Analytical solution for the laminar wake behind a finite heat/mass sink

This work presents an analytical solution for the steady laminar wake generated by a finite wall segment acting as a sink for heat or mass transfer. The classical Lévêque solution is extended to include the wake region downstream of the active surface by employing Laplace transform methods to couple Dirichlet and Neumann boundary value problems through convolution identities. This yields a unified closed-form expression for the scalar field that reduces to the Lévêque result above the sink and provides a new analytical expression for the wake region. Numerical simulations confirm the analytical solution, with errors decreasing systematically under mesh refinement. The derived expressions enable direct calculation of scalar recovery at any point in the wake, providing essential information for designing segmented systems where wake interference between adjacent active elements must be predicted. The solution also serves as a benchmark for numerical methods solving mixed boundary value problems in convective transport.