Sains Malaysiana 40(4)(2011): 391–395

 

MHD Boundary Layer Flow Due to an Exponentially Stretching Sheet with Radiation Effect

(Aliran Lapisan Sempadan MHD Berpunca daripada Regangan HelaianSecara Eksponen dengan Kesan Sinaran)

 

Anuar Ishak*

School of Mathematical Sciences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor D.E., Malaysia

 

Received: 9 December 2009 / Accepted: 21 June 2010

 

ABSTRACT

 

The effect of radiation on magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was studied. The governing system of partial differential equations was transformed into ordinary differential equations before being solved numerically by an implicit finite-difference method. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. It was found that the local heat transfer rate at the surface decreases with increasing values of the magnetic and radiation parameters.

 

Keywords: Boundary-layer; heat transfer; MHD; radiation; stretching sheet

 

ABSTRAK

 

Kesan sinaran terhadap aliran lapisan sempadan magnetohidrodinamik (MHD) bagi bendalir likat di atas helaian meregang secara eksponen dikaji. Sistem persamaan menakluk dalam bentuk persamaan pembezaan separa dijelmakan kepada persamaan pembezaan biasa sebelum diselesaikan secara berangka menggunakan kaedah beza-terhingga tersirat. Kesan parameter-parameter menakluk terhadap ciri-ciri aliran dan pemindahan haba diperoleh dan dibincangkan. Didapati bahawa kadar pemindahan haba setempat pada permukaan berkurang dengan pertambahan nilai parameter magnet dan parameter sinaran.

 

Kata kunci: Lapisan sempadan; MHD; pemindahan haba; regangan helaian; sinaran

 

REFERENCES

 

Aboeldahab, E.M. & El Gendy, M.S. 2002. Radiation effect on MHD free convective flow of a gas past a semi-infinite vertical plate with variable thermophysical properties for high-temperature differences. Can. J. Phys. 80: 1609-1619.

Bataller, R.C. 2008. Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation. Phys. Lett. A 372: 2431-2439.

Bidin, B. & Nazar, R. 2009. Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. Euro J. Sci. Res. 33(4): 710-717.

Carragher, P. & Crane, L.J. 1982. Heat transfer on a continuous stretching sheet. Z. Angew. Math. Mech. 62: 564-573.

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

Cogley, A.C., Vincenty, W.G. & Gilles, S.E. 1968. Differential approximation for radiative transfer in a nongrey gas near equilibrium. AIAA J. 6: 551-553.

Crane, L.J. 1970. Flow past a stretching plate. Z. Angew. Math. Phys. 21: 645-655.

El-Aziz, M.A. 2009. Viscous dissipation effect on mixed convection flow of a micropolar fluid over an exponentially stretching sheet. Can. J. Phys. 87: 359-368.

Ganesan, P. & Palani, G. 2004. Finite difference analysis of unsteady natural convection MHD past an inclined plate with variable surface heat and mass flux. Int. J. Heat Mass Transfer 47: 4449-4457.

Ishak, A. 2009a. Mixed convection boundary layer flow over a vertical cylinder with prescribed surface heat flux. J. Phys. A: Math. Theor. 42: 195501.

Ishak, A. 2009b. Mixed convection boundary layer flow over a horizontal plate with thermal radiation. Heat Mass Transfer 46: 147-151.

Ishak, A., Merkin, J.H., Nazar, R. & Pop, I. 2008a. Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux. Z. Angew. Math. Phys. 59: 100-123.

Ishak, A., Nazar, R. & Pop, I. 2008b. Dual solutions in mixed convection flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transfer 51: 1150-1155.

Ishak, A., Nazar, R. & Pop, I. 2009a. Flow and heat transfer characteristics on a moving flat plate in a parallel stream with constant surface heat flux. Heat Mass Transfer 45: 563-567.

Ishak, A., Nazar, R. & Pop, I. 2009b. The effects of transpiration on the flow and heat transfer over a moving permeable surface in a parallel stream. Chem. Eng. J. 148: 63-67.

Magyari, E. & Keller, B. 1999. Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J. Phys. D: Appl. Phys. 32: 577-585.

Partha, M.K., Murthy, P.V.S.N. & Rajasekhar, G.P. 2005. Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface. Heat Mass Transfer 41: 360-366.

Rosseland, S. 1936. Theoretical Astrophysics. New York: Oxford University.

Sajid, M. & Hayat, T. 2008. Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. Int. Comm. Heat Mass Transfer 35: 347-356.

Seddeek, M.A. 2002. Effects of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field in the case of unsteady flow. Int. J. Heat Mass Transfer 45: 931-935.

Siegel, R. & Howell, J.R. 1992. Thermal Radiation: Heat Transfer 3rd ed. Washington DC: Hemisphere.

Sparrow, E.M. & Cess, R.D. 1978. Radiation Heat Transfer. Washington DC: Hemisphere.

 

*Corresponding author, email: anuar_mi@ukm.my

 

 

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