Magnetohydrodynamics Boundary Layer Flows over a Stretching Surface with Radiation Effect and Embedded in Porous Medium

Authors: Siti Khuzaimah Soid, Zanariah Mohd Yusof, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

Abstract:

A steady two-dimensional magnetohydrodynamics flow and heat transfer over a stretching vertical sheet influenced by radiation and porosity is studied. The governing boundary layer equations of partial differential equations are reduced to a system of ordinary differential equations using similarity transformation. The system is solved numerically by using a finite difference scheme known as the Keller-box method for some values of parameters, namely the radiation parameter N, magnetic parameter M, buoyancy parameter l , Prandtl number Pr and permeability parameter K. The effects of the parameters on the heat transfer characteristics are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M and permeability parameter K increase. Heat transfer rate at the surface decreases as the radiation parameter increases.

Keywords: Keller-box, MHD boundary layer flow, permeability stretching.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330497

References:

[1] Ghaly, A.Y. (2002). Radiation effects on a certain MHD freeconvection flow. Chaos, Solitons and Fractals, 13, pp. 1843-1850.
[2] Raptis, A. (2004). Effect of thermal radiation on MHD flow. Applied Mathematics and Computation, 153, pp. 645-649.
[3] Liu, I.C. (2005). A note on heat and mass tranfer for a hydromagnetic flow over a stretching sheet. International Communications in Heat and Mass Transfer, 32, pp. 1075-1084.
[4] Chen, C.H. (1998). Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat and Mass Transfer, 33, pp. 471- 476.
[5] Ishak, A., Nazar, R., & Pop, I. (2008). Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat Mass Transfer, 44, pp. 921-927.
[6] Mukhopadhyay, S., & Layek, G.C. (2008). Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface. International Journal of Heat and Mass Transfer, 51, pp. 2167-2178.
[7] Abdul Hakeem, a.k., & Sathiyanathan, K. (2009). An analytic solution of an oscillatory flow through a porous medium with radiation effect. Nonlinear Analysis:Hybrid Systems, 3, pp. 288-295.
[8] Seddeek, M.A., & Abdelmeguid, M.S. (2006). Effects of radiation and thermal diffusivity on heat transfer over a stretching surface with variable heat flux. Physics Letter A, 348, pp. 172-179.
[9] Mamun Molla, M., & Anwar Hossain, M. (2007). Radiation effect on mixed convection laminar flow along a vertical wavy surface. International Journal of Thermal Sciences, 46, pp. 926-935.
[10] Chen, C.H. (2010). On the analytic solution of MHD flow and heat transfer for two types of viscoelastic fluid over a stretching sheet wuth energy dissipation, internal heat source and thermal radiation. International Journal of Heat and Mass Transfer, 53, pp. 4264-4273.
[11] Cortell, R. (2008). Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Physics Letters A, 372, pp. 631-636.
[12] Sajid, M., & Hayat, T. (2008). Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. International Communications in Heat and Mass Transfer, 35, pp. 347- 356.
[13] Bataller, R.C. (2008). Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition. Applied Mathematic and Computation, 206, pp. 832-840.
[14] Chamkha, A.J. (1997). Hydromagnetic flow and heat transfer of a heatgenerating fluid over a surface embedded in a porous medium. International Communications Heat Mass Transfer, 24(6), pp. 815-825.
[15] Ouaf, M.E.M. (2005). Exact solution of thermal radiation on MHD flow over a stretching porous sheet. Applied Mathematics and Computations, 170, pp. 1117-1125.
[16] Abbas, Z., & Hayat, T. (2008). Radiation effects on MHD flow in a porous space. International Journal of Heat and Mass Transfer, 51, pp. 1024-1033.
[17] Soid, S.K & Ishak, A. (2011). Thermal boundary layer flow along stretching sheet, IEEE, ICBEIA, pg. 120-122.
[18] Mukhopadhyay, S. (2009). Effect of thermal radiation on unsteady mixed convection flow and heat trabsfer over a porous stretching surface in porous medium. International Journal of Heat and Mass Transfer, 52, pp. 3261-3265.
[19] Grubka, L.J., & Bobba, K.M. (1985). Heat transfer characteristics of a continuous, stretching surface with variable temperature. ASME J. Heat Transfer, 107, pp. 248-250.