The effect of buoyancy forces on laminar convection with viscous dissipation in a vertical channel

The interaction of the viscous dissipation effect with the presence of buoyancy forces is investigated for laminar-flow heat transfer in a parallel-plate vertical channel. One of the channel walls is considered as isothermal with a prescribed temperature, while the other wall is considered as insulated. The velocity field is assumed to be parallel. The velocity field, the temperature field and the Nusselt number are obtained by a perturbation series method which employs the ratio between the Grashof number and the Reynolds number as the perturbation parameter. The radius of convergence of the perturbation series is estimated.