Page 175 - Biosystems Engineering

154 Cha pte r F o u r

Because the model was originally designed for validation, it was mod-
ified such that it conformed to simulation. Thus, the temperature at all
the nodes was estimated in a new part of the model, a static analysis
was used as the initial condition, and the greenhouse air temperature,
the substrate surface temperature, and the heat flow emitted by the
heating element were used as conditions at each step of the analysis.
Dimensioning expressions obtained from the model allowed for
the estimation of the power per unit length of heating cable required
to achieve a given temperature in the root zone. For that purpose, two
reference points were used, both of them 75 mm deep. The first refer-
ence, which was the most favorable, was located at the vertical of the
heating cable, and the second one was located at an intermediate spac-
ing between cables. Because temperature is generally higher at the
vertical of the heating cable, the power per unit length required at that
point was lower, but the temperature values generated were below
the temperature selected for the reference depth. Such differences in
temperature were quantified to allow for a most suitable design.
The authors used the same environmental conditions and identi-
cal operating conditions to model the performance of heating installa-
tions with different heating-cable spacings (Fernandez et al. 2007).
These experimental conditions allowed for an efficient comparison of
energy efficiency and temperature distribution, which would not be
possible under environmental conditions because of the level of detail
of the model. The simulation allowed the authors to analyze the effect
of heating-cable spacing on temperature distribution in the root zone.
In addition, they obtained data of energy consumption and applied
heat flow use which are the two key factors to consider when choosing
a heating system.

4.6 An Analysis of Electric Cable Heating Systems
A heat exchange process is caused by temperature differences between
the warm area of heating elements and soil particles. This results in a
nonuniform region of temperature within the adjacent soil substrate.
As a result of this temperature gradient, heat flow occurs, soil water
potential changes, and mass transport takes place (Hanks 1992). Con-
sequently, heat and mass exchange occurs in the soil bed, which
increases temperature and decreases water content. We can observe
that the influence of radiation practically disappears at a depth of
0.15 m. The increase in temperature is the result of the influence of
two independent flows of heat affecting the substrate: the flow origi-
nating from heating ducts and sunshine radiation. Reduction in mois-
ture content was caused by three forces driving the entire process:
transpiration, infiltration, and evaporation (Kurpaska et al. 2005).
In unheated substrates, heat flows occur mainly in the vertical
direction, and heat exchange occurs through the substrate surface.