New delay differential equation models for heating systems with pipes

There is no doubt on the importance to investigate and develop the efficiency of engineering systems utilizing thermal energy. For this purpose, mathematical modeling is the theoretically established tool to analyze such systems. In this study, new, validated delay differential equation (DDE) models are proposed for rather general heating systems with a heater, pipes and a storage (and optionally a heat exchanger). The flow rate in the pipe, and thus the time delay, can be either time dependent or state dependent. The advantages of the proposed DDE models, compared to the conventional ordinary differential equation (ODE) and partial differential equation (PDE) approaches, are discussed. Based on the comparison of measured and simulated data of a real solar heating system, the validation and the efficiency of the proposed DDE models are demonstrated.Applicability of the models is also discussed along with future research proposals.