UDC 532.5

M. Sajid1, N. Ali2, Z. Abbas2, 
T. Javed2, and M. Imran3

SOME TWO-DIMENSIONAL FLOWS WITH COUPLE STRESSES

The effect of couple stresses on some two-dimensional 
flows is considered. The numerical solutions are obtained by the shooting 
method using the Runge-Kutta algorithm in the four flow problems 
for a couple stress fluid, namely, for the Blasius, Sakiadis, stretching, 
and stagnation-point flows. The obtained solutions are nonsimilar 
for the Blasius and Sakiadis flows. The results are interpreted concerning 
the influence of the couple stress parameter which is a measure of 
the polarity of a fluid. It is shown that for large values of this 
parameter the solution converges to the solution for a Newtonian fluid.

Keywords: two-dimensional flow, couple stresses, Blasius 
flow, Sakiadis flow, stretching flow, stagnation-point flow, numerical 
solution.

1Theoretical Plasma Physics Division, PINSTECH, P.O. 
Nilore, Islamabad 44000, Pakistan; email: sajidqau2002@yahoo.com; 
2Department of Mathematics, Faculty of Basic and Applied Sciences, 
International Islamic University, Islamabad 44000; 3Pakistan 
Department of Mathematics, Lahore University of Management Science 
(LUMS), Lahore, Pakistan. Original article submitted May 27, 2011.