Sains Malaysiana 39(2)(2010): 285–290

 

Aliran Titik Genangan Terhadap Permukaan Meregang dalam Bendalir Mikropolar dengan Fluks Haba Permukaan Boleh Ubah

(Stagnation-point Flow towards a Strecthing Surface Immersed in a  Micropolar Fluid with Prescribed Surface Heat Flux)

 

 

Nor Azizah M. Yacob

Fakulti Sains Komputer dan Matematik, Universiti Teknologi Mara, Pahang

Lintasan Semarak, 26400, Bandar Jengka, Pahang, D.M., Malaysia

 

Anuar Mohd Ishak*

Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi

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

 

Diserahkan: 15 Mei 2009 / Diterima: 26 Ogos 2009

 

ABSTRAK

 

Aliran lapisan sempadan mantap dua matra bersebelahan titik genangan pada permukaan meregang dalam bendalir mikropolar dengan fluks haba permukaan boleh ubah dikaji. Halaju regangan dan halaju aliran bebas diandaikan berubah secara linear dari titik genangan. Persamaan dalam bentuk persamaan pembezaan separa dijelmakan kepada persamaan pembezaan biasa menggunakan penjelmaan keserupaan dan diselesaikan secara berangka menggunakan skim beza-terhingga yang dikenali sebagai kaedah kotak Keller. Kedua-dua aliran membantu dan aliran menentang dipertimbangkan. Lapisan sempadan terbentuk apabila halaju aliran bebas melebihi halaju regangan, sebaliknya, lapisan sempadan yang terbalik terbentuk apabila halaju aliran bebas kurang daripada halaju regangan. Keputusan berangka menunjukkan bahawa daya seretan berkurangan bagi bendalir mikropolar berbanding dengan bendalir Newtonan, dan ini seterusnya mengurangkan kadar pemindahan haba pada permukaan.

 

Kata kunci: Bendalir mikropolar; lapisan sempadan; regangan permukaan; titik genangan

 

                                                              ABSTRACT          

 

The steady two dimensional boundary layer flow adjacent to the stagnation point on a stretching surface immersed in a micropolar fluid was investigated. The stretching and the free stream velocities were assumed to vary linearly from the stagnation point. The governing partial differential equations were transformed into ordinary differential equations before being solved numerically by a finite-difference scheme known as the Keller box method. Both assisting and opposing flows were considered. The boundary layer was formed when the free stream velocity exceeds the stretching velocity, whereas the inverted boundary layer was formed when the free stream velocity is less than the stretching velocity. The numerical results showed that the shear force decreased for micropolar fluid compared to Newtonian fluid, and in consequence decreased the heat transfer rate at the surface.

 

Keywords: Boundary layer; micropolar fluid; stagnation point; stretching surface

 

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*Pengarang untuk surat-menyurat; email: anuar_mi@ukm.my