In the paper we develop methods for stability analysis and control design for single phase, distributed chemical processes in one spatial dimension. The physical phenomena we model include reaction, diffusion. heat transfer and convection. The approach is motivated by the formalism of non-equilibrium thermodynamics, the energy methods of fluid mechanics and the passivity theory of non-linear control. We provide two distinct contributions. First, we give a tutorial overview of background material an examples to illustrate. Second. we introduce a new approach for stabilization of non-equilibrium, fluid flow systems. Some applications to systems of conservation laws are presented and connected with boundary and inventory control. We also develop an approach to study the classical problem of minimum entropy production in stationary flow.