Sains Malaysiana 43(3)(2014): 491–496

Flow and Heat Transfer of a Power-Law Fluid over a Permeable Shrinking Sheet

(Aliran dan Pemindahan Haba bagi Bendalir Hukum-Kuasa di Atas Lembaran Telap yang Mengecut)

NOR AZIZAH YACOB¹& ANUAR ISHAK²*

¹Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Pahang

26400 Bandar Tun Razak Jengka, Pahang, Malaysia

²School of Mathematical Sciences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

Received: 24 August 2012/Accepted: 8 June 2013

ABSTRACT

The steady, two-dimensional laminar flow of a power-law fluid over a permeable shrinking sheet of constant surface temperature is investigated. The governing partial differential equations were transformed into a system of nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by the Runge-Kutta-Fehlberg method with shooting technique. The results are presented graphically and the effects of the power-law index n, suction parameter fw and Prandtl number Pr were discussed. It was found that stronger suction is necessary for the solution to exist for a pseudoplastic fluid (n<1) compared to a dilatant fluid (n>1).

Keywords: Boundary layer; heat transfer; power-law fluid; shrinking sheet

ABSTRAK

Aliran lamina mantap dua matra bendalir hukum-kuasa di atas lembaran telap dengan suhu permukaan malar yang mengecut dikaji. Persamaan pembezaan separa dijelmakan menjadi satu sistem persamaan pembezaan biasa tak linear menggunakan penjelmaan keserupaan, sebelum diselesaikan secara berangka menggunakan kaedah Runge-Kutta-Fehlberg dengan teknik tembakan. Keputusan dibentangkan secara grafik dan kesan indeks hukum-kuasa n, parameter sedutan fw dan nombor Prandtl Pr dibincangkan. Didapati bahawa sedutan yang kuat adalah perlu supaya penyelesaian wujud bagi bendalir pseudoplastik (n<1) berbanding dengan bendalir dilatan (n>1).

Kata kunci: Bendalir hukum-kuasa; lapisan sempadan; lembaran mengecut; pemindahan haba

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*Corresponding author; email: anuar_mi@ukm.my