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
Diserahkan:
9 Disember 2009 / Diserahkan: 21 Jun 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
RUJUKAN
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.
*Pengarang untuk
surat-menyurat, email: anuar_mi@ukm.my
|