Geometric optimization of cross-flow heat exchanger based on dynamic controllability

The operation of heat exchangers and other thermal equipments in the face of variable loads is usually controlled by manipulating inlet fluid temperatures or mass flow rates, where the controlled variable is usually one of the output temperatures. The aim of this work is to optimize the geometry of a tube with internal flow of water and an external cross-flow of air, based on its controllability characteristics. Controllability is a useful concept both from theoretical and practical perspective since it tells us if a particular output can be controlled by a particular input. This concept can also provide us with information about the easiest operating condition to control a particular output. A transient model of a tube in cross-flow is developed, where an implicit formulation is used for transient numerical solutions. The aspect ratio of the tube is optimized, subject to volume constraints, based on the optimum operation in terms of controllability. The reported optimized aspect ratio, water mass flow rate and controllability are studied for deferent external properties of the tube