Effect of Radiation and Magnetohydrodynamic Free Convection Boundary Layer Flow on a Solid Sphere with Convective Boundary Conditions

Hamzeh Taha ALKASASBEH, Mohd Zuki SALLEH, Razman Mat TAHAR, Roslinda Mohd NAZAR, Ioan Mihai POP

Abstract


In this paper, the effect of radiation on magnetohydrodynamic free convection boundary layer flow on a solid sphere with convective boundary conditions, in which the heat is supplied through a bounding surface of finite thickness and finite heat capacity, is considered. The basic equations of the boundary layer are transformed into a non-dimensional form and reduced to nonlinear systems of partial differential equations and solved numerically using an implicit finite difference scheme known as the Keller-box method. Numerical solutions are obtained for the wall temperature, the heat transfer coefficient, local Nusselt number and the local skin friction coefficient, as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, magnetic parameter M, radiation parameter NR, the conjugate parameter g, and the coordinate running along the surface of the sphere, x are analyzed and discussed.

doi:10.14456/WJST.2015.50


Keywords


Convective boundary conditions, free convection, magnetohydrodynamic, radiation effects, solid sphere

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References


RC Bataller. Radiation effects for the blasius and sakiadis flows with a convective surface boundary condition. Appl. Math. Comput. 2008; 206, 832-40.

MM Molla, MA Hossain and S Siddiqa. Radiation effect on free convection laminar flow from an isothermal sphere. Chem. Eng. Comput. 2011; 198, 1483-96.

A Ishak, N Yacob and N Bachok. Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition. Meccanica 2011; 46, 795-801.

MZ Salleh, M Najihah, K Roziena, NS Khasiie, R Nazar and I Pop. Free convection over a permeable horizontal flat plate embedded in a porous medium with radiation effects and mixed thermal boundary conditions. J. Math. Stat. 2012; 8, 122-8.

P Ganesan and G Palani. Finite difference analysis of unsteady natural convection MHD flow past an inclined plate with variable surface heat and mass flux. Int. Comm. Heat Mass. Tran. 2004; 47, 4449-57.

MM Alam, M Alim and MM Chowdhury. Viscous dissipation effects on MHD natural convection flow over a sphere in the presence of heat generation. Nonlinear Anal. Modell. Cont. 2007; 12, 447-59.

MM Molla, M Taher, MM Chowdhury and MA Hossain. Magnetohydrodynamic natural convection flow on a sphere in presence of heat generation. Nonlinear Anal. Modell. Cont. 2005; 10, 349-63.

T Chen and A Mucoglu. Analysis of mixed, forced and free convection about a sphere. Int. Comm. Heat Mass. Tran. 1977; 20, 867-75.

R Nazar, N Amin, T Grosan and I Pop. Free convection boundary layer on an isothermal sphere in a micropolar fluid. Int. Comm. Heat Mass. Tran. 2002; 29, 377-86.

R Nazar, N Amin, T Grosan and I Pop. Free convection boundary layer on a sphere with constant surface heat flux in a micropolar fluid. Int. Comm. Heat Mass. Tran. 2002; 29, 1129-38.

CY Cheng. Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration. Int. Comm. Heat Mass. Tran. 2008; 35, 750-5.

MZ Salleh, R Nazar and I Pop. Modeling of free convection boundary layer flow on a solid sphere with Newtonian heating. Acta Applic. Math. 2010; 112, 263-74.

MZ Salleh, R Nazar and I Pop. Numerical solutions of free convection boundary layer flow on a solid sphere with newtonian heating in a micropolar fluid. Meccanica 2012; 47, 1261-9.

JH Merkin. Natural-convection boundary-layer flow on a vertical surface with Newtonian heating. Int. J. Heat Fluid. Flow. 1994; 15, 392-8.

A Aziz. A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Comm. Nonlinear. Sci. Numer. Simulat. 2009; 14, 1064-8.

A Ishak. Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl. Math. Comput. 2010; 217, 837-42.

O Makinde and A Aziz. MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int. J. Thermal. Sci. 2010; 49, 1813-20.

J Merkin and I Pop. The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition. Comm. Nonlinear Sci. Numer. Simulat. 2011; 16, 3602-9.

S Yao, T Fang and Y Zhong. Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Comm. Nonlinear Sci. Numer. Simulat. 2011; 16, 752-60.

MKA Mohamed, MZ Salleh, R Nazar and A Ishak. Numerical investigation of stagnation point flow over a stretching sheet with convective boundary conditions. Bound. Value Prob. 2013; 2013, Article ID 4.

T Cebeci and P Bradshaw. Physical and Computational Aspects of Convective Heat Transfer. Springer, New York, 1988.

RC Bataller. Radiation effects in the blasius flow. Appl. Math. Comput. 2008; 198, 333-8.

M J Hung and CK Chen. Leminar free convections from a sphere with blowing and suction. J. Heat. Tran. 1987; 109, 529-32.


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