Modelling the Transient Thermal Behaviour of Sand Substrate heated by Electric Cables

The development of optimal control strategies in greenhouses requires precise models of energy transfer. A flexible model that enables the introduction of different substrate parameters and boundary conditions was developed for electric cable heating installations. The model is based on finite element analysis and is implemented by using a commercial code, which provides the two-dimensional description of the thermal state of heated greenhouse substrates. The model presented includes methods for the estimation of apparent thermal conductivity and methods for the estimation of heat capacity per volume given other physical properties of the substrate. The model allows for the variations of moisture and compaction in different substrate layers. The final model is compared with the experimental data obtained from an electric cable heating installation applied to a bench. Temperature data was measured at six locations of the substrate volume. A root mean square error (RMSE) of 0·56 °C was obtained after implementation during a 3-day simulation. This model can be used to monitor and evaluate substrate heating systems.