Optimal Control for Partial Differential Equations of a Heat Exchanger System

Our work is devoted to optimal control of a double-pipe heat exchanger system modeled as coupled hyperbolic partial differential equations (PDEs) of first order in time and space based on adjoint method-calculus of variations, which should be associated with numerical techniques to get solutions. A gradient descent algorithm, which is proved to be convergent after few iterations, is applied to solve the optimal control problem of this heat exchanger (HE) system. Based on the real data in a system, the simulation results demonstrate the effectiveness of the proposed control approach to control the temperatures along the pipes of the HE system, and that the safety of both system and performance is ensured. From these results, we concluded that the gradient descent algorithm is convergent and the method is effective in the optimal control problem of coupled hyperbolic PDEs.

I. Introduction

The double-pipe heat exchanger is a device used to perform the process of mixing fluids having different temperatures, which is very common in the industries of oil refinery and food and an important component in many installations types like heating, air conditioning, and steam power labs. The high effectiveness of the counter-flow heat exchanger makes it one of the most popular types of this device [1] . Besides that, the double-pipe heat exchanger, which is very suited for high pressure and temperature applications and low flow rates, can be used in the applications of small heat transfer surface because of its small amount of heat transfer per section [2] .