Page 172 - Biosystems Engineering

Models for Heat Transfer in Heated Substrates 151

into which the soil was divided for analysis); and (5) environmental
parameters (initial temperatures at all depths, temperature at the
substrate surface, and temperature of the heating cable during the
analysis).
The model correctly simulated variations in substrate tempera-
ture and heat accumulator (sand or heatresistant brick) at different
depths, both in summer, when the heating system was off, and in
winter, when the localized substrate heating was switched on. The
RMSE ranged from 0.44ºC to 0.54ºC. The model that accurately simu-
lated the heating-cable operation predicted the energy consumption
associated with the different localized heating configurations with an
average error less than ±7 percent.
In the experimental installation, use of thermal insulation and heat
accumulators produced energy savings in the range of 14 to 20 percent.
The best configuration in terms of energy conservation was the
configuration with the heating cable buried at 0.20 m, with thermal
insulation and heat-resistant brick placed under the heating cable as a
heat accumulator. The combination of thermal insulation and energy
consumption only during the night reduced costs by 27 percent.
Kurpaska and Slipek (2000) developed a method for optimizing
greenhouse substrate-heating systems with warm-water buried pipes.
The method was based on steady-state heat transfer in soils and used
numerical solutions to solve the two-dimensional Fourier equation in
a portion of the soil in which the heating pipe was embedded.
To optimize heating system design, the authors developed two
quality criteria that accounted for the thermal losses below the depth of
the plant root system, and for temperature variations in the studied
section. The quality criteria developed corresponded to the components
of the function to be minimized, which was then used to find the optimum
solutions under the experimental conditions. The optimization method
considered the physical properties of soil, the characteristics of the crop,
and the thermal and hydraulic characteristics of the greenhouse.
Kurpaska et al. (2005) presented a mathematical model of the
greenhouse substrate-heating process, which occurs when tubes are
positioned in the substrate. The two processes that take place during
substrate warming, heat exchange, and mass exchange (soil water),
together with cultivated plants that were heated by hot-water piping,
were considered in the model. The model included the processes of
transpiration, evaporation, and infiltration. Standard diffusion equa-
tions for the capillary–porous structure, and standard thermal and
hydrophysical characteristics were used to describe the phenomena
occurring in the substrate. Equations were solved numerically by a
differential method. The parameters of the model (thermal and hydro-
physical characteristics) were determined by laboratory methods,whereas
heat and mass transport coefficients were calculated using correlation
equations used in chemical engineering. The following parameters