  The mixed convection flow in a plane channel with adiabatic boundaries is
examined. The boundaries have an externally prescribed relative velocity
defining a Couette-like setup for the flow. A stationary flow regime is
maintained with a constant velocity difference between the boundaries,
considered as thermally insulated. The effect of viscous dissipation induces a
heat source in the flow domain and, hence, a temperature gradient. The
nonuniform temperature distribution causes, in turn, a buoyancy force and a
combined forced and free flow regime. Dual mixed convection flows occur for a
given velocity difference. Their structure is analysed where, in general, only
one branch of the dual flows is compatible with the Oberbeck-Boussinesq
approximation, for realistic values of the Gebhart number. A linear stability
analysis of the basic stationary flows with viscous dissipation is carried out.
The stability eigenvalue problem is solved numerically, leading to the
determination of the neutral stability curves and the critical values of the
P\'eclet number, for different Gebhart numbers. An analytical asymptotic
solution in the special case of perturbations with infinite wavelength is also
developed.
