The fully developed laminar mixed convection with viscous dissipation in an inclined channel with prescribed wall temperatures is studied analytically. The mean fluid temperature is assumed as the reference temperature. Two perturbation expansions are considered. In the first, the forced convection with viscous dissipation is assumed as a starting condition and the effects of buoyancy for fixed values of the Brinkman number are studied. In the second, starting from the solution for mixed convection without viscous dissipation, the effects of the Brinkman number for fixed values of the Grashof number are analysed. The different solution methods allow a cross-check of the results. The dimensionless velocity field, the dimensionless temperature field, the dimensionless pressure field, the friction factors and the Nusselt numbers are determined and discussed. The results show that viscous dissipation enhances the effects of buoyancy and vice versa.