Sains Malaysiana 40(12)(2011): 1369–1374

Heat Transfer at a Stretching/Shrinking Surface Beneath an External Uniform Shear Flow with a Convective Boundary Condition

(Pemindahan Haba Pada Permukaan Meregang/Mengecut di bawah Aliran Ricih Luar yang Seragam dengan Syarat Sempadan Berolak)

Fazlina Aman

Faculty of Science, Arts and Heritage, Universiti Tun Hussein Onn Malaysia

86400 Parit Raja, Batu Pahat, Johor, Malaysia

Anuar Ishak

School of Mathematical Sciences, Faculty of Science and Technology, 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: 21 December 2010 / Accepted: 7 February 2011

ABSTRACT

The heat transfer behaviour of a viscous fluid over a stretching/shrinking sheet driven by a uniform shear in the far field with a convective surface boundary condition is studied. The boundary layer equations governing the flow are reduced to ordinary differential equations using a similarity transformation. Using a numerical technique, these equations are then solved to obtain the temperature distributions and the heat transfer rate at the surface for various values of Prandtl number, stretching/shrinking parameter and convective parameter. Dual solutions are found to exist for the shrinking case, whereas for the stretching case, the solution is unique.

Keywords: Convective boundary condition; dual solutions; heat transfer; shear flow; stretching/shrinking sheet

ABSTRAK

Tingkah laku pemindahan haba bagi bendalir likat di atas helaian meregang/mengecut dipandu oleh aliran ricih seragam dengan syarat sempadan permukaan berolak dikaji. Persamaan-persamaan lapisan sempadan yang menakluk aliran diturunkan kepada persamaan-persamaan pembezaan biasa menggunakan penjelmaan keserupaan. Menggunakan kaedah berangka, persamaan-persamaan tersebut kemudian diselesaikan untuk memperoleh taburan suhu dan kadar pemindahan haba pada permukaan bagi pelbagai nilai nombor Prandtl, parameter meregang/mengecut dan parameter olakan. Penyelesaian dual didapati wujud bagi kes mengecut, manakala bagi kes meregang, penyelesaian adalah unik.

Kata kunci: Aliran ricih; helaian meregang/mengecut; pemindahan haba; penyelesaian dual; syarat sempadan berolak

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*Corresponding author; email: popm.ioan@yahoo.co.uk