Combined free and forced convection flow in a parallel-plate vertical channel is analysed in the fully developed region by taking into account the effect of viscous dissipation. The two boundaries are considered as isothermal and kept either at equal or at different temperatures. The velocity field, the temperature field and the Nusselt numbers are obtained by a perturbation series method which employs a perturbation parameter proportional to the Brinkman number. Dimensionless coefficients which allow the evaluation of the dimensionless mean velocity, of the dimensionless bulk temperature and of the Nusselt numbers are determined.