The effect of viscosity in a tracking regulation problem for a counter-flow heat exchanger

In this paper we consider a tracking problem for a counter-flow heat exchanger. Typical models assume that convection dominates so that diffusion can be ignored and the resulting model is defined by a hyperbolic PDE. When the flow velocity becomes small or zero this hyperbolic system becomes degenerate and controllability can be lost. We employ a full flux model, which can be viewed as a parabolic approximation to the hyperbolic equations, to address this issue and illustrate that the full flux model can be used for set point control and tracking even with zero flow.