Extended ordinary differential equation models for solar heating systems with pipes

There is no doubt on the importance to investigate and develop solar heating systems. Mathematical modeling is the theoretically established tool for this purpose. In this study, improved, validated ordinary differential equation (ODE) models (an extended linear and a nonlinear ones) are proposed for a wide sort of solar heating systems with a solar collector, a heat exchanger, a storage and pipes. The pipes are considered as separated components in the model, so their thermal and delaying effects are taken into account. The advantages of the proposed ODE models, compared to other ODE, partial differential equation and delay differential equation (DDE) 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 ODE models are demonstrated. plicability and the generalizability of the models are also discussed along with future research proposals.