Two-dimensional slow viscous jet from a semi-infinite block channel is investigated on the basis of the Stokes approximation.
In general, two dimensional Stokes flow can be represented by two complex analytic functions. After introducing a conformal transformation from the upper half plane and the physical plane, we find two analytic functions in the transformed plane. For convienience, we have chosen two functions analytic on the transformed upper half plane, which satisfies the asymptotic conditions, and then constructed rest two analytic functions so as to satisfy the no-slip condition, using the integral formula. The boundary values of the analytic functions are determined by solving Fredholm integral equations of the second kind. We find final solutions from the boundary values by using the Cauchy integral.