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A theoretical solution is obtained to an outher Neumann problem coupled through boundary conditions with an inner Dirichlet problem in a circular region. Exterior Neumann problem is defined with Laplace equation and interior Dirichlet problem is defined with coupled advection-diffusion equations. Unique solution of advection-diffusion problem is obtained inside the region by using fundamental solutions and Divergence theorem. Exterior solution is given with Poisson's integral formula with an additive constant which is obtained from the solvability condition. The two solutions are also coupled with the boundary coditions on the circle. The theoretical part of the solution results in solving a system of coupled integral equations on the boundary. The collocation method is made use of to obtain a linear system of equations for the discretized solution of the problem.