A boundary-layer analysis is presented for the mixed convection flow which is produced when a horizontal line heat source, which is embedded in an infinite fluid-saturated porous medium, generates heat at a constant rate. It is shown that the governing equations can be non-dimensionalized so that they do not involve any parameters and thus just one solution of the transformed boundary-layer equations is required. Series solutions which are valid both near the line source and far downstream are obtained and compared with the numerical solution of the full boundary-layer equations.