameter, stretching parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Skin-friction coefficient and Nusselt number at the sheet are computed and discussed. The results reported in the paper are in good agreement with published work in literature by other researchers.





References:
[1] L.J. Crane, "Flow past a stretching plate," The Journal of Applied
Mathematics and Physics (ZAMP), vol. 21, pp 645-647, 1970.
[2] T.R. Mahapatra and A.S. Gupta, "Stagnation-point flow towards a
stretching surface," The Canadian Journal of Chemical Engineering,
vol. 81, pp 258-263, 2003.
[3] P. Singh, N.S. Tomer and D. Sinha, "Numerical study of heat transfer
over stretching surface in porous media with transverse magnetic field,"
Proceeding of International Conference on Challenges and application
of Mathematics in Sciences and Technology 2010, ISBN 023- 032-875-
X, pp 422-430.
[4] P. Singh, N.S. Tomer, S. Kumar and D. Sinha, "MHD oblique
stagnation-point flow towards a stretching sheet with heat transfer,"
International Journal of Applied Mathematics and Mechanics, vol. 6,
no. 13, pp 94-111, 2010.
[5] I. Pop and T. Na, "Unsteady flow past a stretching sheet," Mechanics
Research Communications, vol. 23, no. 4, pp 413-422, 1996.
[6] Elbashbeshy EMA, Bazid MAA. Heat transfer over an unsteady
stretching surface. Heat and Mass Transfer 2004; 41: 1-4.
[7] A. Ishak, R. Nazar and I. Pop, "Heat transfer over an unsteady
stretching permeable surface with prescribed wall temperature,"
Nonlinear Analysis: Real World Applications, vol. 10, pp 2909-2913,
2009.
[8] H.S. Takhar, A.J. Chamkha and G. Nath, "Unsteady three-dimensional
MHD boundary layer due to the impulsive motion of a stretching
surface," Acta Mechanica, vol. 146, pp 59-71, 2001.
[9] A. Ishak , "Unsteady MHD flow and heat transfer over a stretching
plate," Journal of Applied Sciences, vol. 10, no. 18, pp 2127-2131,
2010.
[10] M.S. Abel, N. Mahesha and J. Tawade, "Heat transfer in a liquid film
over an unsteady stretching surface with viscous dissipation in presence
of external magnetic field," Applied Mathematical Modelling vol. 33, pp
3430-3441, 2009.
[11] M.A. El-Aziz, "Flow and heat transfer over an unsteady stretching
surface with Hall effect," Meccanica, vol. 45, pp 97-109, 2010.
[12] A.Y. Ghaly and E.M.E. Elbarbary, "Radiation effect on MHD free -
convection flow of a gas at a stretching surface with a uniform free
stream," Journal of Applied Mathematics, vol. 2, no. 2, pp 93-103,
2002.
[13] I. Pop, S.R. Pop and T. Grosan, "Radiation effects on the flow near the
stagnation point," Technische Mechanik, vol. 2, no. 25, pp 100-106,
2004.
[14] M.A. El-Aziz, "Radiation effect on the flow and heat transfer over an
unsteady stretching sheet," International Communications in Heat and
Mass Transfer, vol. 36, pp 521-524, 2009.