AbstractFree convection is considered in a rectangular trench with an assigned temperature distribution at the bottom and radiative vertical walls. Following a domain perturbation technique, the problem reduces to the Stokes' equation. After proving the existence and uniqueness of the solution, from a functional point of view, the stream function is expressed in closed form via a bi‐harmonic series and the shape of the free surface is also given. An application follows in order to show the convergence characteristics of the solution and the flow structur