Sains Malaysiana 40(10)(2011): 1193–1199

 

MHD Stagnation-Point Flow towards a Stretching Sheet with

Prescribed Surface Heat Flux

(Aliran Titik Genangan MHD terhadap Helaian Meregang dengan Fluks Haba Permukaan Ditetapkan)

 

 

Anuar Ishak* & R. Nazar

School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi

Selangor, Malaysia

 

Norihan M. Arifin & Fadzilah M. Ali

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia

43400 UPM Serdang, Selangor, Malaysia

 

Ioan Pop

Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania

 

Diserahkan: 15 Julai 2010 / Diterima: 6 September 2010

 

 

ABSTRACT

The steady two-dimensional stagnation point flow of an incompressible viscous and electrically conducting fluid, subject to a transverse uniform magnetic field, towards a stretching sheet is investigated. The governing system of partial differential equations are transformed to ordinary differential equations, which are then solved numerically using a finite difference scheme known as the Keller-box method. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. ε>1, and the opposite is observed when ε<1.

 

Keywords: Heat transfer; magnetohydrodynamic; stagnation point flow; stretching surface

 

 

ABSTRAK

Aliran titik genangan mantap dua matra bagi bendalir likat tak termampatkan dan pengkonduksi elektrik terhadap helaian meregang tertakluk kepada medan magnet melintang seragam diselidik. Sistem menakluk persamaan pembezaan separa dijelmakan kepada persamaan pembezaan biasa, yang kemudiannya diselesaikan secara berangka menggunakan skim beza terhingga dikenali sebagai kaedah kotak Keller. Kesan parameter-parameter menakluk terhadap medan aliran dan ciri-ciri pemindahan haba diperoleh dan dibincangkan. Didapati bahawa kadar pemindahan haba pada permukaan meningkat dengan peningkatan parameter magnet apabila halaju aliran bebas melebihi halaju regangan, iaitu ε>1, dan keputusan yang bertentangan diperhatikan apabila ε<1.

 

Kata kunci: Aliran titik genangan; magnetohidrodinamik; pemindahan haba;  permukaan meregang

 

 

RUJUKAN

 

Abbas, Z., Hayat, T., Sajid, M. & Asghar, S. 2008. Unsteady flow of a second grade fluid film over an unsteady stretching sheet. Mathematical and Computer Modelling 48: 518-526.

Abramowitz, M. & Stegun, I.A. 1965. Handbook of Mathematical Functions. New York: Dover.

Andersson, H.I. 1995. An exact solution of the Navier-Stokes equations for magnetohydrodynamic flow. Acta Mechanica 113: 241-244.

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

Char M.I. 1994. Heat transfer in a hydromagnetic flow over a stretching sheet. Heat and Mass Transfer 29: 495-500.

Char, M.I. & Chen, C.K. 1988. Temperature field in non-Newtonian flow over a stretching plate with variable heat flux. International Journal of Heat and Mass Transfer 31: 917-921.

Chen, C.H. 1998. Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat and Mass Transfer 33: 471-476.

Chen, C.K. & Char, M.I. 1988. Heat transfer of a continuous, stretching surface with suction or blowing. Journal of Mathematical Analysis and Applications 135: 568-580.

Chiam T.C. 1997. Magnetohydrodynamic heat transfer over a non-isothermal stretching sheet. Acta Mechanica 122: 169-179.

Crane, L.J. 1970. Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik 21: 645-647.

Dutta, B.K. Roy, P. & Gupta, A.S. 1985. Temperature field in flow over a stretching sheet with uniform heat flux. International Communications in Heat and Mass Transfer 12: 89-94.

Elbashbeshy, E.M.A. 1998. Heat transfer over a stretching surface with variable surface heat flux. Journal of Physics D: Applied Physics 31: 1951-1954.

Grubka, L.J. & Bobba, K.M. 1985. Heat transfer characteristics of a continuous, stretching surface with variable temperature. ASME Journal of Heat Transfer 107: 248-250.

Gupta, P.S. & Gupta, A.S. 1977. Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering 55: 744-746.

Hayat, T., Javed, T. & Abbas, Z. 2009. MHD flow of a micropolar fluid near a stagnation point towards a non-linear stretching surface. Nonlinear Analysis: Real World Applications 10: 1514-1526.

Hayat, T., Javed, T. & Abbas, Z. 2010. Corrigendum to ‘‘MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface’’ [Nonlinear Anal. RWA 10(2009) 1514-1526]. Nonlinear Analysis: Real World Applications 11: 2190.

Ishak, A., Nazar, R. & Pop, I. 2006. Unsteady mixed convection boundary layer flow due to a stretching vertical surface. The Arabian Journal for Science and Engineering 31: 165-182.

Ishak, A., Nazar, R. & Pop, I. 2007. Mixed convection on the stagnation point flow toward a vertical, continuously stretching sheet. ASME Journal of Heat Transfer 129: 1087-1090.

Ishak, A., Nazar, R. & Pop, I. 2008a. Heat transfer over a stretching surface with variable heat flux in micropolar fluids. Physics Letters A 372: 559-561.

Ishak, A., Nazar, R. & Pop, I. 2008b. Heat transfer over an unsteady stretching surface with prescribed heat flux. Canadian Journal of Physics 86: 853-855.

Ishak, A., Nazar, R. & Pop, I. 2008c. Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat and Mass Transfer 44: 921-927.

Ishak, A., Nazar, R. & Pop, I. 2008d. Magnetohydrodynamic (MHD) flow of a micropolar fluid towards a stagnation point on a vertical surface. Computers and Mathematics with Applications 56: 3188-3194.

Ishak, A., Nazar, R. & Pop, I. 2009a. Boundary layer flow and heat transfer over an unsteady stretching vertical surface. Meccanica 44: 369-375.

Ishak, A., Nazar, R. & Pop, I. 2009b. Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature. Nonlinear Analysis: Real World Applications 10: 2909-2913.

Lin, C.R. & Chen, C.K. 1998. Exact solution of heat transfer from a stretching surface with variable heat flux. Heat and Mass Transfer 33: 477-480.

Liu, I.C. 2004. Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to a transverse magnetic field. International Journal of Heat and Mass Transfer 47: 4427-4437.

Liu, I.C. 2005 A note on heat and mass transfer for a hydromagnetic flow over a stretching sheet. International Communications in Heat and Mass Transfer 32: 1075-1084.

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

Pavlov, K.B. 1974. Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika 4: 146-147.

Prasad, K.V., Pal, D. & Datti, P.S. 2009. MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet. Communications in Nonlinear Science and Numerical Simulations 14: 2178-2189.

Wang, C.Y. 1984. The three-dimensional flow due to a stretching surface. Physics of Fluids 27: 1915-1917.

Yacob, N.A. & Ishak, A. 2010. Stagnation-point flow towards a strecthing surface immersed in a micropolar fluid with prescribed surface heat flux. Sains Malaysiana 39: 285-290.

 

 

*Pengarang untuk surat-menyurat; e-mail: anuarishak@yahoo.com

 

 

 

sebelumnya