Asymptotics of a solution of the second boundary value problem for the Laplace equation outside a small neighborhood of a segment

We construct and validate an asymptotic expansion of a solution of the exterior Neumann problem for the Laplace equation outside a small neighborhood of a segment. The width of the neighborhood is characterized by a small parameter. A physical interpretation of the solution is the two-dimensional velocity potential of an ideal fluid in the case of a laminar flow across a thin body.