Journal of Food Engineering 41 (1999) 109±114

www.elsevier.com/locate/jfoodeng

Measurement of thermal conductivity of dairy products

I.H. Tavman a,*, S. Tavman b
a
Dokuz Eyl
ul University, Mechanical Engineering Department, 35100 Bornova, Izmir, Turkey
b
Ege University, Food Engineering Department, 35100 Bornova, Izmir, Turkey
Received 14 July 1997; received in revised form 31 March 1999; accepted 2 April 1999

Abstract
Thermal conductivity of eleven kinds of cheese, four kinds of yogurt and a butter sample has been measured at about 15°C and
30°C. A modi®ed hot wire method was used for thermal conductivity measurements. The e€ect of the water, fat and protein content
on the thermal conductivity has been investigated, the measured thermal conductivity values were linearly dependent on water
content, and inversely dependent on fat and protein contents of the various dairy products. A slight increase in the thermal con-
ductivity with temperature has been noticed for four cheese samples studied over a wider range of temperature, between 4°C and
44°C. Ó 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction water content and temperature was observed. Leiden-

frost (1959) measured the thermal conductivity of the
During processing, all dairy products are heated and condensed milk with a steady-state concentric cylinders
cooled. In order to analyze accurately the rate and method with the sample ®lling the 1 mm annulus be-
amount of heat transfer involved, thermal properties of tween the cylinders. The measurements were done at
the products being processed must be known. There are temperatures varying from 7°C to 87°C for two kinds of
many factors which may a€ect the thermal conductivity milk samples, one with 90% moisture, 7% solids, 3% fat
of foods and food products, e.g., composition, density, content; the other with 50% moisture, 35% solids, 15%
porosity, product temperature, heat treatment and other fat content by weight. The thermal conductivity in-
details of the particular substance. There is a great need creased with increasing water content and temperature.
for thermal conductivity values of dairy products for Konrad and Rambke (1971) worked with whole milk,
processing, preservation and production. The measure- skim milk and cream at di€erent concentrations. A
ment of thermal conductivity of every type of product study by Fernandez-Martin and Montes (1972) included
under every conceivable condition would be an enor- skim milk, half and half milk (10% fat, 10% solids not
mous task, therefore the use of models to predict ther- fat) and whole milk at various concentrations and
mal conductivity using other more easily measured temperatures from 5°C to 75°C. Equations were devel-
properties, such as water content, fat content or density, oped to express thermal conductivity as a function of fat
appears to be the best way to assure the availability of content, solids-not-fat-content, temperature and the ra-
data. Before such models can be generated, considerable tio of fat to solids-not-fat. Artecka, Gogol, Gogol and
data must be collected. Staniszewski (1974) reported the variation of thermal
Many thermal conductivity values are available for conductivity of milk margarine (q ˆ 925 kg/m3 ) with
liquid dairy products in the literature, but very few temperature, between ÿ24°C and 22°C. The thermal
values are encountered for non-liquid dairy products conductivity values are in the range 0.220±0.235 W/m K,
such as cheese and butter. Reidel (1949) measured the minimum being at 0°C. Sweat and Parmelee (1978)
thermal conductivity of whole milk, skimmed milk, used a line heat source probe to measure the thermal
evaporated milk and whey at temperatures varying from conductivity of 28 dairy products and margarines at
2°C to 80°C. An increase of thermal conductivity with 0°C, 20°C and 40°C. The water content of the products
studied ranged from 16.0% to 82.2% by weight, and the
*
Corresponding author. Tel.: +90-232-388-3138; fax: +90-232-388-
fat content ranged from 5.6% to 81.7% by weight, the
7864; e-mail: tavman@textil.ege.edu.tr thermal conductivity values ranged from 0.15 W/m K
0260-8774/99/$ - see front matter Ó 1999 Elsevier Science Ltd. All rights reserved.
PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 0 7 9 - 5
110 I.H. Tavman, S. Tavman / Journal of Food Engineering 41 (1999) 109±114

for whipped margarine at 0°C to 0.54 W/m K for pud- conductivity (ki ) of major pure components of food
ding at 40°C. A linear increase of thermal conductivity products:
with water content expressed as percent by weight has X
been deduced from the experimental results, with a kˆ ki Xiv : …3†
correlation coecient of 0.93:
Thermal conductivity values of each major pure
k ˆ 0:141 ‡ …0:00412  Xwater †; …1† component were expressed by models as a function of
temperature. The thermal conductivity values predicted
whereas, thermal conductivity decreased linearly with
by the model proposed in this study were within 2.91%
fat content, temperature did not appear to be a signi®-
error to the literature values of liquid foods and within
cant factor over the limited temperature range studied.
4.54% error to the experimental values determined from
MacCarthy (1984) measured the e€ective thermal con-
evaporated milk, orange juice and bratwurst sausage.
ductivity of skim milk using a guarded hot plate tech-
The objective of this study was to determine experi-
nique. Values ranged from 0.036 to 0.0109 W/m K in the
mentally the thermal conductivity values of 16 di€erent
temperature range 11.8±49.7°C for bulk densities be-
dairy products and to relate thermal conductivity to
tween 292 and 724 kg/m3 . The e€ective thermal con-
water content, fat content, protein content and tem-
ductivity increased with temperature and with bulk
perature of the sample. Many di€erent samples were
density. More and Prasad (1988) used a steady-state,
tested to broaden the scope of the data.
parallel disk, relative method to determine the thermal
conductivity of whole milk at concentrations from 37%
to 72.4% total solids and temperature range between
40°C and 90°C. The thermal conductivity of milk in- 2. Experimental
creased with rise in temperature and decreased with in-
crease in total solids content and its value varied from 2.1. Dairy product samples
0.278 to 0.491 W/m K. In order to predict the thermal
conductivity of milk from temperature and total solids All dairy products were supplied by PINAR Dairy
content, they proposed an expression developed from Products Inc., Izmir, Turkey and kept refrigerated at
the experimental data. 8°C until tested. Thermal conductivities of eleven types
of cheese, four types of yogurt and one type of butter
k ˆ …0:59 ‡ 0:0012T †…1 ÿ 0:0078 X †; …2† were studied in this research. The composition of all
where, k is the thermal conductivity of the whole milk, X dairy products tested is given in Table 1, as percent by
its total solids percentage (37 < X < 72) and T the tem- weight; the density and pH are given in Table 2. Fat
perature (40 < T < 90°C). content of the samples was determined by GerberÕs
In a more recent study, Reddy and Datta (1994) de- method, and water content with the oven method.
termined the speci®c heat, thermal conductivity, and Protein, carbohydrate and ash contents of the samples
apparent viscosity of milk between concentrations of were determined using AOAC (1990) ocial methods of
40% and 70% and temperatures of 35°C and 65°C. They analysis. It may be noticed that the water content ranges
obtained an expression for the thermal conductivity as from 15.11% to 86.81% and the fat content ranges from
functions of temperature and concentration. 0.19% to 83.59% by weight.
Very few data are found in the literature about
thermal conductivity of yogurt. In the context of Cost 90 2.2. Thermal conductivity measurements
(collaborative measurements of thermal properties of
foods), thermal conductivity and di€usivity of yogurt In our experiments, a Shotherm QTM thermal con-
supplied by Kennerty Farm Dairies, Aberdeen, UK, ductivity meter, produced by Showa Denko K.K. and
were measured by four di€erent laboratories at 6 dif- working with a modi®ed hot wire method, was used for
ferent temperatures from 1°C to 40°C. Results of ther- thermal conductivity measurements of dairy product
mal conductivity measurements ranged from 0.525 W/m samples. A thin straight wire through which a constant
K for 1°C to an average of 0.603 W/m K for 40°C, the electric current is passed generating constant heat (Q)
temperature dependence compares well with published per unit length of wire, per unit time, is placed between
data for pure water (Powell, Ho & Liley, 1966). The two rectangular-shaped materials, (Fig. 1). The ®rst
composition of yogurt used in the measurements was as block is an insulating material of known thermal prop-
follows: 86.2% of water, 4.2% of protein, 1.1% of fat, erties which is a part of the measuring probe and the
1.0% of ash, 7.5% of carbohydrate by weight. second block is the sample rectangular in shape of di-
Choi and Okos (1986) proposed a general model to mensions 10 cm length, 5 cm width and 5 cm height
predict thermal conductivity of food products in a minimum, for which the thermal conductivity has to be
temperature range of ÿ40±150°C. This model was measured. A constant power is supplied to the heater
based on the volume fraction (Xiv ) and the thermal element and the temperature rise DT of the heating wire
 I.H. Tavman, S. Tavman / Journal of Food Engineering 41 (1999) 109±114 111

Table 1
Composition of dairy products used (% by weight)

Product Water Fat Protein Carbohydrate Ash

Butter 15.11 83.59 1.18 0 0.12

Cheddar Cheese 36.00 32.00 25.37 2.56 4.07
Hamburger Cheese 41.00 24.78 20.58 7.80 5.84
Old Kashkaval Cheese 41.00 26.55 26.56 2.01 3.88
Tulum Cheesea 41.00 28.91 24.79 1.54 3.76
Fresh Kashkaval Cheese 43.79 22.75 26.16 4.31 2.99
Mozzarella Cheese 44.35 23.86 26.51 1.96 3.32
Bu€et Kashkaval Cheese 49.84 14.27 31.97 0.56 3.36
Fresh Cream Cheese 56.32 23.54 7.49 10.07 2.58
Labne 69.13 20.94 5.62 3.32 0.99
Low Fat Labne 74.65 10.25 8.99 4.80 1.31
Spreadable Cheese 60.60 16.25 15.38 3.45 4.32
Strained Yogurt 74.23 7.42 9.59 7.45 1.31
Light Yogurt 81.95 1.55 6.90 8.31 1.29
Pasteurized Yogurt 82.48 4.12 5.66 5.60 2.14
Extra Light Yogurt 86.81 0.19 5.98 6.72 0.30
a
A local cheese made of cowÕs milk.

Table 2
Properties of dairy products used

Product Density (kg/m3 ) pH Total solids content (%)

Butter 942.3 4.52 84.89

Cheddar Cheese 1102.0 5.15 64.00
Hamburger Cheese 1114.0 5.60 59.00
Old Kashkaval Cheese 1117.0 5.25 59.00
Tulum Cheese 1110.0 5.21 59.00
Fresh Kashkaval Cheese 1181.7 5.16 56.21
Mozzarella Cheese 1062.4 5.33 55.65
Bu€et Kashkaval Cheese 960.9 5.11 50.16
Fresh Cream Cheese 1014.1 5.38 43.68
Labne 1084.7 4.36 30.87
Low Fat Labne 1085.2 4.41 25.35
Spreadable Cheese 823.8 5.78 39.40
Strained Yogurt 972.1 4.51 25.77
Light Yogurt 1033.1 4.20 18.05
Pasteurized Yogurt 1034.8 4.10 17.52
Extra Light Yogurt 1024.5 4.20 13.19

is measured by a thermocouple and recorded with re- according to the equation given by Carslaw and Jaeger
spect to time during a short heating interval. The ther- (1959):
mal conductivity (k) of the sample is calculated from the
temperature±time (DTÿDt) record and power input (Q) Q ln …t2 =t1 †
kˆF ÿ H; …4†
T2 ÿ T1

where, T1 and T2 are temperatures at times t1 and t2 , Q

the heat ¯ow per unit time, per unit length of the heating
wire, F and H are speci®c constants of the probe to be
determined with materials of known thermal conduc-
tivities. By this method, the thermal conductivity is
measured with an accuracy of ‹ 5% and reproducibility
of ‹ 2%. The time required for each measurement is
Fig. 1. Thermal conductivity measuring probe. about 60 s.
112 I.H. Tavman, S. Tavman / Journal of Food Engineering 41 (1999) 109±114

Table 3
Measured and calculated thermal conductivity values of dairy products

Product k (measured) (W/m K) Standard deviation (W/m K) k (calculated by

Eq. (3) at 15°C)
15°C 30°C 15°C 30°C (W/m K)

Butter 0.227 0.233 0.013 0.009 0.236

Cheddar Cheese 0.345 0.351 0.010 0.001 0.346
Hamburger Cheese 0.381 0.398 0.009 0.005 0.377
Old Kashkaval Cheese 0.368 0.384 0.008 0.007 0.370
Tulum Cheese 0.379 0.377 0.006 0.005 0.368
Fresh Kashkaval Cheese 0.403 0.403 0.009 0.002 0.384
Mozzarella Cheese 0.383 0.380 0.003 0.005 0.384
Bu€et Kashkaval Cheese 0.406 0.409 0.003 0.001 0.413
Fresh Cream Cheese 0.433 0.434 0.005 0.006 0.432
Labne 0.486 0.463 0.007 0.009 0.473
Low Fat Labne 0.548 0.542 0.025 0.010 0.506
Spreadable Cheese 0.476 0.494 0.003 0.016 0.454
Strained Yogurt 0.540 0.539 0.008 0.012 0.510
Light Yogurt 0.571 0.583 0.005 0.004 0.545
Pasteurized Yogurt 0.571 0.593 0.007 0.022 0.543
Extra Light Yogurt 0.584 0.596 0.002 0.003 0.560

3. Results and discussion The similarity of these equations with Eq. (1) from
Sweat and Parmelee for dairy products and margarines
The results of thermal conductivity measurements, in is remarkable.
the solid state, for eleven types of cheese, four types of Fig. 3 illustrates the correlation between thermal
yogurt and one butter sample are given in Table 3. For conductivity and fat content at 15°C. The equations for
each sample, the thermal conductivity is measured ®ve the linear regression lines for the measured thermal
times at average temperatures of 15°C and 30°C, the conductivity versus fat content are as follows:
mean values and the standard deviations are reported. for 15°C : k ˆ 0:5422 ÿ 0:004612Xfat ; R ˆ 0:786; …7†
Fig. 2 illustrates the strong correlation between
thermal conductivity and water content at 15°C for 30°C : k ˆ 0:5483 ÿ 0:004674Xfat ; R ˆ 0:787; …8†
(R ˆ 0.986). The equations for the linear regression lines
where, Xfat is the fat content expressed as percent on a
for the measured thermal conductivity versus water
wet basis.
content are as follows:
There is a general agreement on the qualitative e€ects
for 15°C : k ˆ 0:1696 ‡ 0:00488Xwater ; R ˆ 0:987; …5† of water and protein on the physical properties of cheese
with the casein matrix imparting rigidity and water re-
for 30°C : k ˆ 0:1729 ‡ 0:00491Xwater ; R ˆ 0:969; …6†
ducing rigidity of cheese (Prentice, Langley & Marshall,
where k is the thermal conductivity in W/m K and Xwater 1993). The quantitative contributions of these compo-
the water content expressed as percent on a wet basis. nents, in conjunction with fat, on various properties

Fig. 2. Thermal conductivity versus water content for dairy products. Fig. 3. Thermal conductivity versus fat content for dairy products.
 I.H. Tavman, S. Tavman / Journal of Food Engineering 41 (1999) 109±114 113

have not been characterized thoroughly. In a study conductivity of water increases with temperature, this
conducted by Chen, Larkin, Clark and Irvine (1979) for fact is con®rmed by literature values from Kent et al.
a group of diverse varieties of cheese, a linear correlation (1984).
was obtained between protein content and hardness, Finally, measured thermal conductivity values at
with a correlation coecient of 0.83. Excluding butter, 15°C were compared to those calculated from the Choi
there is a linear decrease of thermal conductivity with and Okos (1986) model, see Table 3. First, the volume
protein content as shown in Fig. 4. The equations for the fraction (Xiv ) of pure components for each sample has
linear regression lines for the measured thermal con- been calculated. Then, the thermal conductivity (ki ) of
ductivity versus protein content are as follows: pure components at 15°C has been calculated using
for 15°C : k ˆ 0:5824 ÿ 0:00752Xprotein ; R ˆ 0:730; …9† equations from Choi and Okos (1986). It may be noticed
from Table 3, that measured thermal conductivity values
for 30°C : k ˆ 0:5861 ÿ 0:00745Xprotein ; R ˆ 0:690; …10† were within ‹ 5% to calculated values, which is ap-
proximately the range of experimental error.
where, Xprotein is the protein content expressed as percent
wet basis.
The e€ect of temperature was not emphasized in this
study as only two temperature levels were included ex- 4. Conclusions
cept for four types of cheese studied over a wider range
of temperature, from 4°C to 44°C (Fig. 5). There is a Thermal conductivity of 16 di€erent dairy products
slight increase in thermal conductivity with temperature were measured at 15°C and 30°C. From this study it
as shown in Fig. 5. For products with high water content may be concluded that thermal conductivity increases
such as yogurts, an increase in thermal conductivity with linearly with increase in water content with a very good
increasing temperature may be expected as the thermal correlation coecient, decreases linearly with increase in
fat and protein contents. From the thermal conductivity
measurements for four types of cheese at temperatures
from 4°C to 44°C, it may be concluded that thermal
conductivity increases slightly with temperature. Fur-
thermore, the measured values were found to be in good
agreement with previous data, especially with data of
similar products from Sweat and Parmelee (1978), and
with the Choi and Okos (1986) model.

Acknowledgements

The authors would like to acknowledge PINAR

Dairy Products Inc. for supplying all the samples for
this work.
Fig. 4. Thermal conductivity versus protein content for dairy prod-
ucts.
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