Numerical Solution of MHD Boundary Layer Flow of Non-Newtonian Casson Fluid on a Moving Wedge with Heat and Mass Transfer and Induced Magnetic Field

Abstract

The paper investigates the numerical solution of the magnetohydrodynamics (MHD) boundary layer flow of non-Newtonian Casson fluid on a moving wedge with heat and mass transfer. The effects of thermal diffusion and diffusion thermo with induced magnetic field are taken in consideration. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying the similarity transformation and solved numerically by using finite difference method (FDM). The effects of various governing parameters, on the velocity, temperature and concentration are displayed through graphs and discussed numerically. In order to verify the accuracy of the present results, we have compared these results with the analytical solutions by using the differential transform method (DTM). It is observed that this approximate numerical solution is in good agreement with the analytical solution. Furthermore, comparisons of the present results with previously published work show that the present results have high accuracy.

Share and Cite:

El-Dabe, N. , Ghaly, A. , Rizkallah, R. , Ewis, K. and Al-Bareda, A. (2015) Numerical Solution of MHD Boundary Layer Flow of Non-Newtonian Casson Fluid on a Moving Wedge with Heat and Mass Transfer and Induced Magnetic Field. Journal of Applied Mathematics and Physics, 3, 649-663. doi: 10.4236/jamp.2015.36078.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Raptis, A. and Perdikis, C. (1984) Free Convection under the Influence of a Magnetic Field. Nonlinear Analysis: Theory, Methods & Applications, 8, 749-756. [2] Kumari, M., Takhar, H.S. and Nath, G. (1990) MHD Flow and Heat Transfer over a Stretching Surface with Prescribed Wall Temperature or Heat Flux. Wärme - und Stoffübertragung, 25, 331-336. [3] Takhar, H.S., Kumari, M. and Nath, G.G. (1993) Unsteady Free Convection Flow under the Influence of a Magnetic Field. Archive of Applied Mechanics, 63, 313-321. http://dx.doi.org/10.1007/BF00793897 [4] Ali, F.M. Nazar, R., Arifin, N.M. and Pop, I. (2011) MHD Stagnation-Point Flow and Heat Transfer towards Stretching Sheet with Induced Magnetic Field. Applied Mathematics and Mechanics, 32, 409-418. [5] Ali, K., Ashraf, M., Ahmad, S. and Batool, K. (2012) Viscous Dissipation and Radiation Effects in MHD Stagnation Point Flow towards a Stretching Sheet with Induced Magnetic Field. World Applied Sciences Journal, 16, 1638-1648. [6] Ali, K. and Ashraf, M. (2012) Thermal Reversal in MHD Stagnation Point Flow towards a Stretching Sheet with Induced Magnetic Field and Viscous Dissipation Effects. World Applied Sciences Journal, 16, 1615-1625. [7] Ali, F.M., Nazar, R., Arifin, N.M. and Pop, I. (2011) MHD mixed Convection Boundary Layer Flow toward a Stagnation Point on a Vertical Surface with Induced Magnetic Field Was Studied. Journal of Heat Transfer, 133, Article ID: 022502, 1-6. [8] Jafar, K., Nazar, R., Ishak, A. and Pop, I. (2013) MHD Boundary Layer Flow Due to a Moving Wedge in a Parallel Stream with the Induced Magnetic Field. J. Boundary Value Problems, 1-14. [9] Nakayama, M. and Sawada, T. (1988) Numerical Study on the Flow of a Non-Newtonian Fluid through an Axisymmetric Stenosis. Journal of Biomechanical Engineering, 110, 137-143. http://dx.doi.org/10.1115/1.3108418 [10] Abdelnaby, M.A., Eldabe, N.T. and Abou-zeid, M.Y. (2006) Numerical Study of Pulsatile MHD Non-Newtonian Fluid Flow With heat and Mass Transfer through a Porous Medium between Two Permeable Parallel Plates. Ind. J. Mech. Cont. & Math Sci, 1, 1-15. [11] Eldabe, N.T., El-Sakka, A.G. and Fouda, A. (2002) Numerical Treatment of the MHD Convective Heat and Mass Transfer in an Electrically Conducting Fluid over an Infinite Solid Surface in Presence of Internal Heat Generation. Zeitschrift für Naturforschung, 58, 601-611. [12] Eldabe, N.T., El-Sayed, M.F., Ghaly, A.Y. and Sayed, H.M. (2007) Peristaltically Induced Transport of a MHD Biviscosity Fluid in a Non-Uniform Tube. Physica A: Statistical Mechanics and its Applications, 383, 253-266. http://dx.doi.org/10.1016/j.physa.2007.05.027 [13] Eldabe, N.T., El-Sayed, M.F., Ghaly, A.Y. and Sayed, H.M. (2008) Mixed Convective Heat and Mass Transfer in a Non-Newtonian Fluid at a Peristaltic Surface with Temperature-Dependent Viscosity. Archive of Applied Mechanics, 78, 599-624. http://dx.doi.org/10.1007/s00419-007-0181-6 [14] Eldabe, N.T. and Hassan, A.A. (1991) Non-Newtonian-Flow Formation in Couette Motion in Magnethohydrodynamics with Time-Varying Suction. Canadian Journal of Physics, 69, 75-85. http://dx.doi.org/10.1139/p91-012 [15] Zhou, J.K. (1986) Differential Transformation and Its Application for Electrical Circuits. Huazhong University Press, Wuhan. [16] Rajagopal, K.R., Gupta, A.S. and Nath, T.Y. (1983) A Note on the Falkner-Skan Flows of a Non-Newtonian Fluid. International Journal of Non-Linear Mechanics, 18, 313-320. http://dx.doi.org/10.1016/0020-7462(83)90028-8 [17] Kuo, B.L. (2003) Application of the Differential Transformation Method to the Solutions of Falkner-Skan Wedge Flow. Acta Mechanica, 164, 161-174. http://dx.doi.org/10.1007/s00707-003-0019-4 [18] Ishak, A., Nazar, R. and Pop, I. (2009) MHD Boundary Layer Flow past a Moving Wedge. Magnetohydrodynamics, 45, 3-10.