Three-dimensional Hiemenz Stagnation-Point Flows

A modification of Hiemenz's two-dimensional outer potential stagnation-point flow of strain rate $a$ is obtained by adding periodic radial and azimuthal velocities of the form $b r \sin 2 \theta$ and $b r \cos 2 \theta$, respectively, where $b$ is a shear rate. This leads to the discovery of a new family of three-dimensional viscous stagnation-point flows depending on the shear-to-strain rate ratio $\gamma = b/a$ that exist over the range $-\infty < \gamma < \infty$ with reflectional symmetry about $\gamma = 0$. Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large-$\gamma$ asymptotic behaviors. Sample similarity profiles are also presented.