Page 171 - Biosystems Engineering

150 Cha pte r F o u r

Kurpaska and Slipek (1996) developed a two-dimensional mathe-
matical model of heat and mass exchange in garden subsoil heated by
warm air released through a perforated pipe. The model studied the
simultaneous development of the soil temperature and soil water pro-
files in the heated subsoil. The input data of the model were (1) tem-
perature, water content, and specific heat of ambient and heated air;
(2) initial temperature, water content, porosity, and thermal and
hydraulic parameters of the soil; and (3) diameter and depth of the heat-
ing pipe and heat and mass transfer coefficients of the heating system.
The model was solved by the difference numerical method, and
results were obtained at a given time. The following assumptions
regarding the soil were made: (1) the medium was considered to be
isotropic and homogeneous; (2) the gravitation potential was not con-
sidered in the description of the movement of soil water; and (3) the
temperature gradient between points was not taken into account. In
addition, thermophysical properties and water conductance of the soil
were a function of the physical state of the soil, whereas thermal dif-
fusivity was not dependent on temperature. The experimental valida-
tion of the model revealed reasonable correlation between estimated
and measured data (R > 0.92) for temperature and water content, with
–1
a RMSE of 0.85°C and 0.02 kg·kg , respectively.
Guaraglia and Pousa (1999) proposed an analog electrical model
to estimate heat flow in soils heated by heaters of cylindrical geome-
try embedded in the soil. The analog model was solved using electrical
circuit analysis software by dividing the soil into thin cylindrical layers,
centered in the line that defined the heater. Values of the resistances
and the capacitors were fitted to the values of the soil and the bound-
ary conditions. The last layer was modeled by a pure resistance
through which capacitors discharged, which represented heat flow
into the soil. Temperatures compared well with analytical solutions
and laboratory experimental data.
De la Plaza et al. (1999) developed a model of the thermal perfor-
mance of a substrate heated by an electric cable and applied the
model to a crop of gerbera. The model was used to predict substrate
temperatures and to estimate the energy consumption of the heating
system. The one-dimensional model was solved by a finite-difference
numerical method, and the algorithms were implemented by using
the C programming language.
The input data of the model were grouped into (1) parameters
of the heating system (depth of the substrate and/or other materials
used as heat accumulator, power of the heating system, heating-cable
depth and spacing); (2) soil parameters (textural composition, air-
entry potential, slope of the moisture curve, and saturated volumetric
moisture content); (3) crop parameters (set point temperature and
depth at which it must be controlled); (4) discretization parameters
for the application of the finite-difference method (number of intervals