Extended ordinary differential equation models for solar heating systems with pipes

• Extended ordinary differential equation models are proposed for solar heating systems.
• The models take into account pipe effects.
• Validation and efficiency of the models are demonstrated based on measured data.
• The advantages of the models are discussed compared to conventional models.
• Generalizability and applicability of the models are discussed.

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.The applicability and the generalizability of the models are also discussed along with future research proposals.