M.R. Rodríguez

VALIDATION OF TEMPERATURE SIMULATION BASED ON FINITE ELEMENT ANALYSIS IN SUBSTRATES HEATED BY ELECTRIC CABLE

This study presents a two-dimensional model of the thermal behavior of electric cable heating systems for substrates in greenhouses, developed in a transient state by using a general-purpose finite element code. In this model, the thermal properties of substrate can be introduced directly by layers or estimated by methods that allow the determination of the apparent thermal conductivity and the heat capacity per volume depending on other physical properties of the substrate, so that variations can be introduced at different depths. The authors performed a more detailed analysis of the surface layer and assigned a lower value to the moisture content in the top 10 mm. To facilitate the simulation of the different geometries of the heating system and of the boundary conditions, the boundary conditions were parameterized. The model was validated by using an experimental test consisting of nine geometric configurations for substrate electric cable heating using a sand substrate. Temperature was measured at nine locations and moisture content was measured at three locations inside the substrate. The experimental validation was conducted after simulating each geometric configuration of heating during three days, under various environmental and operational conditions. The comparison of the simulated results with experimental data from seven temperature probes at different positions revealed an RMSE of 0.80°C. The RMSE was 0.57°C for the substrate layer between the surface and a depth of 150 mm, which was the zone of greater interest in this study. Because the errors are acceptable, and maximum values occur in zones different from the root development zone, the authors claim that the model can describe the thermal state of heated substrates accurately and can be used as a tool to design and monitor this type of installations.

Root temperature and energy consumption at different cable depths in electrically heated substrates

A finite element method-based model of a substrate heated by an electric heating cable buried in a thermal isolated container was experimentally validated with root mean square error values of root zone temperature ranging 0.25 to 0.62 oC. The two-dimensional transient model allowed variations in the physical properties of the substrate with temperature, water content and depth. The operation of nine configurations of a heating cable buried in sand at different depths (50 to 450 mm, at 50 mm intervals) at 200 mm spacing was simulated and assessed. The validated model was used to perform 24-h simulations applying boundary conditions, and substrate moisture content was experimentally obtained at a mean substrate surface temperature of 13.98 oC. Such simulations reproduced the operation of the heating system by setting a reference temperature of 20 oC at the control point in the root zone. Burying the heating cable in the surface layers of the substrate caused large temperature gradients and high heat losses through the substrate surface. Accordingly, average temperature in the root zone increased with heating cable depth, up to the 200 mm depth. For greater depths, temperature in the root zone was constant. The ON/OFF control was most effective with the heating cable buried in the root zone and at control point temperatures of 20 ± 1 oC. Burying the heating cable in the surface layers required higher energy consumption, up to 28 % at 50 mm. The most efficient heating cable depth was 350 mm, with a daily energy consumption of 6750 kJ m-2.