- Email: [email protected]
Cost 90 collaborative measurements of thermal properties of foods
Journal of Food Engineering
3 (1984)
117-l 50
Cost 90 Collaborative Measurements Properties of Foods
of Thermal
M. Kent,* K. Christiansen,t I.A. van Haneghem,“” E. Holtz,$ M.J. Morley,*** P. Nesvadba,* and K.P. Paulsen? * Torry Research Station, 135 Abbey Road, Aberdeen AB9 8DG, UK t The Technical University of Denmark, Lyngby, Denmark ** Department of Physics and Meteorology, Agricultural University, Wageningen, The Netherlands $ Division of Food Engineering, Lund University, Alnarp, Sweden *** Meat Research Institute, Langford, Bristol, UK
ABSTRl
CT
Collaborative measurements of the thermal properties of foods and model foods are reported. They were part of a European Cooperation in Science and Technology (COST) project and provide data on thermal difbsivity and thermal conductivity of fish paste, meat paste, yoghurt, milk powder, apple pulp. ‘Model’ foods also examined were various mixtures of carrageenan, sugar and water and a monodisperse ‘powder’ of glass beads. Dependence of the measured properties on temperature, density and composition was also examined.
1. INTRODUCTION The decision in 1978 by the Council of the European Communities to support a coordinated programme on the physical properties of foodstuffs, COST 90 (Cooperation in Science and Technology: Project 90, Physical Properties of Foods) led, through the differentiation of the project into subgroups (thermal properties, water activity, rheology), to a working party investigating the experimental collection of thermal properties data both of food materials and substances described as ‘model’ foods or reference materials. Preliminary results of this collaborative exercise were reported by Ohlsson (1983) at the final seminar 117 Journal of Food Engineering 0260-8774/84/$03.00 - @ Elsevier Applied Publishers Ltd, England, 1984. Printed in Great Britain
Science
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of the Project in Leuven. However, these results were limited in scope: only four laboratories took part, diffusivity alone was studied and only two reference materials were measured. One of these materials was in any case found by the participants to be extremely difficult to prepare and handle. With the end of COST 90 a new project COST 90 bis was begun with different physical properties to examine. However, it was felt worthwhile and necessary to conclude the collaborative work on thermal properties with one more laboratory taking part and with real food materials being measured. In addition it was hoped that the data so acquired would enable the precision of various predictive models to be gauged. The objectives were therefore as follows: 1. To compare different methods of measuring thermal conductivity and diffusivity in different laboratories using reference materials. 2. To comment on the usefulness of reference materials for calibration purposes. 3. To establish precision of measurement of each method from within-laboratory variances and between-laboratory variances. 4. To measure various food materials of different types and present the data for comparison with prediction from the known compositional data.
2. DESCRIPTION
OF METHODS
2.1. Method classification Each laboratory had developed, over recent years, its own apparatus for thermal property measurements. In most cases these were based on well-known published methods all of which have been reviewed and classified recently by Nesvadba (I 982~). Accordingly the description of each technique is preceded by a classification in the terms used by Nesvadba. Of five laboratories, three used methods based on the heated probe with cylindrical symmetry. The other two used methods with symmetry about a central plane (rectangular block samples). All were transient methods.
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2.2. Laboratory 1 (direct use of temperature profiles to identify thermal properties)
Conductivity and diffusivity were measured simultaneously in the following manner. The sample, in the form of a block 200 X 170 X 60 mm, was insulated on its four minor surfaces with the two major surfaces in contact with metal heat exchangers (Fig. 1). The temperatures of these two heat exchangers were approximately the same and could be varied between - 50°C and + 60°C to generate approximately symmetrical transient temperature profiles across the sample (x direction). These profiles were measured using a specially constructed probe embedded in the sample consisting of 20 thermocouples bonded to and supported by a thin plastic strip 60 mm wide. The spacing between the thermocouple junctions was 2.54 mm. The heat flux at one of the major surfaces (at x = xb = 0) was measured by a calibrated sensor of the ThCry type (ThCry and MarCchal, 1980). The temperatures and the heat flow data were logged at 60 s intervals and processed off-line by a digital computer.
b
b Fig. 1. Laboratory 1: apparatus for thermal conductivity and thermal diffusivity determination, generating and measuring temperature profiles and heat flux. (a) Flow of hot or cold ethanol; (b) aluminium heat exchanger;(c) ‘Tufnol’ frame; (d) thermal insulation around sample; (e) sample; (f) thermocouple junctions; (g) plastic strip supporting thermocouples; (h) cable to data logger; (i) heat flux sensor.
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The thermal conductivity X was temperature, Tb, from the Fourier law
h(Tb)=-q
computed
dT
I I a;
_
for
each
boundary
(1)
x-xb
where CJ is the heat flux and aT/ax is the temperature gradient in the sample obtained by differentiation of a least-squares parabola fitted to part of the temperature profile. The thermal diffusivity, a, was computed at each temperature T, of the maxima or minima of the temperature profiles (occurring at x = x, ‘v 30 mm) using the expression (Nesvadba, 1982b) a(T,l =
aT/at
a27yax2
x=xe
(2)
in which the derivatives with respect to time, t, and coordinate, x, were evaluated from least-squares cubic splines fitted to the temperature data.
2.3.
Laboratory
2 (heated probe method)
A needle shaped probe was used consisting of 0.1 mm thick doubly folded constantan heating wire and a 0.1 mm thick manganin-constantan thermocouple junction fitted into a stainless steel envelope. In order to fix the position of the heating wire and the thermocouple the remaining space in the envelope was filled with silicone rubber. The overall diameter of the probe was 1 mm and its length was 2 10 mm. This probe was immersed in the material to be examined contained within a cylinder 120 mm in diameter and 240 mm long. A reference element of identical dimensions to the probe but only consisting of the cold junction of the thermocouple was similarly immersed in the sample material in a second identical cylinder. Both cylinders were placed in a constant temperature bath and equilibrated to the same temperature. During the measuring time of several minutes in which heat was generated in the probe by a d.c. current, the temperature was logged every second. The whole apparatus is shown diagrammatically in Fig. 2. Depending on the thermal properties of the sample (thermal conductivity X and volumetric heat capacity pc) there is a slower or faster heat transport through the medium, resulting in a faster or slower rate of
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‘e
Fig. 2.
Laboratory 2 (heated probe method). (a) Thermocouple hot junction; (b) heater; (c) probe; (d) cylinder with sample; (e) temperature-controlled bath; (f) digital voltmeters; (g) precision resistance; (h) direct current source; (i) timer; (j) thermocouple cold junction; (k) computer; (1) amplifier; (m) switch to start measurement.
temperature rise of the probe. The contact resistance r between the probe and the sample must also be considered. For the calculation of X and pc a model is used in which the probe is seen as a compound cylinder system consisting of three coaxial cylinders: the heating wire, the insulating material and the tube of the probe. Between the probe and the sample a contact resistance is assumed as
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mentioned temperature
above. For sufficiently large values of the rise 8 (r) of the probe can be written as
time
C, the
(3) where the coefficients A, B, D and E depend on the dimensions and the thermal properties of the probe, the thermal properties of the sample and the contact resistance. From an accurate mathematical analysis of the measured 8 versus t curve the coefficients A, B, D and E can be determined and hence values for h, pc and F (van Haneghem, 1981; Bruijn et aE., 1982; van Haneghem et al., 1982).
2.4.
Laboratory 3 (heated probe method)
Measurements of thermal conductivity X and diffusivity a, were carried out simultaneously with a heated probe method (Morley, 1966). The dimensions of the probe were approximately: length 150 mm, diameter 1 mm. As can be seen from Fig. 3 it was substantially the same construction as for Laboratory 2 the major difference being in the filling material - epoxy resin instead of silicone rubber. Thermal diffusivity was obtained from the intercept, B, and gradient, G, of the linear region of the increase in temperature e(t) versus logarithm of the time t. For a probe with heat production per unit length ql, radius R and conductivity h, in a medium of conductivity X and diffusivity a the equation for the temperature rise e(t) at a radial distance Y (de Vries and Peck, 1958) becomes, for large c and negligible contact resistance between the probe and the medium 8(t) = G lnt + B where gradient
(4)
G = y1/47rX, yielding h, and the intercept -0.5772-$ln
(5) P
which after rearrangement
gives
R2
a =-exp
4
$+
0.5772 + 2 D
I
(6)
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of thermal properties of foods
a
I I I C
b
\
2
IW
e
3
1
4
d
f
h I
L
I
B *
150mm
4
-e-e__ __ _______________ __-_________________________---------
_-__-
--e--w
_______
_-
__---
m
3
____ - -__
l.Omm
-1
-2
I’
‘4
Fig. 3. Laboratory 3 (heated probe method). (A) Apparatus. (B) Probe details. (a) CBM microcomputer system, controller 4032 and disc drive 4040; (b) constant temperature cabinet; (c) constant current supply; (d) digital ammeter; (e) digital voltmeter; (f) thermocouple cold junction (ice); (g) probe; (h) sample; (i) IEEE bus; (j) heater; (k) steel tube; (1) copper-constantan thermocouple hot junction; (m) epoxy resin filler.
where D=----ln(r/R) 2ah, The probe constant D was determined known thermal diffusivity, e.g. glycerol.
by calibration
in materials
of
124
2.5.
M. Kent et al.
Laboratory 4 (heated probe and regular phase methods)
As in the cases of Laboratory 2 and Laboratory 3 the experiment consisted of immersing or embedding a probe (a linear heater) axially in the sample contained within a cylinder. The sample was assumed to be infinite. However, in this case two separate experiments were performed to measure conductivity and diffusivity and two different probes were employed, one 93 mm long the other 155 mm. Each had a diameter of 1-O mm and the cylinder dimensions were: diameter 48.3 mm and length 200 mm. The experimental arrangements are shown in Figs 4 and 5. For conductivity the sample was initially equilibrated to a uniform temperature. As for Laboratory 2 the heater temperature was then recorded as a function of time after the start of heat generation. The temperature rise AT between times tr and tz (tz > tr), measured from the start of heating, is given by the expression AT=Gln?
(7) t1
where G is defined as in eqn (4) and yields X. This expression, as in eqn (4), neglects contact resistance. Diffusivity was measured in the following manner. The sample and probe were equilibrated as for conductivity but the whole cylinder of
d
Fig. 4. Laboratory 4 (regular phase method: determination of thermal diffusivity)., (a) Heater (not used); (b) thermocouple hot junction; (c) thermocouple cold junction; (d) probe;(e) chart recorder.
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of thermal properties of foods
e l_______J d
Fig. 5. Laboratory 4 (heated probe method: determination of thermal conductivity). (a) Heater: (b) thermocouple hot junction; (c)thermocouple cold junction; (d) probe; (e) two-channel chart recorder; (f) precision resistance; (g) constant current source.
radius R was then instantly immersed in a well-stirred bath of temperature T,. The subsequent temperature T, at the axis of the cylinder was then recorded as a function of time. It can be demonstrated that the graph of ln(T - T,) against time has a linear portion whose slope - l/f is related to the thermal diffusivity a by the expression (PorsdalPoulsen, 1982) 0.173
a=---R=
2.6.
f
(8)
Laboratory 5 (direct use of temperature profiles to identify thermal properties)
For the determination of thermal diffusivity alone the temperature profiles generated within the material were used. The equipment consisted of two Teflon-coated aluminium plates, each 130 mm square, normally used as a doublesided frying table but in this case used merely as heat exchangers (Fig. 6). Thermocouples were placed on the surface of each plate and a few millimetres away.within the sample. A further thermocouple was placed at the centre of the sample. Between the plates was a mould of stainless steel with holes for insertion of the
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M. Kent et
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130mm
Fig. 6.
Laboratory 5 (temperature matching method). (a) Thermocouples; heating plates; (c) mould.
(b)
thermocouples. This physical constraint enabled it to be used for viscous non-solid materials and defined the sample thickness (20 mm). The sample was prepared and placed between the plates in the mould after which it was cooled to about 10°C. The temperature of each plate was controlled to be about 10°C above that at the centre of the sample requiring a temperature rise of about O.l”C s-l. Thermal diffusivity was calculated from the measured time-temperature relationships in the following manner. The one-dimensional Fourier heat equation may be written as aT
a2T (9)
-=52 at This may be rearranged
and approximated
by
aT (Ax)’ a=-._-_._ at 2AT where aT/at
is the rate of temperature
(10)
rise at the centre of the sample,
COST 90 collaborative measurements
of thermal properties of foods
Ax is the distance between the centre and adjacent AT is the corresponding temperature difference.
thermocouples
127
and
3. REFERENCE MATERIALS AND DESIGN OF COLLABORATIVE EXPERIMENT In the preliminary work described by Ohlsson (1983) two reference materials had been studied. The first was a ‘model food’ consisting of a water binding agent with carbohydrate and water added. The second was a carrageenan gel (98% water) the values of thermal conductivity and diffusivity of which were very close to the theoretical values for pure water: the material could thus be regarded as immobilised water, convective heat transfer being eliminated. As mentioned earlier the first material was found to be difficult to handle, becoming aerated to varying degrees and setting very rapidly. In this later work this water binding agent was abandoned. Instead two preparations of carrageenan gel (Hercules Ltd, Copenhagen Pectin factory) were used: 1. 69.8% water, 1.0% carrageenan, phosphate (Na2HP0,); 2. 98% water, 2% carrageenan.
28.9% sucrose and 0.3% disodium
The carrageenan powder was added slowly to cold distilled water, while stirring, and mixed well. After complete dispersion the solution was heated to boiling point and any further solutes added where appropriate. All factors which decrease the solubility of the carrageenan had the desirable effect of helping dispersal of the powder without lump formation. The other reference material used was a quantity of free-flowing monodisperse glass beads (English Glass Co., Leicester, UK) of diameter O-1 mm. These beads were first washed in sodium carbonate solution, rinsed with distilled water and then dried in an air oven. In order to facilitate the proper analysis of variance of the results the following experimental regime was adopted at each laboratory. All samples were measured at at least one temperature (25°C) and if possible at 10°C and 40°C also. All samples were divided into three replicates and each replicate was measured three times. In the case of the glass beads, replicates were obtained by removal of the sample from the apparatus following the three measurements, then replacing it. This was done twice to provide the three replicates.
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4. FOOD MATERIALS
The food materials obtained and distributed as follows:
from one laboratory were
1. yoghurt supplied by Kennerty Farm Dairies, Aberdeen, UK; 2. whole milk powder supplied by the Milk Marketing Board, Twin Spires Creamery, Aberdeen, UK; 3. apple pulp supplied by Stokes Bomford (Holdings) Ltd, Worcester, UK; 4. meat paste supplied by Sutherlands Foods, Sheffield, UK; 5. fish paste supplied by Princes-Buitoni, Liverpool, UK. The composition of these materials as measured by Laboratory using standard methods is shown in Table 1.
3
5. RESULTS FOR REFERENCE MATERIALS AND STATISTICAL ANALYSIS 5.1. Variance (general remarks)
Mean values of diffusivity and conductivity for each laboratory, temperature and material are given in Table 2. These are the means of the nine measurements at each temperature. Tables 3 and 4 contain estimates of percentage standard deviations for diffusivity and conductivity.
Composition Sample
Yoghurt Milk powder Apple pulp Meat paste Fish paste
TABLE 1 of Food Samples Used (Carbohydrate Water
86.2 2.2 88.6 69.2 71.8
by Difference)
Pro rein
Fat
Ash
Carbohydrate
4.2 28.3 0.2 12.9 16.1
1.1 15.7 _ 12.4 4.7
1 .o 6.8 0.2 2.0 3.1
7.5 47 11 3.5 4.3
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TABLE 2 Reference Materials Material
TemperaCure, “C
Lab. 1
Lab. 2
Lab. 3
Lab. 4
Lob. 5
-
1.70 1.69 1.62
1.22 1.31
Mean values: thermal diff sivity, x IO-’ m ’ s- 1
Glass beads
Carrageenan 70% Hz0 Carrageenan 98% Hz0
10 25 40
1.45 1.47
1.40 1.45
1.50
1.50
10 25 40
1.25 1.25
1.28
1.36 1.42 1.49
1.33 1.37 1.40
1.29 1.39 1.38
1.00 1.14
10 25 40
1.38 1.45 1.55
1.43 1.52 1.60
I.38 1.47
1.50
1.41 1.73 1.41
_ 1.32 1.45
Mean values: thermal conductivity, W m-l K-’
Glass beads
10 25 40
0.161 0.164 0.165
0.154 0.160 0.165
0.166 0.170 0.171
0.180 0.181 0.179
Carrageenan 70% Hz0
10 25 40
0.485 0.485 0.494
0.524 0.549 0.574
0.503 0.522 0.53 1
0.593 0.687 0.694
Carrageenan 98% H20
10 25 40
0.556 0.586 0.627
o-597 0.630 0.662
0.581 0.610 0.620
0.632 0.610 0.671
The ‘between replicates standard deviation’ is a measure of the repeatability of the method of measurement used at each laboratory and is shown for each temperature. Similarly the ‘between samples standard deviation’ was derived from each set at each temperature and each laboratory. The between-laboratories deviation was similarly derived from an analysis of variance for a three-level nested design allowing for the occasional different number of samples within each laboratory and different number of replicates within each sample on the occasions when the experimental design was not rigidly followed.
130
M. Kent et al.
1.9 3.2
25
40 *
*
0.9
1.4 * *
1.0
4.4 4.0
S
* Negative variance for between samples variation. r, Between replicates standard deviation. s, Between samples standard deviation.
0.9
10
98% Gel
1.4 l-8 3.0
0.8
40
10 25 40
2.3 1-8
r
Lab. 1
10 2.5
Temperature, “C
70% Gel
Glass beads
Sample
0.1
0.1
0.1
0.2 0.1 0.1
0.5
0.5 0.5
r
s
0.1
0.2
0.2
o-2 0.2 0.2
0.5
0.7 O-3
Lab. 2
0.3
0.1
0.3
0.2 0.5 0.3
0.3
0.3 0.3
r
s
*
0.3
*
0.7 0.2 0.6
3.0
3.5 3.0
Lab. 3
3.9
3.5
4.0
4.7 3-1 3.8
2.9
5.5 6.2
s
5.5
*
1-o
2.9 * *
5.7
* 5.3
Lab. 4 r
TABLE 4 Thermal Conductivity Standard Deviations (%)
-
r
Lab. 5
-
-
-
-
-
s
3.5
3.0
5.3
8.8 15.7 15.1
3.5
6.2 4.8
Between labs
w
z. 9 0 2 8 ,a
j
% 1
2 s x x 2
E
;
z 2 % W 2 9 a.
M. Kent et al.
132
TABLE 5 Source
Degrees of jkeedom
Between samples Between replicates within a sample
2 6
Mean square
MSs MSR
Standard deviation estimates were obtained as follows. For each set of nine values at each temperature (three samples X three replicates) the analysis of variance is calculated in the usual way. Details of degrees of freedom, etc., are given in Table 5. The F-value is defined as F = MSs/MSR MS,
is an estimate of the replicates variance UK. MSs includes a contribution from ui as well as a$, the sample variance and is an estimate of 3ai + a$. Therefore, if MSs is less than MS,, F will be less than unity and a spuriously negative estimate for CJ~will result. Such an occurrence indicates that laboratory means are closer than would normally be expected by chance. This can occur for example when data are truncated to give three identical values for replicate measurements. 5.2. Glass beads (see Tables 2,3 and 4) 5.2.1.
Diffusivity
Laboratories 1 and 2 showed good agreement on means, the data from the other two laboratories being more widely distributed around these means. Laboratory 3 was unable to contribute to this measurement. Lower replicate variances led to a low standard deviation of - 2% for Laboratories 1, 2 and 4 whilst those for Laboratory 5 varied between 4% and 5%. Sample variances were negative for Laboratories 2 and 5 leading to non-calculable standard deviations but standard deviations for Laboratories 1 and 4 were 4% and 6% respectively. The betweenlaboratories variances were much greater, standard deviations being 9, 12 and 8% at 10, 2.5 and 40°C respectively.
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5.2.2. Conductivity
There was reasonable agreement between most of the laboratories; no standard deviations exceeding 6%. There was a tendency for the variation to decrease both absolutely and relatively with increasing temperature. Laboratory 5 contributed only diffusivity data so is excluded from this comparison. 5.3. Carrageenan gel (70%) water (see Tables 2, 3 and 4) 5.3.1.
Diffusivity
Temperature had some effect on the calculated variances. Laboratory 5 provided no data at 10°C but the other laboratories agreed well at this temperature, laboratory-to-laboratory deviation being only some 3%. At the other two temperatures the inclusion of data from Laboratory 5 which tends to be low and to have higher replicate standard deviations (7-8%) increased the laboratory-to-laboratory variation to lo-14%. Apart from Laboratory 1, no temperature dependence of the replicate variation was discernible in the laboratories. 5.3.2.
Conductivity
Laboratory 4 data were higher than those from all other laboratories, with much higher between replicates deviation than in general (3-S% compared to O.l-3%). It should also be noted that the mean values at each temperature exceed published data for pure water (Powell et al., 1966). Qashou et al. (1972) used pure water data to demonstrate the unreliability of some published food data which with water as the major component should not exceed the value for water itself. For the purposes of this comparative study of reference material the data from Laboratory 4 will be used but Qashou’s criterion will be applied later for selection of reasonable values for food data. Between-laboratory standard deviations range from 9 to 16% over the temperature range. 5.4. Carrageenan gel (98%) water (see Tables 2,3 and 4) 5.4.1. Diffusivity
The four laboratories which provided data at 10°C were in good agreement, the between-laboratories standard deviation being only 2%. At
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134
TABLE 6
Grand Means of Thermal Conductivity of 98% Carrageenan Gel Compared to That of Pure Water; Water Values Interpolated from Powell ef al. (1966) Temperature, “C
he, Wm-’ K-’
Standard deviation
h wkr W m-l K-l
10 2.5 40
0.592 0.609 0.645
O-031 0.018 0.022
0.579 0.606 0.627
25°C there is a great increase in this deviation due to Laboratory 4 reporting an abnormally high value and Laboratory 5 being low. The laboratory-to-laboratory deviation at this temperature is 10%. At 40°C this is reduced to 5% indicating more reasonable agreement between laboratories. 5.4.2. Conductivity The problem of unrealistically high values is common to nearly all laboratories in this measurement. This particular material can be thought of as immobilised water and so should have a conductivity comparable with that of pure water. However, given the between-laboratory deviation of 3-5% the overall mean values at each temperature are very close to the expected values (Table 6) which lie within the error limits. Replicate standard deviations were very low being 1% for Laboratories 2 and 3, l-3% for Laboratory 1 and 4% for Laboratory 4.
6. FOOD MATERIALS: 6.1.
RESULTS
AND DISCUSSION
General remarks
Tables 7-16 list the values obtained at each laboratory for thermal conductivity and diffusivity for the foodstuffs listed in Section 4. It was arranged that where possible all laboratories would make at least three measurements at 25°C and the variation calculated for all the data at that temperature would be used as an indication of variation at all
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135
other temperatures regardless of how many laboratories made measurements at those temperatures. In the case of thermal diffusivity, certain extreme outliers were found and it was considered appropriate to eliminate these from the calculation of mean values. Such exclusions are indicated in the tables. In the case of conductivity no such extreme outliers were identified but nevertheless, using the criterion of Qashou et al. discussed in
2.0
I
L
1
10
,
20
30
40
50
60
70
a0
40
50
60
70
00
“C
t 10
I
1
20
30
I
“C
Fig. 7. Thermal diffusivity’, a, and conductivity, A. versus temperature for yoghurt. Dashed line is based on literature data for pure water. Standard deviation displayed is that computed for all data at 2.5’C.
M. Kent et al.
136
Section 5, those data sets whose means exceeded the published values for pure water at the temperatures concerned were eliminated. Figures 7-l 1 show the grand means of the data versus temperature. Also shown in several graphs is the interpolated thermal conductivity curve for pure water. 6.2. Yoghurt (Tables 7 and 8, Fig. 7) Surprisingly, despite considerations of transport and shelf life, the data for yoghurt are in close accord. The only problem arose from the data provided by Laboratory 4 on conductivity which were excluded as Table 8 shows. This exclusion left no data at 8°C and reduced the set at 25°C to only nine measurements but neither of these were serious shortcomings. The remaining data were of extremely low variation and
TABLE 7 Thermal Diffusivity of Yoghurt (x 10-7mZs-1) 10°C
20°C
25°C
1
1.27 1.36 1.20
1.28 1.36 1.29
1.33 1.38 1.30
2
1.37 1.33 1.37
1.42 1.40 1.44
1.44 1.42 1.46
1.33 1.28 1.38
-
1.41 1.25 1.36
Laboratory
1°C
3
1.28 (2) 1.28 (0) 1.28 (4)
4
_
5
_ _
Mean * standard deviation
1.28 15%
1.32 4.5%
1.40 8.6%
Values in square brackets rejected as outliers.
40°C
50°C
1.30 1.36 1.34
1.45 1,39 1.40
1.46 1.44 1.49
-
_ _
_ _ _
_ _
_ _ -
_
_
_ _ _
_ _
_ _ _
1.46 1.7%
1.33 2.2%
1.43 2.1%
30°C
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TABLE 8 Thermal Conductivity of Yoghurt (W m-’ K-l) Laboratory
1°C
10°C
8°C
1
O-550 o-550 0.540
2
0.548 0.543 0.543
3
0.525 (5) O-525 (0) 0.525 (5)
Mean + standard deviation
1
0.525 0.06%
25°C
30°C
O-580 O-580 0.590 0.570 0.570 0.570
0.547 0.545 0.552
01646 0.560 [ 0.690 O-584
4
20°C
0.578 0.579 0.576
40°C 0.600 0.610 O-600
O-587 0.588 0.588
o-570 0.568 0.565 0.665 0.665 0.632
0.632 0.546 0.7%
0.570
0.576 1.3%
0.588 0.1%
0.603 1.O%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculations of the grand means. the temperature (Fig. 7).
dependence
compares
well with that
of pure water
6.3.Whole milk powder (Tables 9 and 10, Figs 8 and 9) The major problem with milk powder lay in the control of its density. Laboratory 2 investigated in more detail the effects of density on thermal conductivity at 25°C and these results are shown in Fig. 9. All measurements made by other laboratories were accompanied by a determination of density as well. Comparison of the data in Table 10 with Fig. 9 shows that all laboratories were working with densities in the range 586-750 kg mV3 and that density in this range seems to have less effect on thermal conductivity than at lower values. The data in
138
M. Kent et al.
Thermal Diffusivity Laboratory
Density, kg me3
TABLE 9 of Milk Powder (1 Om7m2 s-l)
10°C
20°C
-
25°C
40°C
50°C
-
1
586
0.976 0.99 1 1.03
0.999 1.04 1.11
1.09 1.06 1.10
2
591
0.81 0.80 0.83
0.83 0.82 0.85
0.86 0.85 0.87
_
_
690
627 7.8%
1.18 1.09 1.06 0.88 0.88 0.90 -
-
0.676
640
Mean f standard deviation
30°C
0.827 0.80 0.98 0.96
0.906 11.5%
0.904 16.7%
_
0.952 11.9%
1.06 1.16 1.15 0.880 1.4%
1 .l 10 5.6%
1.049 14.8%
-
Fig. 9 appear to depend in a non-linear fashion on density in such a way that for the measurement reported any variation with density would be totally obscured by all other sources of variation. For this reason the results in Fig. 8 are shown without regard to density. Some temperature dependence can be seen. 6.4.
Apple pulp (Tables 11 and 12, Fig. 10)
This material presented some problems for Laboratory 5 in their measurement of diffusivity. Abnormally high results were obtained which may have arisen from the generation of convective currents in the material, though Laboratory 1 with a similar sample configuration had no such problem. Another explanation may be that the upper surface of the sample was not in good contact with the upper heating plate. The conductivity data from Laboratory 4 were also rejected on the comparison with pure water, On the whole this method seemed to
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139
TABLE 10 Thermal Conductivity of Milk Powder (W rn-’ K-l) Density, kg mV3
10°C
1
586
0.120 0.120 0.110
2
591
o-077 0.078 0.078
3
750
O~lOO(5) O.lOO(7) O.lOO(6) o-099 (9) O.lOO(2) O.lOO(9)
Laboratory
740
4
690
696 698 630 586 615 628 Mean f standard deviation
perform materials 6.5.
65.5 9.3%
20°C
25°C
30°C
40°C
0.130 o-1 20 o-1 30 o-079 O-080 0.080
0.082 0.082 O-082 0.103 (4) 0.103(3) 0.103(4) 0.102(7) 0.102(7) 0.102(3)
50°C
0.150 0.140 0.140 0.084 0.085 0.085 O-106(3) O-106(7) 0.106(4) 0.103(9) 0.105(7) 0*105(5)
0.101 0.117 0.117 0.136 0.118 0.106 0.105 0.099 0.112 0.0987 0.0957 0.1049 0.0847 0.106 14.9% _l9.3% 15.7% 0.7% 1.O%
0.119 0.124 0.124
0.133 9.2%
badly with high moisture foods although with reference the agreement with other laboratories had been better.
Meat paste (Tables 13 and 14, Fig. 11)
There was reasonably good agreement between the laboratories for meat paste, only one set of data being rejected. The diffusivity seems
M. Kent et al.
140
A (WdK-
0.10 i
0.05
I
, 10
20
30
40
50
60
70
80
“C
Fig. 8. Thermal diffusivity, a, and conductivity, X, versus temperature for whole milk powder. Standard deviation displayed is that computed for all data at 25°C.
to have a marked temperature dependence but since only Laboratory 5 measured the material at 75°C the high value recorded at that temperature may be in error because this laboratory showed a marked tendency to produce high results. 6.6. Fish paste (Tables 15 and 16, Fig. 12) Similar comments apply here as to meat paste, the overall moisture contents being approximately the same. However, a large body of conductivity data had to be excluded at 10°C and 50°C. The variability in conductivity for both meat and fish pastes was much larger than for
COST 90 collaborative measurements
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141
1
N 2.5 % f
density
Fig. 9.
103Kg
m3
Variation of thermal conductivity of milk powder with density as measured by Laboratory 2.
TABLE 11 Thermal Diffusivity of Apple Pulp (1 0m7m2 s-‘) Laboratory
10°C
20°C
25°C
40°C
50°C
1
1.36 1.35 1.26
1.33 1.40 1 e32
1.31 ’ 1.48 1.35
1.47 I .50 1.47
l-48 1.55 1.50
2
1.37 1.35 1.38
1.44 1.42 1.46
1.53 1.51 1.55
3
1.46 (7) 1.47 (5) 1.47 (1)
4
0.346 [ 0.839
5
1
1.16
1
1.96 1.98 1.93
[ 1.77 l-80 1 G35 Mean f standard deviation
1.345 3.2%
1,350 3.3%
Values in square brackets rejected as outliers.
1.430 4.3%
1.505 2.1%
1.422 12.4%
142
M. Kent et al. TABLE 12
Thermal Conductivity Laboratory
10°C
of Apple Pulp (W m-l K-l) 20°C
25°C
1
0.540 0.550 0.550
0.590 0.600 0.630
2
0.562 0.562 0.561
o-594 0.593 0.593
40°C
5o”c 0.650 O-640 0.650
0.63 1 0.630 0,630
0.588 (0) 0.588 (7) 0.588 (7) -0.848 0.961 -0.901
1
/ 0.824 0.750 0.780 I 0.556 1.4%
Mean + standard deviation
[O-800] 4.3%
0.596 2.2%
0,630 0.1%
0.647 1 .O%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculation of the grand mean.
yoghurt
handling, laboratory
and
apple
different affecting
This was attributed to difficulties in sample amounts of air possibly being entrapped at each the density and possibly also the contact resistance.
pulp.
7. CONCLUSIONS
The study of potential reference materiak for thermal property measurement has shown that in general the best agreement between laboratories was found with a 98% water carrageenan gel. With this material the between-laboratories standard deviation at 25’C was 9.9% for thermal diffusivity and only 3.0% for conductivity measurements. Conductivity
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of thermal properties of foods
143
I
10
20
30
40
50
60
70
00
OC
l.O-
A (wfli’i;’) --•---______.i_----------
___________-..* _..- --------.
0.5-
10
20
30
40
50
60
70
00
OC
Fig. 10.
Thermal diffusivity, a, and conductivity, A, versus temperature for apple pulp. Dashed line is based on literature data for pure water. Standard deviation displayed is that computed for all data at 25’C.
measurements were usually (though not always) more accurate than diffusivity and with this material there is the added advantage of a direct comparison with published values for pure water. The heated probe method of Laboratory 2 gave consistently precise results and this may be due in part, for the measurement of diffusivity in glass beads at least, to compensation for thermal contact resistance between the probe and the sample, a variable ignored by other labora-
144
hf. Kent et al.
TABLE 13 Thermal Diffusivity of Meat Paste (10e7 m2 s-l)
Luboratoly 1
10°C
20°C
1.20 l-18
1.23 1.24
1.15 2
1.24
1.29
1.25
I-35 1.38
1.31 1.29 1.33
1.51 1.40 1.42
1.28 1.29 1.36
1.34 1.33 1.34 1.31 1.31 1.32
4
40°C
1.25 1.29
3
(7) (7) (3) (7) (3) (0)
1.272 2.9%
75°C
1.08 1.47 1.50 1,42
1.177 2.1%
50°C
1.31 (1) 1.33 (1) 1.37 (7)
[0.617]
5
Mean f standard deviation
2s”c
1.382 4.6%
1.60
1.61 1.66 1.325
3.3%
1.424 14.6%
2.14 1.97 2.05 2.053 4.14%
Values in square brackets rejected as outliers.
and which for most of these samples is negligible. The method used by Laboratory 5 was found to be unsuitable for liquid or semiliquid samples. The accuracy of measurement and the degree of agreement reached in this work is remarkable when compared to a similar comparative exercise recently published in which thermal conductivity of steel reference samples had been measured. The seven laboratories involved in that work could not agree to better than 40% (with one laboratory excluded the scatter dropped to 10%) (Goldratt and Greenfield, 1982). The measurement of real food materials as distinct from model systems has also been conducted with such accuracy that the data tories
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TABLE 14 Thermal Conductivity of Meat Paste (W rn-’ K-l) Laboratory 1
IO"C
2o"c
O-458 0.458 0.458
3
o-504 0.498 0.478
0.448 0.458 0.465 0.496 O-496 0.501
1
0.610 O-610 [ 0.610 0.343 7.3%
0.458
50°C 0.450 0.460 0.470
0.487 O-486 0.486 0.487 0.486 0.487
4
Mean + standard deviation
40°C
0.380 0.450 o-430
0.340 0.370 0.320
2
25°C
0.678 O-604 o-571 0.472 7.4%
0.457 1.8%
0.525 14.5%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculation of the grand mean.
presented here can be considered authoritative. The criterion of not exceeding pure water data has enabled more acceptable and reliable values to be presented for conductivity. The data obtained is now available with full composition information for comparison with that obtainable from the predictive equations evaluated in the COST 90 project (van Beek and Veerkamp, 1982; Miles etal.,1983). Examining the objectives described in Section 1, therefore, in the light of the complete collaborative experiments it can be said that all these have been met. The various methods available to us have been
hf. Kent et al.
146
0.5 t
lo
20
30
40
50
t
t
40
50
1
60
70
80
60
70
80
“C
l,O-
A (W&K-‘) 0.5-
tt t
10
20
30
1
“C
Fig. 11. Thermal diffusivity, a, and conductivity. X, versus temperature for meat paste. Standard deviation displayed is that computed for all data at 25°C.
compared as described and the reference materials used have been evaluated, the 98% water carrageenan gel being considered the most suitable. The precision of measurements has been determined and, for this range of temperature, in which phase changes and hence no large latent heat terms were encountered, the heated probe method has been found to give the highest precision. Finally, measurements on food
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of thermal properties of foods
TABLE 15 Thermal Diffusivity of Fish Paste (low7 m2 s-l) Laboratory
1
10°C
20°C
25°C
40°C
5o”c
1.25 1.18 1.23
l-25 1.22 l-24
1.26 1-2.5 l-25
1.35 1.34 1.38
1.40 1.41 1.40
1.31 1.29 l-34
1.32 1.30 1.34
l-6 1.33 1.36
2
1.32 1.32 1.36
1.32 1.38 1.35
[0.61] 0.982 1.02 1.01
Mean * standard deviation
0.996 l-04 1.22 1.26 1.22 l-48 1.42 1.42
5
1.22 3.0%
1.180 11.7%
75Y
1.337 5.5%
1.353 1.3%
1.73 1.67 1.64
1.98 1.91 1.90
1.360 15.8%
1.93 2.2%
Values in square brackets rejected as outliers.
materials of various types and compositions further comparison with predictive models.
have been collected
for
ACKNOWLEDGEMENTS Firstly the authors would like to thank the authorities of the countries participating in COST 90 for enabling this work to take place. The project itself was led by Professor Ronald Jowitt and we thank him for his able leadership and guidance during the past few years. Our thanks
M. Kent et
148
al.
TABLE 16
Thermal Conductivity
Laboratory 1
10°C
of Fish Paste (W rn-’ K-‘)
2o”c
0.444 0.430 0.430
2
25°C
40°C
0.430 0.440 0.440 0.478 0.480 0.479
0.483 0.481 0.480
0.440 0.450 0.470 0.495 0.49 1 0.488
0.513 0.513 0.515
0.523 0.528 0.527 0.591 0.59 1 0.59 1 0.6730.797 0.799 0.745 0.696 0.686,
-0.716 0.707 0.712 0.760 0.726 _0.729 _
Mean f standard deviation
0.433 1.4%
0.479 0.2%
50°C
0.477 7.1%
0.49 1 0.8%
0.523 11.5%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculation of the grand mean.
are due to Princes-Buitoni, Sutherlands Foods, Stokes Bomford (Holdings), Milk Marketing Board and Kennerty Farm Dairies who supplied the samples of food materials for this work and Hercules Ltd. Copenhagen Pectin Co. and the English Glass Co. who supplied the reference materials. Finally, a great deal of this work could not have been achieved without the efforts and advice of the Torry Research Station statistician Gordon Smith who although not appearing as an author devised the strategy of the exercise and contributed all of the statistical analysis.
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2.0I
1.5a (16Wi)
t t
t
10
20
t
1
40
50
60
70
BO
40
50
60
70
80
l.O-
0.5-
I
1
30
1.0
“C
A (wm’d)
i
I
10
1
20
30 9
Fig. 12. Thermal diffusivity, a, and conductivity, A, versus temperature for fish paste. Standard deviation displayed is that computed for all data at 25°C.
REFERENCES van Beek, C. and Veerkamp, C. H. (1982). Een programma voor bet berekenen van thermische eigenschappen van voedingsmiddelen. Voedingsmiddelentechnologie, 15,63-6.
M. Kent et al.
150
Bruijn, P. J., van Haneghem, I. A. and Schenk, J. (1982). An improved non-steadystate probe method for measurements in granular materials. Part I: Theory. 8th European Conference on Thermophysical Properties, Baden-Baden. Carslaw, H. S. and Jaeger, J. C. (1959). Conduction of Heat in Solids, 2nd edn, Oxford University Press, Oxford. Goldratt, E. and Greenfield, A. J. (1982). Comparison of anomalous behaviour of the thermal and electrical conductivity of standard reference material SRM-735. J. Appl. Phys., 53,4975-9. van Haneghem, I. A. (1981). Een niet-stationaire naaldmethode (warmtegeleiding, warmtecapaciteit contactweerstand). PhD Thesis, LH Wageningen, The Netherlands. van Haneghem, I. A., Schenk, J. and Boshoven, H. P. A. (1982). An improved nonsteady-state probe method for measurements in granular materials. Part II: Experimental results. 8th European Conference on 27zermophysical Properties. Baden-Baden. Miles, C., van Beek, G. and Veerkamp, C. H. (1983). In: Physical Properties of Foods, eds R. Jowitt, F. Escher, B. Hallstrom, H. F. Th. Meffert, W. E. L. Spiess and G. Vos, Applied Science Publishers, London, p. 269. Morley, M. J. (1966). Thermal conductivities of muscles, fats and bones. J. Food Technology, 1,303-l 1. Nesvadba, P. (1982a). Methods for the measurement of thermal conductivity and diffusivity of fo0dstuffs.J. Food Engineering, 1,93-l 13. Nesvadba. P. (1982b). A new transient method for the measurement of temperature dependent thermal diffusivity. J. Phys. D: Appl. Phys., 15, 725-38. Ohlsson, T. (,1983). In: Physical Properties of Foods, eds R. Jowitt, F. Escher. B. Hallstrom, H. F. Th. Meffert, W. E. L. Spiess and G. Vos, Applied Science Publishers, London, p. 3 13. Porsdal-Poulsen, K. (1982). Thermal diffusivity of foods measured by simple equipment. J. Food Engineering, 1. 115-22. Powell, R. W., Ho, C. Y. and Liley, P. E. (1966). Thermal conductivity of selected materials. NSRDS-NBS-8 PB 189-698. Nat. Tech. Int. Service, US Department of Commerce, Springfield, Virginia. Qashou, H. S., Vachon, R. I. and Touloukian, Y. S. (1972). Thermal conductivity of foods. ASHRAE Transactions, 78 (Research Report No. 2224 RP62), pp. 165-83. Thtry. P. and Mar&ha], J. C. (1980). Etude et caracterisation d’un nouveau fluxmetre calorifique. J. Phys. E: Sci. Inst.. 13, 860-5. de Vries, D. A. and Peck. A. J. (1958). On the cylindrical probe method of measuring thermal conductivity with special reference to soils. Aust. J. Phys., 11, 25571.
3 (1984)
117-l 50
Cost 90 Collaborative Measurements Properties of Foods
of Thermal
M. Kent,* K. Christiansen,t I.A. van Haneghem,“” E. Holtz,$ M.J. Morley,*** P. Nesvadba,* and K.P. Paulsen? * Torry Research Station, 135 Abbey Road, Aberdeen AB9 8DG, UK t The Technical University of Denmark, Lyngby, Denmark ** Department of Physics and Meteorology, Agricultural University, Wageningen, The Netherlands $ Division of Food Engineering, Lund University, Alnarp, Sweden *** Meat Research Institute, Langford, Bristol, UK
ABSTRl
CT
Collaborative measurements of the thermal properties of foods and model foods are reported. They were part of a European Cooperation in Science and Technology (COST) project and provide data on thermal difbsivity and thermal conductivity of fish paste, meat paste, yoghurt, milk powder, apple pulp. ‘Model’ foods also examined were various mixtures of carrageenan, sugar and water and a monodisperse ‘powder’ of glass beads. Dependence of the measured properties on temperature, density and composition was also examined.
1. INTRODUCTION The decision in 1978 by the Council of the European Communities to support a coordinated programme on the physical properties of foodstuffs, COST 90 (Cooperation in Science and Technology: Project 90, Physical Properties of Foods) led, through the differentiation of the project into subgroups (thermal properties, water activity, rheology), to a working party investigating the experimental collection of thermal properties data both of food materials and substances described as ‘model’ foods or reference materials. Preliminary results of this collaborative exercise were reported by Ohlsson (1983) at the final seminar 117 Journal of Food Engineering 0260-8774/84/$03.00 - @ Elsevier Applied Publishers Ltd, England, 1984. Printed in Great Britain
Science
M. Kent et al.
118
of the Project in Leuven. However, these results were limited in scope: only four laboratories took part, diffusivity alone was studied and only two reference materials were measured. One of these materials was in any case found by the participants to be extremely difficult to prepare and handle. With the end of COST 90 a new project COST 90 bis was begun with different physical properties to examine. However, it was felt worthwhile and necessary to conclude the collaborative work on thermal properties with one more laboratory taking part and with real food materials being measured. In addition it was hoped that the data so acquired would enable the precision of various predictive models to be gauged. The objectives were therefore as follows: 1. To compare different methods of measuring thermal conductivity and diffusivity in different laboratories using reference materials. 2. To comment on the usefulness of reference materials for calibration purposes. 3. To establish precision of measurement of each method from within-laboratory variances and between-laboratory variances. 4. To measure various food materials of different types and present the data for comparison with prediction from the known compositional data.
2. DESCRIPTION
OF METHODS
2.1. Method classification Each laboratory had developed, over recent years, its own apparatus for thermal property measurements. In most cases these were based on well-known published methods all of which have been reviewed and classified recently by Nesvadba (I 982~). Accordingly the description of each technique is preceded by a classification in the terms used by Nesvadba. Of five laboratories, three used methods based on the heated probe with cylindrical symmetry. The other two used methods with symmetry about a central plane (rectangular block samples). All were transient methods.
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119
2.2. Laboratory 1 (direct use of temperature profiles to identify thermal properties)
Conductivity and diffusivity were measured simultaneously in the following manner. The sample, in the form of a block 200 X 170 X 60 mm, was insulated on its four minor surfaces with the two major surfaces in contact with metal heat exchangers (Fig. 1). The temperatures of these two heat exchangers were approximately the same and could be varied between - 50°C and + 60°C to generate approximately symmetrical transient temperature profiles across the sample (x direction). These profiles were measured using a specially constructed probe embedded in the sample consisting of 20 thermocouples bonded to and supported by a thin plastic strip 60 mm wide. The spacing between the thermocouple junctions was 2.54 mm. The heat flux at one of the major surfaces (at x = xb = 0) was measured by a calibrated sensor of the ThCry type (ThCry and MarCchal, 1980). The temperatures and the heat flow data were logged at 60 s intervals and processed off-line by a digital computer.
b
b Fig. 1. Laboratory 1: apparatus for thermal conductivity and thermal diffusivity determination, generating and measuring temperature profiles and heat flux. (a) Flow of hot or cold ethanol; (b) aluminium heat exchanger;(c) ‘Tufnol’ frame; (d) thermal insulation around sample; (e) sample; (f) thermocouple junctions; (g) plastic strip supporting thermocouples; (h) cable to data logger; (i) heat flux sensor.
M. Kent et al.
120
The thermal conductivity X was temperature, Tb, from the Fourier law
h(Tb)=-q
computed
dT
I I a;
_
for
each
boundary
(1)
x-xb
where CJ is the heat flux and aT/ax is the temperature gradient in the sample obtained by differentiation of a least-squares parabola fitted to part of the temperature profile. The thermal diffusivity, a, was computed at each temperature T, of the maxima or minima of the temperature profiles (occurring at x = x, ‘v 30 mm) using the expression (Nesvadba, 1982b) a(T,l =
aT/at
a27yax2
x=xe
(2)
in which the derivatives with respect to time, t, and coordinate, x, were evaluated from least-squares cubic splines fitted to the temperature data.
2.3.
Laboratory
2 (heated probe method)
A needle shaped probe was used consisting of 0.1 mm thick doubly folded constantan heating wire and a 0.1 mm thick manganin-constantan thermocouple junction fitted into a stainless steel envelope. In order to fix the position of the heating wire and the thermocouple the remaining space in the envelope was filled with silicone rubber. The overall diameter of the probe was 1 mm and its length was 2 10 mm. This probe was immersed in the material to be examined contained within a cylinder 120 mm in diameter and 240 mm long. A reference element of identical dimensions to the probe but only consisting of the cold junction of the thermocouple was similarly immersed in the sample material in a second identical cylinder. Both cylinders were placed in a constant temperature bath and equilibrated to the same temperature. During the measuring time of several minutes in which heat was generated in the probe by a d.c. current, the temperature was logged every second. The whole apparatus is shown diagrammatically in Fig. 2. Depending on the thermal properties of the sample (thermal conductivity X and volumetric heat capacity pc) there is a slower or faster heat transport through the medium, resulting in a faster or slower rate of
COST PO collaborative measurements
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121
‘e
Fig. 2.
Laboratory 2 (heated probe method). (a) Thermocouple hot junction; (b) heater; (c) probe; (d) cylinder with sample; (e) temperature-controlled bath; (f) digital voltmeters; (g) precision resistance; (h) direct current source; (i) timer; (j) thermocouple cold junction; (k) computer; (1) amplifier; (m) switch to start measurement.
temperature rise of the probe. The contact resistance r between the probe and the sample must also be considered. For the calculation of X and pc a model is used in which the probe is seen as a compound cylinder system consisting of three coaxial cylinders: the heating wire, the insulating material and the tube of the probe. Between the probe and the sample a contact resistance is assumed as
122
M. Kent et al.
mentioned temperature
above. For sufficiently large values of the rise 8 (r) of the probe can be written as
time
C, the
(3) where the coefficients A, B, D and E depend on the dimensions and the thermal properties of the probe, the thermal properties of the sample and the contact resistance. From an accurate mathematical analysis of the measured 8 versus t curve the coefficients A, B, D and E can be determined and hence values for h, pc and F (van Haneghem, 1981; Bruijn et aE., 1982; van Haneghem et al., 1982).
2.4.
Laboratory 3 (heated probe method)
Measurements of thermal conductivity X and diffusivity a, were carried out simultaneously with a heated probe method (Morley, 1966). The dimensions of the probe were approximately: length 150 mm, diameter 1 mm. As can be seen from Fig. 3 it was substantially the same construction as for Laboratory 2 the major difference being in the filling material - epoxy resin instead of silicone rubber. Thermal diffusivity was obtained from the intercept, B, and gradient, G, of the linear region of the increase in temperature e(t) versus logarithm of the time t. For a probe with heat production per unit length ql, radius R and conductivity h, in a medium of conductivity X and diffusivity a the equation for the temperature rise e(t) at a radial distance Y (de Vries and Peck, 1958) becomes, for large c and negligible contact resistance between the probe and the medium 8(t) = G lnt + B where gradient
(4)
G = y1/47rX, yielding h, and the intercept -0.5772-$ln
(5) P
which after rearrangement
gives
R2
a =-exp
4
$+
0.5772 + 2 D
I
(6)
COST 90 collaborative measurements
123
of thermal properties of foods
a
I I I C
b
\
2
IW
e
3
1
4
d
f
h I
L
I
B *
150mm
4
-e-e__ __ _______________ __-_________________________---------
_-__-
--e--w
_______
_-
__---
m
3
____ - -__
l.Omm
-1
-2
I’
‘4
Fig. 3. Laboratory 3 (heated probe method). (A) Apparatus. (B) Probe details. (a) CBM microcomputer system, controller 4032 and disc drive 4040; (b) constant temperature cabinet; (c) constant current supply; (d) digital ammeter; (e) digital voltmeter; (f) thermocouple cold junction (ice); (g) probe; (h) sample; (i) IEEE bus; (j) heater; (k) steel tube; (1) copper-constantan thermocouple hot junction; (m) epoxy resin filler.
where D=----ln(r/R) 2ah, The probe constant D was determined known thermal diffusivity, e.g. glycerol.
by calibration
in materials
of
124
2.5.
M. Kent et al.
Laboratory 4 (heated probe and regular phase methods)
As in the cases of Laboratory 2 and Laboratory 3 the experiment consisted of immersing or embedding a probe (a linear heater) axially in the sample contained within a cylinder. The sample was assumed to be infinite. However, in this case two separate experiments were performed to measure conductivity and diffusivity and two different probes were employed, one 93 mm long the other 155 mm. Each had a diameter of 1-O mm and the cylinder dimensions were: diameter 48.3 mm and length 200 mm. The experimental arrangements are shown in Figs 4 and 5. For conductivity the sample was initially equilibrated to a uniform temperature. As for Laboratory 2 the heater temperature was then recorded as a function of time after the start of heat generation. The temperature rise AT between times tr and tz (tz > tr), measured from the start of heating, is given by the expression AT=Gln?
(7) t1
where G is defined as in eqn (4) and yields X. This expression, as in eqn (4), neglects contact resistance. Diffusivity was measured in the following manner. The sample and probe were equilibrated as for conductivity but the whole cylinder of
d
Fig. 4. Laboratory 4 (regular phase method: determination of thermal diffusivity)., (a) Heater (not used); (b) thermocouple hot junction; (c) thermocouple cold junction; (d) probe;(e) chart recorder.
COST 90 collaborative measurements
125
of thermal properties of foods
e l_______J d
Fig. 5. Laboratory 4 (heated probe method: determination of thermal conductivity). (a) Heater: (b) thermocouple hot junction; (c)thermocouple cold junction; (d) probe; (e) two-channel chart recorder; (f) precision resistance; (g) constant current source.
radius R was then instantly immersed in a well-stirred bath of temperature T,. The subsequent temperature T, at the axis of the cylinder was then recorded as a function of time. It can be demonstrated that the graph of ln(T - T,) against time has a linear portion whose slope - l/f is related to the thermal diffusivity a by the expression (PorsdalPoulsen, 1982) 0.173
a=---R=
2.6.
f
(8)
Laboratory 5 (direct use of temperature profiles to identify thermal properties)
For the determination of thermal diffusivity alone the temperature profiles generated within the material were used. The equipment consisted of two Teflon-coated aluminium plates, each 130 mm square, normally used as a doublesided frying table but in this case used merely as heat exchangers (Fig. 6). Thermocouples were placed on the surface of each plate and a few millimetres away.within the sample. A further thermocouple was placed at the centre of the sample. Between the plates was a mould of stainless steel with holes for insertion of the
126
M. Kent et
al.
130mm
Fig. 6.
Laboratory 5 (temperature matching method). (a) Thermocouples; heating plates; (c) mould.
(b)
thermocouples. This physical constraint enabled it to be used for viscous non-solid materials and defined the sample thickness (20 mm). The sample was prepared and placed between the plates in the mould after which it was cooled to about 10°C. The temperature of each plate was controlled to be about 10°C above that at the centre of the sample requiring a temperature rise of about O.l”C s-l. Thermal diffusivity was calculated from the measured time-temperature relationships in the following manner. The one-dimensional Fourier heat equation may be written as aT
a2T (9)
-=52 at This may be rearranged
and approximated
by
aT (Ax)’ a=-._-_._ at 2AT where aT/at
is the rate of temperature
(10)
rise at the centre of the sample,
COST 90 collaborative measurements
of thermal properties of foods
Ax is the distance between the centre and adjacent AT is the corresponding temperature difference.
thermocouples
127
and
3. REFERENCE MATERIALS AND DESIGN OF COLLABORATIVE EXPERIMENT In the preliminary work described by Ohlsson (1983) two reference materials had been studied. The first was a ‘model food’ consisting of a water binding agent with carbohydrate and water added. The second was a carrageenan gel (98% water) the values of thermal conductivity and diffusivity of which were very close to the theoretical values for pure water: the material could thus be regarded as immobilised water, convective heat transfer being eliminated. As mentioned earlier the first material was found to be difficult to handle, becoming aerated to varying degrees and setting very rapidly. In this later work this water binding agent was abandoned. Instead two preparations of carrageenan gel (Hercules Ltd, Copenhagen Pectin factory) were used: 1. 69.8% water, 1.0% carrageenan, phosphate (Na2HP0,); 2. 98% water, 2% carrageenan.
28.9% sucrose and 0.3% disodium
The carrageenan powder was added slowly to cold distilled water, while stirring, and mixed well. After complete dispersion the solution was heated to boiling point and any further solutes added where appropriate. All factors which decrease the solubility of the carrageenan had the desirable effect of helping dispersal of the powder without lump formation. The other reference material used was a quantity of free-flowing monodisperse glass beads (English Glass Co., Leicester, UK) of diameter O-1 mm. These beads were first washed in sodium carbonate solution, rinsed with distilled water and then dried in an air oven. In order to facilitate the proper analysis of variance of the results the following experimental regime was adopted at each laboratory. All samples were measured at at least one temperature (25°C) and if possible at 10°C and 40°C also. All samples were divided into three replicates and each replicate was measured three times. In the case of the glass beads, replicates were obtained by removal of the sample from the apparatus following the three measurements, then replacing it. This was done twice to provide the three replicates.
M. Kent et al.
128
4. FOOD MATERIALS
The food materials obtained and distributed as follows:
from one laboratory were
1. yoghurt supplied by Kennerty Farm Dairies, Aberdeen, UK; 2. whole milk powder supplied by the Milk Marketing Board, Twin Spires Creamery, Aberdeen, UK; 3. apple pulp supplied by Stokes Bomford (Holdings) Ltd, Worcester, UK; 4. meat paste supplied by Sutherlands Foods, Sheffield, UK; 5. fish paste supplied by Princes-Buitoni, Liverpool, UK. The composition of these materials as measured by Laboratory using standard methods is shown in Table 1.
3
5. RESULTS FOR REFERENCE MATERIALS AND STATISTICAL ANALYSIS 5.1. Variance (general remarks)
Mean values of diffusivity and conductivity for each laboratory, temperature and material are given in Table 2. These are the means of the nine measurements at each temperature. Tables 3 and 4 contain estimates of percentage standard deviations for diffusivity and conductivity.
Composition Sample
Yoghurt Milk powder Apple pulp Meat paste Fish paste
TABLE 1 of Food Samples Used (Carbohydrate Water
86.2 2.2 88.6 69.2 71.8
by Difference)
Pro rein
Fat
Ash
Carbohydrate
4.2 28.3 0.2 12.9 16.1
1.1 15.7 _ 12.4 4.7
1 .o 6.8 0.2 2.0 3.1
7.5 47 11 3.5 4.3
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129
TABLE 2 Reference Materials Material
TemperaCure, “C
Lab. 1
Lab. 2
Lab. 3
Lab. 4
Lob. 5
-
1.70 1.69 1.62
1.22 1.31
Mean values: thermal diff sivity, x IO-’ m ’ s- 1
Glass beads
Carrageenan 70% Hz0 Carrageenan 98% Hz0
10 25 40
1.45 1.47
1.40 1.45
1.50
1.50
10 25 40
1.25 1.25
1.28
1.36 1.42 1.49
1.33 1.37 1.40
1.29 1.39 1.38
1.00 1.14
10 25 40
1.38 1.45 1.55
1.43 1.52 1.60
I.38 1.47
1.50
1.41 1.73 1.41
_ 1.32 1.45
Mean values: thermal conductivity, W m-l K-’
Glass beads
10 25 40
0.161 0.164 0.165
0.154 0.160 0.165
0.166 0.170 0.171
0.180 0.181 0.179
Carrageenan 70% Hz0
10 25 40
0.485 0.485 0.494
0.524 0.549 0.574
0.503 0.522 0.53 1
0.593 0.687 0.694
Carrageenan 98% H20
10 25 40
0.556 0.586 0.627
o-597 0.630 0.662
0.581 0.610 0.620
0.632 0.610 0.671
The ‘between replicates standard deviation’ is a measure of the repeatability of the method of measurement used at each laboratory and is shown for each temperature. Similarly the ‘between samples standard deviation’ was derived from each set at each temperature and each laboratory. The between-laboratories deviation was similarly derived from an analysis of variance for a three-level nested design allowing for the occasional different number of samples within each laboratory and different number of replicates within each sample on the occasions when the experimental design was not rigidly followed.
130
M. Kent et al.
1.9 3.2
25
40 *
*
0.9
1.4 * *
1.0
4.4 4.0
S
* Negative variance for between samples variation. r, Between replicates standard deviation. s, Between samples standard deviation.
0.9
10
98% Gel
1.4 l-8 3.0
0.8
40
10 25 40
2.3 1-8
r
Lab. 1
10 2.5
Temperature, “C
70% Gel
Glass beads
Sample
0.1
0.1
0.1
0.2 0.1 0.1
0.5
0.5 0.5
r
s
0.1
0.2
0.2
o-2 0.2 0.2
0.5
0.7 O-3
Lab. 2
0.3
0.1
0.3
0.2 0.5 0.3
0.3
0.3 0.3
r
s
*
0.3
*
0.7 0.2 0.6
3.0
3.5 3.0
Lab. 3
3.9
3.5
4.0
4.7 3-1 3.8
2.9
5.5 6.2
s
5.5
*
1-o
2.9 * *
5.7
* 5.3
Lab. 4 r
TABLE 4 Thermal Conductivity Standard Deviations (%)
-
r
Lab. 5
-
-
-
-
-
s
3.5
3.0
5.3
8.8 15.7 15.1
3.5
6.2 4.8
Between labs
w
z. 9 0 2 8 ,a
j
% 1
2 s x x 2
E
;
z 2 % W 2 9 a.
M. Kent et al.
132
TABLE 5 Source
Degrees of jkeedom
Between samples Between replicates within a sample
2 6
Mean square
MSs MSR
Standard deviation estimates were obtained as follows. For each set of nine values at each temperature (three samples X three replicates) the analysis of variance is calculated in the usual way. Details of degrees of freedom, etc., are given in Table 5. The F-value is defined as F = MSs/MSR MS,
is an estimate of the replicates variance UK. MSs includes a contribution from ui as well as a$, the sample variance and is an estimate of 3ai + a$. Therefore, if MSs is less than MS,, F will be less than unity and a spuriously negative estimate for CJ~will result. Such an occurrence indicates that laboratory means are closer than would normally be expected by chance. This can occur for example when data are truncated to give three identical values for replicate measurements. 5.2. Glass beads (see Tables 2,3 and 4) 5.2.1.
Diffusivity
Laboratories 1 and 2 showed good agreement on means, the data from the other two laboratories being more widely distributed around these means. Laboratory 3 was unable to contribute to this measurement. Lower replicate variances led to a low standard deviation of - 2% for Laboratories 1, 2 and 4 whilst those for Laboratory 5 varied between 4% and 5%. Sample variances were negative for Laboratories 2 and 5 leading to non-calculable standard deviations but standard deviations for Laboratories 1 and 4 were 4% and 6% respectively. The betweenlaboratories variances were much greater, standard deviations being 9, 12 and 8% at 10, 2.5 and 40°C respectively.
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133
5.2.2. Conductivity
There was reasonable agreement between most of the laboratories; no standard deviations exceeding 6%. There was a tendency for the variation to decrease both absolutely and relatively with increasing temperature. Laboratory 5 contributed only diffusivity data so is excluded from this comparison. 5.3. Carrageenan gel (70%) water (see Tables 2, 3 and 4) 5.3.1.
Diffusivity
Temperature had some effect on the calculated variances. Laboratory 5 provided no data at 10°C but the other laboratories agreed well at this temperature, laboratory-to-laboratory deviation being only some 3%. At the other two temperatures the inclusion of data from Laboratory 5 which tends to be low and to have higher replicate standard deviations (7-8%) increased the laboratory-to-laboratory variation to lo-14%. Apart from Laboratory 1, no temperature dependence of the replicate variation was discernible in the laboratories. 5.3.2.
Conductivity
Laboratory 4 data were higher than those from all other laboratories, with much higher between replicates deviation than in general (3-S% compared to O.l-3%). It should also be noted that the mean values at each temperature exceed published data for pure water (Powell et al., 1966). Qashou et al. (1972) used pure water data to demonstrate the unreliability of some published food data which with water as the major component should not exceed the value for water itself. For the purposes of this comparative study of reference material the data from Laboratory 4 will be used but Qashou’s criterion will be applied later for selection of reasonable values for food data. Between-laboratory standard deviations range from 9 to 16% over the temperature range. 5.4. Carrageenan gel (98%) water (see Tables 2,3 and 4) 5.4.1. Diffusivity
The four laboratories which provided data at 10°C were in good agreement, the between-laboratories standard deviation being only 2%. At
M. Kent et al.
134
TABLE 6
Grand Means of Thermal Conductivity of 98% Carrageenan Gel Compared to That of Pure Water; Water Values Interpolated from Powell ef al. (1966) Temperature, “C
he, Wm-’ K-’
Standard deviation
h wkr W m-l K-l
10 2.5 40
0.592 0.609 0.645
O-031 0.018 0.022
0.579 0.606 0.627
25°C there is a great increase in this deviation due to Laboratory 4 reporting an abnormally high value and Laboratory 5 being low. The laboratory-to-laboratory deviation at this temperature is 10%. At 40°C this is reduced to 5% indicating more reasonable agreement between laboratories. 5.4.2. Conductivity The problem of unrealistically high values is common to nearly all laboratories in this measurement. This particular material can be thought of as immobilised water and so should have a conductivity comparable with that of pure water. However, given the between-laboratory deviation of 3-5% the overall mean values at each temperature are very close to the expected values (Table 6) which lie within the error limits. Replicate standard deviations were very low being 1% for Laboratories 2 and 3, l-3% for Laboratory 1 and 4% for Laboratory 4.
6. FOOD MATERIALS: 6.1.
RESULTS
AND DISCUSSION
General remarks
Tables 7-16 list the values obtained at each laboratory for thermal conductivity and diffusivity for the foodstuffs listed in Section 4. It was arranged that where possible all laboratories would make at least three measurements at 25°C and the variation calculated for all the data at that temperature would be used as an indication of variation at all
COST 90 collaborative measurements
of thermal properties of foods
135
other temperatures regardless of how many laboratories made measurements at those temperatures. In the case of thermal diffusivity, certain extreme outliers were found and it was considered appropriate to eliminate these from the calculation of mean values. Such exclusions are indicated in the tables. In the case of conductivity no such extreme outliers were identified but nevertheless, using the criterion of Qashou et al. discussed in
2.0
I
L
1
10
,
20
30
40
50
60
70
a0
40
50
60
70
00
“C
t 10
I
1
20
30
I
“C
Fig. 7. Thermal diffusivity’, a, and conductivity, A. versus temperature for yoghurt. Dashed line is based on literature data for pure water. Standard deviation displayed is that computed for all data at 2.5’C.
M. Kent et al.
136
Section 5, those data sets whose means exceeded the published values for pure water at the temperatures concerned were eliminated. Figures 7-l 1 show the grand means of the data versus temperature. Also shown in several graphs is the interpolated thermal conductivity curve for pure water. 6.2. Yoghurt (Tables 7 and 8, Fig. 7) Surprisingly, despite considerations of transport and shelf life, the data for yoghurt are in close accord. The only problem arose from the data provided by Laboratory 4 on conductivity which were excluded as Table 8 shows. This exclusion left no data at 8°C and reduced the set at 25°C to only nine measurements but neither of these were serious shortcomings. The remaining data were of extremely low variation and
TABLE 7 Thermal Diffusivity of Yoghurt (x 10-7mZs-1) 10°C
20°C
25°C
1
1.27 1.36 1.20
1.28 1.36 1.29
1.33 1.38 1.30
2
1.37 1.33 1.37
1.42 1.40 1.44
1.44 1.42 1.46
1.33 1.28 1.38
-
1.41 1.25 1.36
Laboratory
1°C
3
1.28 (2) 1.28 (0) 1.28 (4)
4
_
5
_ _
Mean * standard deviation
1.28 15%
1.32 4.5%
1.40 8.6%
Values in square brackets rejected as outliers.
40°C
50°C
1.30 1.36 1.34
1.45 1,39 1.40
1.46 1.44 1.49
-
_ _
_ _ _
_ _
_ _ -
_
_
_ _ _
_ _
_ _ _
1.46 1.7%
1.33 2.2%
1.43 2.1%
30°C
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137
TABLE 8 Thermal Conductivity of Yoghurt (W m-’ K-l) Laboratory
1°C
10°C
8°C
1
O-550 o-550 0.540
2
0.548 0.543 0.543
3
0.525 (5) O-525 (0) 0.525 (5)
Mean + standard deviation
1
0.525 0.06%
25°C
30°C
O-580 O-580 0.590 0.570 0.570 0.570
0.547 0.545 0.552
01646 0.560 [ 0.690 O-584
4
20°C
0.578 0.579 0.576
40°C 0.600 0.610 O-600
O-587 0.588 0.588
o-570 0.568 0.565 0.665 0.665 0.632
0.632 0.546 0.7%
0.570
0.576 1.3%
0.588 0.1%
0.603 1.O%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculations of the grand means. the temperature (Fig. 7).
dependence
compares
well with that
of pure water
6.3.Whole milk powder (Tables 9 and 10, Figs 8 and 9) The major problem with milk powder lay in the control of its density. Laboratory 2 investigated in more detail the effects of density on thermal conductivity at 25°C and these results are shown in Fig. 9. All measurements made by other laboratories were accompanied by a determination of density as well. Comparison of the data in Table 10 with Fig. 9 shows that all laboratories were working with densities in the range 586-750 kg mV3 and that density in this range seems to have less effect on thermal conductivity than at lower values. The data in
138
M. Kent et al.
Thermal Diffusivity Laboratory
Density, kg me3
TABLE 9 of Milk Powder (1 Om7m2 s-l)
10°C
20°C
-
25°C
40°C
50°C
-
1
586
0.976 0.99 1 1.03
0.999 1.04 1.11
1.09 1.06 1.10
2
591
0.81 0.80 0.83
0.83 0.82 0.85
0.86 0.85 0.87
_
_
690
627 7.8%
1.18 1.09 1.06 0.88 0.88 0.90 -
-
0.676
640
Mean f standard deviation
30°C
0.827 0.80 0.98 0.96
0.906 11.5%
0.904 16.7%
_
0.952 11.9%
1.06 1.16 1.15 0.880 1.4%
1 .l 10 5.6%
1.049 14.8%
-
Fig. 9 appear to depend in a non-linear fashion on density in such a way that for the measurement reported any variation with density would be totally obscured by all other sources of variation. For this reason the results in Fig. 8 are shown without regard to density. Some temperature dependence can be seen. 6.4.
Apple pulp (Tables 11 and 12, Fig. 10)
This material presented some problems for Laboratory 5 in their measurement of diffusivity. Abnormally high results were obtained which may have arisen from the generation of convective currents in the material, though Laboratory 1 with a similar sample configuration had no such problem. Another explanation may be that the upper surface of the sample was not in good contact with the upper heating plate. The conductivity data from Laboratory 4 were also rejected on the comparison with pure water, On the whole this method seemed to
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of thermal properties of foods
139
TABLE 10 Thermal Conductivity of Milk Powder (W rn-’ K-l) Density, kg mV3
10°C
1
586
0.120 0.120 0.110
2
591
o-077 0.078 0.078
3
750
O~lOO(5) O.lOO(7) O.lOO(6) o-099 (9) O.lOO(2) O.lOO(9)
Laboratory
740
4
690
696 698 630 586 615 628 Mean f standard deviation
perform materials 6.5.
65.5 9.3%
20°C
25°C
30°C
40°C
0.130 o-1 20 o-1 30 o-079 O-080 0.080
0.082 0.082 O-082 0.103 (4) 0.103(3) 0.103(4) 0.102(7) 0.102(7) 0.102(3)
50°C
0.150 0.140 0.140 0.084 0.085 0.085 O-106(3) O-106(7) 0.106(4) 0.103(9) 0.105(7) 0*105(5)
0.101 0.117 0.117 0.136 0.118 0.106 0.105 0.099 0.112 0.0987 0.0957 0.1049 0.0847 0.106 14.9% _l9.3% 15.7% 0.7% 1.O%
0.119 0.124 0.124
0.133 9.2%
badly with high moisture foods although with reference the agreement with other laboratories had been better.
Meat paste (Tables 13 and 14, Fig. 11)
There was reasonably good agreement between the laboratories for meat paste, only one set of data being rejected. The diffusivity seems
M. Kent et al.
140
A (WdK-
0.10 i
0.05
I
, 10
20
30
40
50
60
70
80
“C
Fig. 8. Thermal diffusivity, a, and conductivity, X, versus temperature for whole milk powder. Standard deviation displayed is that computed for all data at 25°C.
to have a marked temperature dependence but since only Laboratory 5 measured the material at 75°C the high value recorded at that temperature may be in error because this laboratory showed a marked tendency to produce high results. 6.6. Fish paste (Tables 15 and 16, Fig. 12) Similar comments apply here as to meat paste, the overall moisture contents being approximately the same. However, a large body of conductivity data had to be excluded at 10°C and 50°C. The variability in conductivity for both meat and fish pastes was much larger than for
COST 90 collaborative measurements
of thermal properties of foods
141
1
N 2.5 % f
density
Fig. 9.
103Kg
m3
Variation of thermal conductivity of milk powder with density as measured by Laboratory 2.
TABLE 11 Thermal Diffusivity of Apple Pulp (1 0m7m2 s-‘) Laboratory
10°C
20°C
25°C
40°C
50°C
1
1.36 1.35 1.26
1.33 1.40 1 e32
1.31 ’ 1.48 1.35
1.47 I .50 1.47
l-48 1.55 1.50
2
1.37 1.35 1.38
1.44 1.42 1.46
1.53 1.51 1.55
3
1.46 (7) 1.47 (5) 1.47 (1)
4
0.346 [ 0.839
5
1
1.16
1
1.96 1.98 1.93
[ 1.77 l-80 1 G35 Mean f standard deviation
1.345 3.2%
1,350 3.3%
Values in square brackets rejected as outliers.
1.430 4.3%
1.505 2.1%
1.422 12.4%
142
M. Kent et al. TABLE 12
Thermal Conductivity Laboratory
10°C
of Apple Pulp (W m-l K-l) 20°C
25°C
1
0.540 0.550 0.550
0.590 0.600 0.630
2
0.562 0.562 0.561
o-594 0.593 0.593
40°C
5o”c 0.650 O-640 0.650
0.63 1 0.630 0,630
0.588 (0) 0.588 (7) 0.588 (7) -0.848 0.961 -0.901
1
/ 0.824 0.750 0.780 I 0.556 1.4%
Mean + standard deviation
[O-800] 4.3%
0.596 2.2%
0,630 0.1%
0.647 1 .O%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculation of the grand mean.
yoghurt
handling, laboratory
and
apple
different affecting
This was attributed to difficulties in sample amounts of air possibly being entrapped at each the density and possibly also the contact resistance.
pulp.
7. CONCLUSIONS
The study of potential reference materiak for thermal property measurement has shown that in general the best agreement between laboratories was found with a 98% water carrageenan gel. With this material the between-laboratories standard deviation at 25’C was 9.9% for thermal diffusivity and only 3.0% for conductivity measurements. Conductivity
COST 90 collaborative measurements
I
of thermal properties of foods
143
I
10
20
30
40
50
60
70
00
OC
l.O-
A (wfli’i;’) --•---______.i_----------
___________-..* _..- --------.
0.5-
10
20
30
40
50
60
70
00
OC
Fig. 10.
Thermal diffusivity, a, and conductivity, A, versus temperature for apple pulp. Dashed line is based on literature data for pure water. Standard deviation displayed is that computed for all data at 25’C.
measurements were usually (though not always) more accurate than diffusivity and with this material there is the added advantage of a direct comparison with published values for pure water. The heated probe method of Laboratory 2 gave consistently precise results and this may be due in part, for the measurement of diffusivity in glass beads at least, to compensation for thermal contact resistance between the probe and the sample, a variable ignored by other labora-
144
hf. Kent et al.
TABLE 13 Thermal Diffusivity of Meat Paste (10e7 m2 s-l)
Luboratoly 1
10°C
20°C
1.20 l-18
1.23 1.24
1.15 2
1.24
1.29
1.25
I-35 1.38
1.31 1.29 1.33
1.51 1.40 1.42
1.28 1.29 1.36
1.34 1.33 1.34 1.31 1.31 1.32
4
40°C
1.25 1.29
3
(7) (7) (3) (7) (3) (0)
1.272 2.9%
75°C
1.08 1.47 1.50 1,42
1.177 2.1%
50°C
1.31 (1) 1.33 (1) 1.37 (7)
[0.617]
5
Mean f standard deviation
2s”c
1.382 4.6%
1.60
1.61 1.66 1.325
3.3%
1.424 14.6%
2.14 1.97 2.05 2.053 4.14%
Values in square brackets rejected as outliers.
and which for most of these samples is negligible. The method used by Laboratory 5 was found to be unsuitable for liquid or semiliquid samples. The accuracy of measurement and the degree of agreement reached in this work is remarkable when compared to a similar comparative exercise recently published in which thermal conductivity of steel reference samples had been measured. The seven laboratories involved in that work could not agree to better than 40% (with one laboratory excluded the scatter dropped to 10%) (Goldratt and Greenfield, 1982). The measurement of real food materials as distinct from model systems has also been conducted with such accuracy that the data tories
COST 90 collaborative measurements
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145
TABLE 14 Thermal Conductivity of Meat Paste (W rn-’ K-l) Laboratory 1
IO"C
2o"c
O-458 0.458 0.458
3
o-504 0.498 0.478
0.448 0.458 0.465 0.496 O-496 0.501
1
0.610 O-610 [ 0.610 0.343 7.3%
0.458
50°C 0.450 0.460 0.470
0.487 O-486 0.486 0.487 0.486 0.487
4
Mean + standard deviation
40°C
0.380 0.450 o-430
0.340 0.370 0.320
2
25°C
0.678 O-604 o-571 0.472 7.4%
0.457 1.8%
0.525 14.5%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculation of the grand mean.
presented here can be considered authoritative. The criterion of not exceeding pure water data has enabled more acceptable and reliable values to be presented for conductivity. The data obtained is now available with full composition information for comparison with that obtainable from the predictive equations evaluated in the COST 90 project (van Beek and Veerkamp, 1982; Miles etal.,1983). Examining the objectives described in Section 1, therefore, in the light of the complete collaborative experiments it can be said that all these have been met. The various methods available to us have been
hf. Kent et al.
146
0.5 t
lo
20
30
40
50
t
t
40
50
1
60
70
80
60
70
80
“C
l,O-
A (W&K-‘) 0.5-
tt t
10
20
30
1
“C
Fig. 11. Thermal diffusivity, a, and conductivity. X, versus temperature for meat paste. Standard deviation displayed is that computed for all data at 25°C.
compared as described and the reference materials used have been evaluated, the 98% water carrageenan gel being considered the most suitable. The precision of measurements has been determined and, for this range of temperature, in which phase changes and hence no large latent heat terms were encountered, the heated probe method has been found to give the highest precision. Finally, measurements on food
COST 90 collaborative measurements
147
of thermal properties of foods
TABLE 15 Thermal Diffusivity of Fish Paste (low7 m2 s-l) Laboratory
1
10°C
20°C
25°C
40°C
5o”c
1.25 1.18 1.23
l-25 1.22 l-24
1.26 1-2.5 l-25
1.35 1.34 1.38
1.40 1.41 1.40
1.31 1.29 l-34
1.32 1.30 1.34
l-6 1.33 1.36
2
1.32 1.32 1.36
1.32 1.38 1.35
[0.61] 0.982 1.02 1.01
Mean * standard deviation
0.996 l-04 1.22 1.26 1.22 l-48 1.42 1.42
5
1.22 3.0%
1.180 11.7%
75Y
1.337 5.5%
1.353 1.3%
1.73 1.67 1.64
1.98 1.91 1.90
1.360 15.8%
1.93 2.2%
Values in square brackets rejected as outliers.
materials of various types and compositions further comparison with predictive models.
have been collected
for
ACKNOWLEDGEMENTS Firstly the authors would like to thank the authorities of the countries participating in COST 90 for enabling this work to take place. The project itself was led by Professor Ronald Jowitt and we thank him for his able leadership and guidance during the past few years. Our thanks
M. Kent et
148
al.
TABLE 16
Thermal Conductivity
Laboratory 1
10°C
of Fish Paste (W rn-’ K-‘)
2o”c
0.444 0.430 0.430
2
25°C
40°C
0.430 0.440 0.440 0.478 0.480 0.479
0.483 0.481 0.480
0.440 0.450 0.470 0.495 0.49 1 0.488
0.513 0.513 0.515
0.523 0.528 0.527 0.591 0.59 1 0.59 1 0.6730.797 0.799 0.745 0.696 0.686,
-0.716 0.707 0.712 0.760 0.726 _0.729 _
Mean f standard deviation
0.433 1.4%
0.479 0.2%
50°C
0.477 7.1%
0.49 1 0.8%
0.523 11.5%
Values in square brackets indicate data sets whose mean values exceed the value for pure water at that temperature and are excluded from the calculation of the grand mean.
are due to Princes-Buitoni, Sutherlands Foods, Stokes Bomford (Holdings), Milk Marketing Board and Kennerty Farm Dairies who supplied the samples of food materials for this work and Hercules Ltd. Copenhagen Pectin Co. and the English Glass Co. who supplied the reference materials. Finally, a great deal of this work could not have been achieved without the efforts and advice of the Torry Research Station statistician Gordon Smith who although not appearing as an author devised the strategy of the exercise and contributed all of the statistical analysis.
COST 90 collaborative measurements
of thermal properties of foods
149
2.0I
1.5a (16Wi)
t t
t
10
20
t
1
40
50
60
70
BO
40
50
60
70
80
l.O-
0.5-
I
1
30
1.0
“C
A (wm’d)
i
I
10
1
20
30 9
Fig. 12. Thermal diffusivity, a, and conductivity, A, versus temperature for fish paste. Standard deviation displayed is that computed for all data at 25°C.
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