Page 180 - Biosystems Engineering

Models for Heat Transfer in Heated Substrates 159

increases in the power required amount to 4.4 percent for the ana-
lyzed temperatures and geometries.
Generally, the increase in spacing causes an overall decrease in
temperatures that mainly affects the zone between cables near the
substrate surface. For a heating cable buried at a depth of 225 mm, the
largest differences are found for spacings between 100 and 150 mm,
with a decrease of 1.02°C in the value of the average temperature that
mainly affects the surface layer of the substrate (< 75 mm deep). For
larger spacings between cables, between 150 and 350 mm, an increase
of 50 mm in heating-cable spacing causes slight decreases in tempera-
ture, as shown in Fig. 4.7.
The time of operation of the heating cable increases with spacing.
Conversely, energy consumption decreases with increased heating-
cable spacing. By analyzing installations with the heating cable bur-
ied at a depth of 225 mm and at different spacings (100 to 350 mm), it
has been observed that the increase in spacing causes a decrease in
energy consumption, reaching a value of 33.4 percent. The largest dif-
ference in energy consumption is found between spacings of 100 and
150 mm, with a value of 1323 kJ during a 24-h period, whereas the
differences for spacings larger than 150 mm are smaller, with values
in the range 300 to 750 kJ during a 24-h period. Such variations are
represented in Fig. 4.7, where we can clearly observe that the energy
savings induced by the increase in heating-cable spacing cause slight
decreases in temperature at spacings larger than 150 mm.

30 10

Temperature (°C) 20 8 Energy (MJ)

Maximum temperature
10
Average temperature
Minimum temperature
Energy consumption
0 6
100 150 200 250 300 350
Heating-cable spacing (mm)
FIGURE 4.7 Variation in maximum, average, and minimum temperatures in the
root zone and in energy consumed during 24 h by a heating cable buried at a
depth of 225 mm as a function of spacing (Fernandez et al. 2007).