In this paper, we consider the 2D second grade fluid past an obstacle
satisfying the standard non-slip boundary condition at the surface of the
obstacle. Second grade fluid model is a well-known non-Newtonian model, with
two parameters: α representing length-scale, while ν>0
corresponding to viscosity. We prove that, under the constraint condition ν=o(α34​), the second grade fluid with a suitable initial
velocity converges to the Euler fluid as α tends to zero. Moreover, we
estimate the convergence rate of the solution of second grade fluid equations
to the one of Euler fluid equations as ν and α approach zero