Exact solution to the governing PDE of a hot water-to-air finned tube cross-flow heat exchanger

A new dynamic coil model is presented. This model is developed via the exact solution of a previously unsolved partial differential equation that governs the coil dynamics for a step change in water flow rate. This new model is the first step toward developing a future model that can accurately predict the coil dynamics for several varying coil inlet conditions expected to occur under MIMO control. The new model is compared with previously published simplified PDE coil models, which used an approximation to this exact solution, and against actual measured coil dynamics. The new coil model is shown to have superior performance in predicting the actual coil behavior.