The flow due to the presence of a solid surface at  in planar stagnation-point flow was described first by Karl Hiemenz in 1911, whose numerical computations for the solutions were improved later by Leslie Howarth. A familiar example where Hiemenz flow is applicable is the forward stagnation line that occurs in the flow over a circular cylinder.
The solid surface lies on the . According to potential flow theory, the fluid motion described in terms of the stream function  and the velocity components  are given by
The stagnation line for this flow is . The velocity component  is non-zero on the solid surface indicating that the above velocity field do not satisfy no-slip boundary condition on the wall. To find the velocity components that satisfy the no-slip boundary condition, one assumes the following form 
where  is the Kinematic viscosity and  is the characteristic thickness where viscous effects are significant. The existence of constant value for the viscous effects thickness is due to the competing balance between the fluid convection that is directed towards the solid surface and viscous diffusion that is directed away from the surface. Thus the vorticity produced at the solid surface is able to diffuse only to distances of order ; analogous situations that resembles this behavior occurs in asymptotic suction profile and von Kármán swirling flow. The velocity components, pressure and Navier–Stokes equations then become
The requirements that  at  and that  as  translate to 
The condition for  as  cannot be prescribed and is obtained as a part of the solution. The problem formulated here is a special case of Falkner-Skan boundary layer. The solution can be obtained from numerical integrations and is shown in the figure. The asymptotic behaviors for large  are
where  is the displacement thickness.