Z. Naturforsch. **68a,** 693 – 700
(2013)

doi:10.5560/ZNA.2013-0047

Stagnation-Point Flow and Heat Transfer Towards a Shrinking Sheet with Suction in an Upper Convected Maxwell Fluid

Yian Yian
Lok^{1},
Anuar
Ishak^{2}, and
Ioan
Pop^{3}

^{1 }Mathematics Section, School of Distance Education, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia

^{2 }School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia

^{3 }Department of Mathematics, Babeş-Bolyai University, R-400048 Cluj-Napoca, Romania

Received October 21, 2012 / revised June 25, 2013 / published online August 21, 2013

A steady two-dimensional boundary-layer flow and heat transfer of an upper convected Maxwell fluid near a stagnation-point of a permeable shrinking sheet is studied numerically. The effects of elasticity, shrinking, and suction parameters on the flow and heat transfer characteristics are investigated. A similarity transformation reduces the governing equations to third-order nonlinear ordinary differential equations which are then solved numerically. For a fixed value of elastic parameter, it is found that dual solutions exist for some values of shrinking and suction parameters. The plotted streamlines show that for upper branch solutions, the effects of shrinking and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag to the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions.

*Key words:* Stagnation-Point Flow; Shrinking Sheet; Maxwell Fluid; Boundary Layer; Suction.