Sains Malaysiana 40(11)(2011): 1291–1296

Falkner-Skan Solution for Gravity-Driven Film Flow of a Micropolar Fluid

(Penyelesaian Falkner-Skan bagi Aliran Filem Graviti-Terpacu dalam Bendalir Mikrokutub)

Kartini Ahmad

Centre for Foundation Studies, International Islamic University Malaysia, Jalan Universiti,

46350 Petaling Jaya, Selangor, Malaysia

Roslinda Nazar*

Centre for Modelling & Data Analysis, School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia,43600 UKM Bangi

Selangor, Malaysia

Solar Energy Research Institute, Universiti Kebangsaan Malaysia,43600 UKM Bangi

Selangor, Malaysia

Ioan Pop

Faculty of Mathematics

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

Received: 22 February 2010/ Accepted: 23 March 2011

ABSTRACT

In this paper, the steady Falkner-Skan solution for gravity-driven film flow of a micropolar fluid is theoretically investigated. The resulting nonlinear ordinary differential equations are solved numerically using an implicit finite-difference scheme. The results obtained for the skin friction coefficient as well as the velocity and microrotation or angular velocity profiles are shown in table and figures for different values of the material or micropolar parameter K.

Keywords: Boundary layer; Falkner-Skan solution; gravity-driven film flow; micropolar fluid

ABSTRAK

Dalam makalah ini, penyelesaian Falkner-Skan mantap bagi aliran filem graviti-terpacu dalam bendalir mikrokutub dikaji secara teori. Persamaan pembezaan biasa tak linear yang terhasil diselesaikan secara berangka menggunakan skema beza-terhingga tersirat. Keputusan yang diperoleh bagi pekali geseran kulit beserta profil halaju dan profil mikroputaran atau halaju sudut dipersembahkan dalam jadual dan rajah untuk beberapa nilai parameter bahan atau mikrokutub K.

Kata kunci: Aliran filem graviti-terpacu; bendalir mikrokutub; lapisan sempadan; penyelesaian Falkner-Skan

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*Corresponding author; email: rmn@ukm.my