Numerical methods for optimal control of heat exchangers

Heat exchangers are thermal fluid systems that are basic components in many industrial devices. Heat exchangers are modeled by coupled hyperbolic and parabolic partial differential equations and the structure of these equations depends on the geometry of the heat exchanger. In this paper we consider approximation methods for optimal control of a counter flow heat exchanger. We show the system is well-posed in standard product spaces and develop a numerical scheme based on averaging approximations (AVE scheme). Numerical examples are provided to illustrate the applicability of this scheme to both simulation and optimal control. We also discuss other schemes based on finite elements and suggest future areas of research.