Chemistry Reference
In-Depth Information
The equation is valid for the temperature range 40
<<
908C and the %TS
range 37
<
TS
<
72%.
The equations so far mentioned for predicting the thermal conductivity
of milk products are semi-empirical (Equations 63 and 65) or empirical.
Fern´ ndez-Martin and Montes (1977) attempted to take a fundamental
approach. They compared their experimentally determined thermal conduc-
tivities of creams with nine different theoretical equations for predicting the
thermal conductivity of two-phase systems in which the dispersed phase
consists of spherical particles. Agreement between experimental and pre-
dicted values was good for
fat
<
0.2 for all but one of the theoretical models.
Agreement was more variable for
fat
>
0.2. Fern´ ndez-Martin and Montes
(1977) chose one of the theoretical equations and, by using their data and
suitable regression methods, adjusted its constants to yield the following
semi-empirical relationship:
l
¼ð
0
:
5279
þ
0
:
0021
0
:
00000732
2
Þð
1
ð
0
:
843
þ
0
:
0019
Þ
fat
Þ
ð
Wm
1
K
1
Þ
(66)
This equation, which is valid for fat contents in the range 20
<
F
<
40% and
the temperature range 5
<<
758C, fitted the experimental data to within
10%. It is not dissimilar to Equation 63. When
fat
¼
0, Equation 66 reduces
to the empirical quadratic equation relating the thermal conductivity of skim
milk to temperature that was developed by Fern´ ndez-Martin and Montes
(1972).
15.9.3.
Thermal Diffusivity
The property thermal diffusivity is the ratio of thermal conductivity to
volumetric specific heat. It is defined by the equation
¼
l
c
(67)
where
is thermal diffusivity (m
2
s
1
), l is thermal conductivity (W m
1
K
1
),
is density (kg m
3
), c is specific heat capacity (J kg
1
K
1
) and
c is
volumetric specific heat (J m
3
K
1
). The thermal diffusivity of a material is a
measure of the rate of temperature propagation that occurs in the material
during unsteady state heating or cooling; it is a measure of the ability of the
material to dissipate temperature gradients within itself.
Kostaropoulos et al. (1975) gave the following representative values of
the thermal diffusivity of fluid milk products:
