where \(u\), \(v\) are the velocity components in \(x,y\) direction
respectively, \(\rho\) is the viscosity,\(\beta=\mu_{B}\sqrt{2\pi_{c}}/P_{y}\) is the non-Newtonian or Casson
parameter, \(U_{w}=bx\) is the shrinking/stretching velocity for the
sheet with \(b\) being the shrinking/stretching constant, \(b<0\)corresponds to shrinking, \(b>0\) corresponds to stretching and\(U_{\infty}=\text{ax}\) is straining velocity of the stagnation point
flow with \(a(>0)\) being straining constant.
The stream functions \(u=\partial\psi/\partial y\) and\(v=-\partial\psi/\partial x\) satisfies the continuity Eq. (2). In
order to simplify the mathematical analysis of the problem, we introduce
the following similarity variables