Sains Malaysiana 47(11)(2018): 2907–2916

http://dx.doi.org/10.17576/jsm-2018-4711-34

 

MHD Stagnation-Point Flow over a Stretching/Shrinking Sheet in a Micropolar Fluid with a Slip Boundary

(Aliran Titik Genangan MHD terhadap Lembaran Meregang/Mengecut dalam Bendalir Mikrokutub dengan Gelinciran Sempadan)

 

SITI KHUZAIMAH SOID¹, ANUAR ISHAK^2* & IOAN POP³

 

¹Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 UiTM Shah Alam, Selangor Darul Ehsan, Malaysia

 

²School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

³Department of Mathematics, Babeș-Bolyai University, 400084 Cluj-Napoca, Romania

 

Received: 15 January 2018/Accepted: 20 July 2018

 

ABSTRACT

The problem of stagnation point flow over a stretching/shrinking sheet immersed in a micropolar fluid is analyzed numerically. The governing partial differential equations are transformed into a system of ordinary (similarity) differential equation and are then solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The effects of various parameters on the velocity and the angular velocity as well as the skin friction coefficient and the couple stress are shown in tables and graphs. The noticeable results are found that the micropolar and the slip parameters decrease the skin friction coefficient and the couple stress in the existence of magnetic field. Dual solutions appear for certain range of the shrinking strength. A stability analysis is performed to determine which one of the solutions is stable. Practical applications include polymer extrusion, where one deals with stretching of plastic sheets and in metallurgy that involves the cooling of continuous strips.

 

Keywords: Micropolar fluid; stability analysis; stagnation point flow; stretching/shrinking

 

ABSTRAK

Masalah aliran titik genangan di atas lembaran meregang/mengecut yang direndam dalam bendalir mikrokutub dianalisis secara berangka. Persamaan menakluk pembezaan separa dijelmakan menjadi sistem persamaan pembezaan biasa (keserupaan) dan kemudian diselesaikan secara berangka menggunakan penyelesai masalah nilai sempadan (bvp4c) dalam perisian Matlab. Kesan pelbagai parameter terhadap profil halaju dan halaju sudut serta pekali geseran kulit dan tegasan kupel ditunjukkan dalam jadual dan graf. Hasil yang ketara didapati bahawa parameter mikrokutub dan gelinciran menurunkan pekali geseran kulit dan tegasan kupel dengan kehadiran medan magnet. Penyelesaian dual diperoleh untuk kekuatan tertentu regangan. Analisis kestabilan dilakukan untuk menentukan penyelesaian mana yang stabil antara dua penyelesaian yang diperoleh ini. Aplikasi praktikal termasuk penyemperitan polimer dengan peregangan lembaran plastik dan metalurgi yang melibatkan penyejukan jalur berterusan.

 

Kata kunci: Aliran titik genangan; analisis kestabilan; bendalir mikrokutub; meregang/mengecut

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*Corresponding author; email: anuar_mi@ukm.edu.my