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Sains Malaysiana 38(4)(2009): 559–565
(Aliran MHD dan Perpindahan Haba Berhampiran Satu Lapisan yang Mengecut dalam Suatu Medium Telap)
Noor Fadiya Mohd Noor
Faculty of Applied Science and Mathematics
Universiti Industri Selangor, 45600 Bestari Jaya, Selangor,Malaysia
Ishak Hashim*
Centre for Modeling & Data Analysis
School of Mathematical Sciences, Universiti Kebangsaan Malaysia
43600 Bangi,
Selangor D.E., Malaysia
Received: 28 April 2008 / Accepted: 25 November 2008
ABSTRACT
The magnetohydrodynamic (MHD) boundary-layer flow and heat transfer due to a shrinking sheet in a
porous medium is considered for the first time. The Navier-Stokes
equations and the heat equation are reduced to two nonlinear ordinary
differential equations via similarity transformations. The transformed
equations are solved by a semi-analytic method. The effects of the suction and
porosity parameters, the Prandtl and Hartmann numbers
on the skin friction, heat transfer rate, velocity and
temperature profiles are discussed and presented, respectively.
Keyword:
Boundary-layer; heat transfer; MHD; porous medium; shrinking sheet
ABSTRAK
Aliran lapisan sempadan magnetohidrodinamik (MHD) dan perpindahan haba dari lapisan yang mengecut dalam satu medium telap dipertimbangkan untuk pertama kali. Persamaan Navier-Stokes dan persamaan haba dipermudahkan menjadi dua persamaan pembezaan biasa tak linear melalui penjelmaan keserupaan. Persamaan yang terjelmakan itu diselesaikan dengan kaedah separa-analisis. Kesan parameter sedutan dan keliangan, nombor Prandtl dan Hartmann terhadap pekali geseran kulit, pekali pemindahan haba, profil halaju dan suhu dibincang dan ditunjukkan.
ata kunci: Lapisan sempadan; lapisan mengecut; MHD; medium telap; perpindahan haba
REFERENCES
Adomian, G. 1994. Solving Frontier Problems of Physics: The Decomposition Method. Dordrecht: Kluwer Academic.
Ariel, P.D., Hayat, T. & Asghar, S. 2006. Homotopy perturbation method and axisymmetric flow over a
stretching sheet. Int. J. Nonlin. Sci. Numer. Simul. 7: 399-406.
Awang Kechil, S. & Hashim, I.
2007. Series solution for unsteady boundary-layer flows due to impulsively stretching
plate. Chin. Phys. Lett. 24(1): 139-142.
Awang Kechil, S., Hashim, I.
& Jiet, S.S. 2007. Approximate
analytical solutions for a class of laminar boundary-layer equations. Chin.
Phys. Lett. 24(7): 1981-1984.
Awang Kechil, S. & Hashim, I.
2008. Non-perturbative solution of
free-convection boundary-layer equation by Adomian decomposition method. Phys. Lett. A 363: 110-114.
Awang Kechil, S. & Hashim, I.
2008. Series solution of flow over nonlinearly stretching sheet
with chemical reaction and magnetic field. Phys. Lett.
A 372: 2258-2263.
Awang Kechil, S. & Hashim, I.
2008. Series solutions of boundary-layer flows in porous media with
lateral mass flux. Heat Mass Transfer 44(10): 1179-1186.
Ayub,
M., Zaman, H., Sajid, M.
& Hayat, T. 2008. Analytical solution of stagnation-point flow of a viscoelastic fluid towards a stretching surface. Commun. Nonlin. Sci. Numer. Simul. 13: 1822-1835.
Boyd, J.P. 1997. Padé approximant algorithm for
solving nonlinear ordinary differential equation boundary value problems on an
unbounded domain. Comput. Phys. 11: 299-303.
Cortell, R. 2005. Flow
and heat transfer of a fluid through a porous medium over a stretching surface
with internal heat generation/absorption and suction/blowing. Fluid Dyn. Res. 37:
231-245.
Cortell, R. 2007. MHD flow and mass transfer of an electrically conducting fluid of
second grade in a porous medium over a stretching sheet with chemically
reactive species. Chem. Eng. Process. 46: 721-728.
Crane, L.J. 1970. Flow past a stretching
plate. ZAMP 21: 645- 647.
Gupta, P.S. &
Gupta, A.S. 1977. Heat and mass transfer on a
stretching sheet with suction and blowing. Can. J. Chem. Eng. 55:
744-746.
Hashim, I. 2006. Comments on “A new algorithm for solving classical Blasius equation” by L. Wang. Appl. Math. Comput. 176: 700-703.
Hayat,
T. & Javed, T. 2007. On analytic
solution for generalized three-dimensional MHD flow over a porous stretching
sheet. Phys. Lett. A 370: 243-250.
Hayat,
T., Abbas, Z. & Javed,
T. 2008. Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet. Phys. Lett.
A 372: 637-647.
Hayat,
T., Abbas, Z., Javed, T.
& Sajid, M. 2007. Three- dimensional rotating flow induced by a
shrinking sheet for suction. Chaos Solitons Fractals 39: 1615-1626.
Ishak,
A., Nazar, R. & Pop, I. 2008. Hydromagnetic flow and heat transfer adjacent to a
stretching vertical sheet. Heat Mass Transfer 44(8): 921-927.
Miklavcic,
M. & Wang, C.Y. 2006. Viscous flow due to a shrinking
sheet. Quart. Appl. Math. 64:283-290.
Sajid,
M., Javed, T. & Hayat,
T. 2008. MHD rotating flow of a viscous fluid over a shrinking
surface. Nonlin. Dyn. 51: 259-265.
Sajid,
M. & Hayat, T. 2007. The application of homotopy analysis
method for MHD viscous flow due to a shrinking sheet. Chaos Solitons Fractals 39: 1317-1323.
Wang, C.Y. 1984. The three dimensional flow
due to a stretching flat surface. Phys. Fluids 27: 1915-1917.
Wang, C.Y. 1990. Liquid
film on an unsteady stretching sheet. Quart. Appl. Math. 48: 601-610.
Wang, C.Y. 2008. Stagnation flow towards a shrinking sheet. Int. J.
Non-linear Mech. 43: 377-382.
Xu,
H., Liao, S.J. & Pop, I. 2007. Series solutions of unsteady
three-dimensional MHD flow and heat transfer in the boundary layer over an
impulsively stretching plate. Eur. J. Mech. B/Fluids 26: 15-27.
Yahaya,
F., Hashim, I., Ismail, E.S. & Zulkifle, A.K. 2007. Direct solutions of nth-order
initial value problems in decomposition series. Int. J. Nonlin. Sci. Numer. Simul. 8: 385-397.
Zhu, Y., Chang, Q. & Wu, S. 2005. A new algorithm for calculating Adomian polynomials. Appl. Math. Comput. 169: 402-416.
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