Page 173 - Biosystems Engineering

152 Cha pte r F o u r

were determined: water content in substrate, soil water potential, soil
water diffusivity coefficient in substrate, heat-diffusion coefficient, ther-
mal conductivity of the substrate, heat-transfer coefficient from the
heating pipe to the surrounding substrate, heat-transfer coefficient in
free convection flow (for horizontal surface), mass-transfer coefficient in
free convection flow (for horizontal surface), time, and source function.
In addition, an experiment was carried out in a greenhouse where
pepper was cultivated. The substrate consisted of peat, tree bark, and
pearlstone. The watering system in the soil bed was switched off for the
duration of the experiment. The climatic parameters inside the green-
house (temperature and air humidity) were monitored throughout the
experiment, as well as substrate temperature, moisture, and leaf sur-
face. Additionally, the radiation intensity (sunshine) was measured
inside the greenhouse. Microclimate parameters inside the greenhouse
were measured 1 m above ground level. The comparison between mea-
sured and calculated values revealed considerable convergence. The
RMSE between the analyzed values did not exceed 0.73°C (tempera-
3
ture) and 0.003 m m (moisture content). The tests demonstrated a high
–3
correlation between the predicted values and the measured values, with
coefficients of correlation (R) of 0.94 (temperature) and 0.91 (moisture
content). The observed differences could be due to the adoption of sim-
plified conditions, homogeneity, and isotropy of the studied substrate.
The complexity of the physical phenomenon studied makes it diffi-
cult to offer explicit equations to determine the capacity to be installed in
heated substrates. To overcome such difficulties, Rodriguez et al. (2004)
used experimental techniques combined with appropriate estimation
methods that led to broad-based practical knowledge of that phenome-
non. The parameters on which the proposed solution was based were
defined by variables such as the power of the heating cable to be used or
its depth and spacing. Dimensional analysis was applied because of the
complexity of the energy transfers occurring in the substrate.
The method proposed by the authors combined heat-transfer theory
with data obtained experimentally through dimensional analysis,
and allowed for simple estimation of the parameters that defined the
heating design: depth, spacing, and power per unit length of the elec-
tric cable. A number of variables were required for estimation, among
which were thermal properties of the substrate, ambient temperature,
and substrate temperatures required to grow the relevant crop.
Later, Fernandez et al. (2005a) developed a two-dimensional FEM
model using a general-purpose finite element code (ANSYS) that was
capable of describing the thermal state of substrates heated by electric
cable based on the geometry of the heating system and on the thermal
properties of the substrate and insulator. This model allowed for (1) the
introduction of different properties of compaction and moisture, and
mixture of materials in the modeled substrate, (2) the transient analysis
of the system, showing the two-dimensional distribution of tempera-
tures at each step, and allowing heat-flow assessment, and (3) the use