Sains Malaysiana 40(10)(2011): 1179–1186

MHD Stagnation Point Flow with Suction Towards a Shrinking Sheet

(Aliran Titik Genangan MHD dengan Sedutan terhadap Kepingan yang Mengecut)

Lok Yian Yian*

Mathematics Division, School of Distance Education, Universiti Sains Malaysia

11800 USM, Pulau Pinang, Malaysia

Anuar Ishak

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

Selangor D.E. Malaysia

Ioan Pop

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

Received: 7 July 2010/Accepted: 10 November 2010

ABSTRACT

A steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of a viscous and electrically conducting fluid over a permeable shrinking sheet has been studied. The governing partial differential equations are reduced to the nonlinear ordinary differential equations by a similarity transformation. The resulting differential equations are then solved numerically using an implicit finite difference method. It is found that the solutions are non-unique for weak magnetic field, strong suction and large velocity ratio between free stream velocity and wall shrinking velocity.

Keyword: MHD; shrinking sheet; stagnation point; suction

ABSTRAK

Aliran titik genangan dua matra mantap magnetohidrodinamik (MHD) terhadap kepingan meregang telah dikaji. Persaman pembezaan separa menakluk diturunkan kepada persamaan pembezaan biasa tak linear dengan menggunakan penjelmaan keserupaan. Persamaan pembezaan biasa yang terhasil itu kemudiannya diselesaikan secara berangka menggunakan kaedah beza terhingga tersirat. Didapati bahawa penyelesaian adalah tidak unik untuk medan magnet yang lemah, sedutan yang kuat dan nisbah halaju yang besar antara halaju aliran bebas dengan halaju pengecutan dinding kepingan.

Kata kunci: Lapisan mengecut; MHD; sedutan; titik genan

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*Corresponding author; email: lyianyian@yahoo.com