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.