- Email: [email protected]
Thermal properties of dough and bakery products: A review of published data
Jownal of Food Engineering
9 (1989) 167-193
Thermal Properties of Dough and Bakery Products: A Review of Published Data Christina Rask Department
of Food Engineering,
University of Lund, PO Box 124, S-22 1 00 Lund, Sweden
(Received 27 April 1988; revised version received 23 January 1989; accepted 6 February 1989)
ABSTRACT To date, no summary of the thermal properties of dough, bread and bakery products is available. This review is therefore an attempt to rectify this situation. The aim has not been to evaluate critically the published studies, but rather to give an overview of the literature in this field to facilitate the estimation of values for the properties of a product of known moisture content and density. The thermal properties covered are specific heat, thermal conductivity and thermal di@sivity. These are tabulated together with the moisture content and the density. The properties of dough and bread are plotted versus moisture content and density. Expressions for calculating the thermal properties are both given in the text and tabulated.
NOTATION a
? B
cP C PDM CP
W
CV H N t
Thermal diffusivity (m”/s) Effective thermal diffusivity (m”/s) Constant Constant Specific heat at constant pressure (J/kg K) Specific heat of dry matter (kJ/kg K) Specific heat of water &J/kg K) Specific heat at constant volume (J/kg K) Bread height (m) Dimensionless time step Temperature (“C) 167
of Food Engineering 0260-8774/89/$03.50 Publishers Ltd, England. Printed in Great Britain
Journal
- 0
1989
Elsevier
Science
168
C. Rask
Mean volume temperature (“C) Temperature (K) Volume ( m3) Volume fraction of air Volume fraction of solid matter Volume fraction of water Moisture content on dry basis (kg/kg) Moisture content on wet basis (kg/kg) Thermal conductivity (W/m K) Thermal conductivity of air (W/m K) Effective thermal conductivity (W/m K) Thermal conductivity of solid matter (W/m K) Time-dependent thermal conductivity (W/m K) Thermal conductivity of water (W/m K) Density (kg/m3) Dimensionless time Time (s) Porosity
INTRODUCTION When dough is exposed to a high temperature in an oven, the temperature of the dough surface rises and water from the outer layer evaporates. The moisture content of a bread dough will thus change with time during baking and the crust will contain less water than the interior, i.e. the crumb. The temperatures in the crust and in the crumb are also quite different. Depending on the oven conditions, the crust can reach a temperature of nearly 200°C. The final temperature in the crumb, however, does not exceed 100°C (Tichy, 1974; Auerman, 1977; Kriems & Reinhold, 1980~3; Johnsson & Skjoldebrand, 1984; Rask, in press). Another characteristic change is the increase in volume of the product. This occurs in the initial stage of baking and is mainly due to the expansion of the gas enclosed in the porous dough structure (Auerman, 1977). The pore size in the crust may be very different from that in the crumb, the crust having a more dense structure than the crumb. Accordingly, the thermal properties are different in the dough, the crumb and the crust, and this should be appreciated when measuring and using thermal properties of ‘bread’. Thermal properties for a number of foods may be found in the literature and some comprehensive collections have been published (e.g.
Thermal properties of dough and bakery products
169
Mohsenin, 1980; Rao & Rizvi, 1986; Wallapapan et al., 1986). These collections contain both data and detailed discussions of measurement techniques. Methods were also discussed by Ohlsson (1983) and by Nesvadba (1982). The latter published a critical review of methods for the determination of thermal conductivity and thermal diffusivity including sources of errors connected to the measurements. Equations for estimation of thermal properties have been published by Miles et al. (1983). Despite this, the information regarding thermal properties of dough and bakery products is scarce. This paper therefore aims to give an overview of the published data on thermal properties of such products and to summarize them for engineering purposes. The review might also be of interest as a base for scientists in their future work. In this review, the products have been divided into two groups namely, bread and other bakery products - and the data are given in Tables 1 and 2. Most of the values are extracted from studies which are briefly discussed in the text. Some of the data, however, originate from published tables in which the methods of measurement have not been reported. Some equations for calculating the properties are summarized in Table 3. The review concludes with a comparison of the tabulated values and values calculated from equations given in the text. For a more detailed description of different methods the reader is referred to the collections mentioned above. The properties covered are specific heat, thermal conductivity and thermal diffusivity. Whenever possible, the moisture content and the density of the product are given. In the publications the moisture content is given either on dry or wet basis. In this collection the moisture content is recalculated where necessary and given on wet basis. The recalculated values are marked in the tables. Another inconsistency in the literature is that in some of the publications (Kulacki & Kennedy, 1978; Unklesbay et al., 198 1; Johnsson & Skjoldebrand, 1984) the amount of added water is reported instead of the moisture content of the product. Of course, this makes an evaluation and a comparison more difficult.
BREAD AND BREAD DOUGH Time dependence In two of the published studies (Unklesbay et al. 1981; Bakshi & Yoon, 1984) the relationship between the bread properties and the baking time was determined by interrupting the baking process after certain time intervals and then measuring the properties. One disadvantage with this
Bread rye/wheat 100/O 10 40 O/l00 10 40
Dough
crust
Dough Bread solids Bread smin 1omin Bread crumb
Product
min min min min
30 100 100 150 35
Temperature CC)
0
34” 41 41
33.4’ 26.9 (
Moisture content (%, wet basis)
290d
430d
202 ‘ 181’
Density (k&n-V
1656’ 1500-1900~~
2560 = 2626 ‘
2151.42’ 1951-77’
05-0.6
0.085’ o-093 L
O-386 0.309 ‘
d
Wlm W
(Jlk W 1130.44
Thermal conductivity
Specific heat
TABLE 1 Moisture Content, Density and Thermal Properties of Dough and Bread
24 52d 43d 138
3.67 ‘
40.7
Thermal diffusivity (m’ls) X I@
Kafiev et al. (1987) Kriems and Reinhold (19806)
Johnsson and SkjGldebrand (1984)
Bakshi and Yoon (1984)
Reference
5
n
0
rye
rye Crumb wheat
rye crust wheat
Dough wheat
Bread solids
CNSt
Bread crumb loaf tin loaf
Dough wheat
Dough
18 18 120-160 l-24
28
- 435 - 285 - 22.0 165 23.0 -38 -28 - 16 19 21
450 500
45.9 h
417 443
750 820
402 340 300
623
1100 1100 1100 1100 1100 1100 1100 1100 1100 1100
44.4 h
0 0
44.4 h 45.9 h
41.8 42.8 0 36.6 35.6-37.0
42
43.5 43.5 43.5 43.5 43.5 46.1 46.1 46.1 46-l 46.1
3000
2800
1680 1680
2800 3000
3190 2975 1470-1680 1558 657
2883
1760 1940 2760 1760 1880 2810 -
0.980 0.500 -
0.28 0.315’ 0.37 0.356 (
0.055 0.055
0.5 0.6
0.298 0.244 0.066-0.43
0.414
-
0.460 1.030 -
0880 -
0.920 -
24.7
22.2
7.85 7.39
23.75 24.34
16-22.3 24.2 2.68
13.3-22.2
43.5 ( 16.3’
14.5’ 53.0
47.8 ( 39.5 ‘
Marmheim et al. (1957) Nebelung (1979)
Makljukow and Makljukow (1983)
Lind (1988)
a 3 g
$-
x
i? a
g q P. 2
9
2
2 2 3
Bread rye/wheat Dough wheat
19.16 19.16
44.8 45.1
Thermal dijjksivity (m2/s) X IOY
55.8 0.314 0327
0.361 0.378
0.6 d
(wlm W
Thermal conductivity
46.7 b 2801 2805
1260’ 2516’
30 O-30 3 24
0 44.4 h
dry wet Bread solids
2720-2850 2850
1600’,d
(Jlkg W
Specific heat
44-4.5 48.5
586 629
(Wm-7
Density
Bread white brown Dough
41.7
Moisture content (%, wet basis)
1880-2180
O-100 O-100
Temperature
(“Cl
contd.
Dough
Dough
Product
Table 1 -
Tschubik and Maslow (1973)
Tichy (1974)
Tadano (1987)
Polak (1984)
Neznanova et al. (1978) Ordinanz (1946)
Reference
F ??
n
420 300
0 0
307.3 284.6 275.1 263.6
545 500
718 701
42.5 45.0
53.6 53.9
“Added amount of water as % of total weight. Talculated from moisture content on dry basis (%). (Calculated. “Estimated from diagram. ‘Volumetric specific heat ( Crp ).
Bread loaf tin loaf Crust loaf tin loaf Bread, white 8 min 16 min 24 min 32 min
rye
1675 1675
2742 2805
3023 3027
0.64 f 0.02
0.72 + 0.04 O-67 f 0.02 0.66 * 0.03
0.055 0.041
0.248 0.232
0.407 0.396
8.00
16.66
18.75 18.75
Unklesbay (1981)
et al.
S-
3Y 2. c % %
3 & :
2
55,65,75
KY)
Temperature
41.5’ 40’ 40’ 39’ 39’ 36.5 ‘ 37.5 ( 34’ 35.5 L 50,55,60
4.1” 8.5”
3.15h 353h 3.87 h 2.72 h 255 h
Moisture content (%, wet basis)
“Added amount of water as % of the total weight. Walculated from moisture content on dry basis (%). “Estimated from diamarn.
Yellow cake batter edge l/4 done centre l/4 done edge l/2 done centre l/2 done edge 314 done centre 314 done edge done centre done Tortilla dough
Biscuit dough AACC hard-sweet Biscuit
Cracker
Biscuit
Product
693.5 815’ 815’ 360’ 290’ 265 ’ 265 ( 285’ 300 ( 1102-1173
1252.3 + 17.6 1286.6 + 8.8
(Wm-‘)
Density
2800 298-317
2950
2940 + 170 2804 f 380
0.223 0.239 0.228 0.147 0.195 0.132 0.135 0.119 0.121 0*0366-0.1079
0.405 f 0.022 0.390 f 0.037 0.07 0.16
(wlm W
(‘I& K)
1875.7 1942.7 1934.3 1595-2 1570.1
Thermal conductivity
Specific heat
10.9 8.6 8.6 21.4 16.1 18.5 16.9 15-O 14.3 10.5-30.8
8-12 8-12
Thermal di@sivity (m’/s) X I@
TABLE 2 Moisture Content, Density and Thermal Properties of Bakery Products Other Than Bread
Griffith (1985)
Kulacki and Kennedy (1978) Standing (1974) Sweat (1973)
Hwang and Hayakawa (1979)
Reference
$ *
n
5
Thermal properties of dough and bakery products
175
method is that after short periods of time in the oven the dough has not stabilized and it therefore collapses easily after being taken out of the oven. This affects the accuracy of determination of the volume and hence the density. Unklesbay et al. (1981) measured the moisture loss, the volume, the bulk density, a porosity ratio and the thermal conductivity of white bread loaves baked in tins. Four loaves, in eight replicates, were baked for 8, 16, 24 and 32 min. As a result of the increase in volume and loss of water, the bulk density decreased during the heating. The decrease was most pronounced between 8 and 16 min of baking. A line heat-source probe, described by Sweat and Haugh ( 1974), was used to measure the thermal conductivity. This measurement was performed on bread cooled for 12 h at 20°C. A slight decrease in the thermal conductivity with increased baking time, from 0.72 W/m K to 0.64 W/m K, was registered. The difference, however, could not be verified statistically. Bakshi and Yoon ( 1984) measured the water content, density, specific heat and thermal conductivity of bread rolls baked for 10 min. Samples were removed during baking and the changes related to time of baking. Both the moisture content and the density decreased with heating time and the time dependence was described by the following relationships: Xwh= 41.53 x IO-“‘“lx’ 5 o = 225 x
10-04095
(Oh)
t (hdm3)
The specific heat was measured by a calorimetric method; an indirect method of mixing developed by Hwang and Hayakawa (1979) who stated that the method could be used even at temperatures above the boiling point of water. Bakshi and Yoon, however, did not report the temperature of the samples at their measurements. According to the authors the specific heat of the bread solids was 1130.44 J/kg K. In this case the definition of bread solids is not clear. For the bread rolls the specific heat was a linear function of the moisture content expressed by: CP = 30.56 X,, + 1130.44
(J/kgK)
The thermal conductivity was measured with a line source probe similar to that used by Unklesbay et al. ( 198 1). The change in the thermal conductivity during baking was related to the change in the density and the moisture content. The following regression equation was derived: il = 0.6792 - 0.0551 X,, + 0.0020 p +
0*0009 Xi,, - 0.000024 X,, p
(W/m K)
White bread
Bread crumb Bread crust
Dough wheat 20-90°C
Johnsson and Skjoldebrand (1984)
Mete1 et al. (1986)
Prodr4ct
Bakshi and Yoon (1984)
Reference
Equations for Calculation
w0673S3r,.
/
= 2272.2 - 4,97 T d= -@23+0.178x lo-‘T I, = 1.38 -0.023X,, ,I=0~31-0~82x10-‘X,,+0~13x10-~T a=(15~41+0134~10-‘T)~10-~ a = (2658 - 0*16X,,) X lo-* a=(16*15-0.113x lo-‘X,,,,+O.l26X lo-‘T)X a=(17*65-0.84x lo-“p-0.49X 10-2X,,+0.89~ p
e++ = o,oooo3 le’ a
C,=1.60(1-X,,)t+X,,CvS+1373(1-X,,) C,=2.62(1-X,,)t+X,,Cv1+1263(1-X,,)
Cr, = 3056X,, + 1130.44 A= 0.6792 - 0.055 1X,,,, + 0.002Op + 0.0009X;, b - O.O00024X,,p
X =41_53 x lO~“‘“lX”’ $225 x 10-ll.u~lYsr
Eql4atiorrs
TABLE 3 of Moisture Content, Density, Thermal Properties of Bakery Products
1Omx lo-*T)x
- O.O00024X,,p
10mx
*
e
a
n
Thermal properties of dough and bakery products
-II
177
178
C. Rask
The thermal conductivity was also represented by Poppendiek et al. ( 1966):
by a model proposed
where V,, l?, and V, are the volume fractions and A,, A,, and ;2, are the thermal conductivities of water, solids and air, respectively. The thermal conductivity of unproofed dough, referred to as bread solids, was 0.386 W/m”C, compared with the calculated value of 0.309 W/m”C. The deviation of the calculated values from the measured thermal conductivity in bread rolls was within 5% except for the first 2 min when the deviation was greater due to the collapse of the dough. Neznanova et al. (1978) and Kafiev et al. (1987) have reported on measurement of volumetric specific heat (Crp) and thermal conductivity in bread during baking. The details of the methods are not given in the articles, but are published elsewhere (Ginsburg et d, 1975, 1980). The results were published as diagrams. The study by Neznanova et al. showed the change in thermal conductivity and volumetric specific heat with time of baking. The experiments were made both in a Brabender oven and an infrared (IR) oven. According to the diagrams the initial value of the thermal conductivity was about 0.5-0.6 W/m K and that of the volumetric specific heat 1.6 x lo3 kJ/m3 K. Both the thermal conductivity and the volumetric specific heat decreased rapidly during the first minutes of baking. The thermal conductivity reached a minimum within 3-4 min and then increased to its initial value at the end of baking. The volumetric specific heat continued to decrease and the final value was about 0.5-0.75 x lo3 kJ/m3 K. The graphs also indicate that the properties measured depended on the type of oven. The baking time, defined by the time elapsed before the crumb reached a temperature of 97-98°C was shorter in the IR oven. Similar changes in volumetric specific heat and thermal conductivity were reported by Kafiev et al. (1987). They investigated the effect of additives, such as diacetyl tartaric acid esters of monoglycerides, and one bread improver named Volzski-2. The moisture content, the density and other dough characteristics were not specified so it is difficult to draw any generally useful conclusions about the changes in the thermal properties from these results.
The influence of temperature and moisture content The effect of temperature on thermal diffusivity was studied by Johnsson and Skjiildebrand ( 1984). By means of thermocouples they measured the temperature at specified locations in white bread during baking. The
Thermal properties of dough and bakery products
179
temperature dependence of the thermal diffusivity was calculated using the Fourier equation. The crust was assumed to be a finite slab and the shape of the interior was assumed to be a cylinder. Since mechanisms other than pure conduction were involved in the heating and contributed to the change in temperature, an effective thermal diffusivity was derived. The effective thermal diffusivity of the crust was expressed as: aeff= AeB’“’ In this expression t,, is the mean volume temperature in accordance with Lykow (1955), while A and B are constants. The values of A and B, determined by regression analysis, were stated to be 0*000031 and -0.067383, respectively, with a correlation coefficient of 0.96. The error in the effective thermal diffusivity due to imprecision in the temperature measurements was 0.1 x 10 - 8 m?/s. No calculation of the error due to the accuracy of thickness measurement was given. The authors stated that, for the interior, this model was valid only at temperatures between 30°C and 6O”C, and for this temperature range a constant thermal diffusivity of 40.7 x lop8 m2/s was given. This calculation model thus failed to show the dependence on temperature of the thermal diffusivity within the bread. To determine the specific heat of the crust and the crumb Johnsson and Skjoldebrand (1984) used differential scanning calorimetry (DSC). The measurements were performed at three different water contents (0, 9 and 17% in the crust, and 0,9 and 29% in the crumb). The samples were heated from 17°C to 127°C at a scanning rate of lO”C/min. The DSC measurements are carried out at constant volume, which is indicated in the following equations obtained by linear regression: crust C, = 2*62( 1 - X,,) t +X,,,,, C,,w+ 1263( 1 -X,,) crumb C, = l-60( 1 - X,,) t +XwbCvw + 1373( 1 - X,,,,)
(J/kgK)
(J/kgK)
The specific heat of water was taken as constant, at 4200 J/kg K. However, according to Polak (1984) the temperature dependence of the specific heat of water can be expressed as: C,W=[4~179-0~000217t+0~000013t~].103
(J/kgK)
At a temperature of 32°C which is in the normal temperature range of a dough after proofing, C’,*calculated from the above expression is 4 185 J/kg K. Mohsenin ( 1980) has given a value of 4179 J/kg K at this temperature. At 100°C the specific heat of water is 42 16 J/kg K (Polak), and 4287 J/kg K (Mohsenin). The specific heat of dried doughs at a temperature t”C can, according to Polak ( 1984) be derived from: C,=[1*114+0-00486tl.10” (J/kgK)
180
C. Rask
The mean value over the temperature from:
range 0°C to PC can be calculated
(J/kgK)
CP=[1~114+0~00243t].103 For moist dough the corresponding c,,=[cp”;~~cpw]
relationship .103
is: (J/kgK)
or C,=[(l
-XV,)
cp,,+xvbCp,l.103
(J/kgK)
The influence of moisture content, temperature and density on the thermal conductivity and the thermal diffusivity has been reported by Mete1 et al. (1986). They investigated yeast doughs within the temperature range 20-90°C. The density varied from 480 kg/m3 to 770 kg/m3 and the moisture content from 39.5% to 45%. The expressions, derived by regression anlaysis, are given in Table 3. The thermal conductivity of the solid phase in white bread was investigated by Tadano (1987). The bread was compressed to obtain different degrees of porosity and then freeze dried. An effective thermal conductivity was determined at 3°C and 24°C both before and after drying. Two different methods were used: a hot-wire method and a stationary parallel-plate method. From the measured effective values the thermal conductivity of bread solids was calculated from various seriesparallel models described in the literature. These calculations gave a thermal conductivity of O-361 W/m K and 0,378 W/m K at 3°C and 24”C, respectively. The specific heat has also been measured at low temperatures. Mannheim et al. (1957) not only determined the specific heat of white and whole-wheat bread solids below and above 0°C but also calculated the ice fraction and enthalpy at different temperatures. The bread sample to be tested was packed into a can and cooled to the test temperature (from + 1°C to - 200°C). The can was then put into the calorimeter, i.e. a Dewar flask. Distilled water was used as heat exchange medium and held at a constant temperature of 24°C. The moisture content of the samples was determined by drying. Assuming that the specific heat of bread solids and water, respectively, contributed to the specific heat of the bread in proportion to their mass fractions, the specific heat of bread solids was calculated from the heat balance at a particular moisture content. Based on the observation that the apparent specific heat was constant in the temperature range - 200°C to - 70°C
Thermal properties of dough and bakery products
181
at 657 J/kg K, it was assumed that at - 70°C all the water present was in a frozen state. At - 40°C the fraction of unfrozen water was 11.2% (white bread) and 16.0% (whole-wheat bread), compared with that reported by Pham (1987) of 36.2% in white bread and of 26.5% in whole-wheat bread. The specific heat, the latent heat of fusion, the ice fraction, the thermal conductivity and the thermal diffusivity of non-fermented doughs during thawing were determined by Lind (1988). Differential scanning calorimetry was used for the determination of the specific heat and the latent heat, whilst the transient hot-strip (THS) method according to Gustavsson et al. (1979) was used for the determination of the two other properties. The THS method was difficult to apply to the measurement of thermal diffusivity of dough. Lind therefore also calculated the thermal diffusivity from specific heat, thermal conductivity and density. The THS method could not be used during the phase transition and, in the region of melting, thermal conductivity and thermal diffusivity were calculated from the ice fraction. At - 40°C 35% of the total water was unfrozen. An equation for calculating the enthalpy of low-fat foods has been published by Riedel(1978). The equation, given in Table 3, was valid in the temperature range - 40°C to + 40°C. Modelling of the baking process Tichy (1974) derived a mathematical model of heat and mass transfer during baking. To be able to simulate the course of the temperature and the changes in water content of bread, Tichy used the finite difference method. From the temperature history of the centre of the bread he calculated an equivalent or effective thermal diffusivity (a,,):
where His the height of the bread in metres, r, is the time in seconds and r* is dimensionless time defined as r* = N X 0.00 1524. N is the dimensionless time step; N= O,..., 160. For a fixed rye and wheat bread of 1500 g, Tichy calcualted a mean effective thermal diffusivity of 55.8 x 10e8 m2/s. The total baking time was 55 mm. The method of Tichy has also been used by Kriems and Reinhold (1980a, 1980b). They calculated an equivalent thermal diffusivity after baking times of 10, 20, 30 and 40 min. The calculations were made for rye bread, wheat bread and for bread made from a mixture of rye and
182
C. Rask
wheat in different proportions and the results were given as a function of time and final density. For all breads investigated, there was only a slight increase in the thermal diffusivity between the 10th and 20th minute. The largest increase occurred between the 20th and 30th minute of baking. The final density was largely dependent on the amount of wheat flour present. The greater the proportion of wheat flour the less was the final density, i.e. the greater was the porosity due to a greater increase in volume during baking. The thermal diffusivity ranged from 0.24 X 10e6 m2/s, for rye bread after a baking time of 10 min, to 1.38 X lo-” m2/s, for the wheat bread after 40 min. Thus the thermal diffusivity increased with decreasing density and increasing baking time. The effective thermal diffusivity was also calculated after storage for 24 h at a temperature of 25°C and found to be 125 x lo-* m2/s. It was not reported how this measurement was made, but the fact that the thermal diffusivity in this case was independent of the density, was regarded as evidence of the contribution to heat transfer by steam in the interior of the dough during heating (compare with Nebelung in the next paragraph). A mathematical model describing the baking process has also been prop&ed by Nebelung ( 1979). He used one model for the oven and one for the product. By combining the two, the baking process could be simulated. For the crumb, Nebelung calculated the thermal conductivity with the porosity ( I,V) as a variable:
Thethermal conductivity of the gas in the pores (A,) was assumed to be equal to that of saturated air at 20°C. The porosity was calculated from the difference between the volume of the crumb and the initial volume of the dough.
w,l_b Vtotal
For bread made with wheat flour Nebelung found a porosity of 0.226 and a thermal conductivity of O-315 W/m K. Corresponding values for rye bread were: porosity 0.221 and thermal conductivity 0.356 W/m K. Nebelung stated that during baking the heat was not transferred by conduction alone. Heat transfer by evaporation and condensation of steam must also be taken into account, resulting in an effective thermal conductivity, Leff, consisting of one constant term, Adough,and one timerelated term, jlvap,the latter depending on the evaporation of water in the dough. The effective diffusivity, a,,, was calculated for the whole baking
Thermal properties of dough and bakery products
183
according to:
It was assumed that the mean value of the specific heat was constant while the mean density changed during baking. In this model, &, and hence also jleff were dependent on the external heat transfer. This means that the thermal diffusivity was dependent on both the properties of the product and the conditions in the oven. Nebelung showed this for two different kinds of oven: a laboratory oven and a tunnel oven with several temperature zones. Nebelung ( 1974) has also published thermal property values for dough, crust and crumb. These are mean values taken mainly from the East European literature. The values are listed in Table 1 together with the thermal conductivities of white bread and rye bread calculated from Nebelung’s model.
OTHER BAKERY PRODUCTS Hwang and Hayakawa (1979) have developed a method for measuring the specific heat of highly hygroscopic foods, or samples at a temperature above 100°C. Among the materials tested were crackers and biscuits. The results can be found in Table 2. Hwang and Hayakawa (1980) also developed a method to estimate the bulk density of cookies during baking. Samples were collected from 11 locations in a multi-zone band oven at a local bakery. When corrected for shrinkage, both during and after baking, the density during baking could be correlated to temperature and water content. The following relationship was found for the three different kinds of cookies examined: ~=[Boo+B,~T+B~,Xdb+B,lT.Xdh].lO~
(kg/m3)
The values of the constants ‘B’ had to be determined for each of the cookies. The validity of the relationship has not been tested for other products. To determine the heat transfer in a band oven, Standing (1974) estimated the thermal conductivity in biscuits by measuring the temperature at two locations, 2 and 5 mm from their base. During these measurements the biscuits were heated by conduction from a hot plate. The plate temperature was varied from 159°C to 208°C and the thermal
184
C. Rask
conductivity was calculated from a heat balance over the hot plate and the biscuit. Thus the calculated conductivity included the resistance to heat transfer between the plate and the surface of the product. The thermal conductivity was greater 5 mm from the base (0.16 W/m K) than at a distance of 2 mm (O-07 W/m K). The experiments also indicated that the conductivity decreased at higher plate temperatures. Kulacki and Kennedy (1978) measured the density, the specific heat, the thermal conductivity and the thermal diffusivity of two commercial biscuit doughs (AACC dough and hard-sweet dough). The density was derived by weighing a known volume of dough. The determination was carried out at 25°C and the results appear in Table 2. The specific heat was measured using the method of mixtures at three different temperatures. The tabulated values are the averages of the three values. The thermal conductivity was determined by a single-plate method and was measured at several temperatures in the interval 24-64°C. Because of an unexplainable decrease in the conductivity at the higher temperatures the tabulated values are mean values valid for the lower temperatures only. The thermal diffusivity was calculated from p, CP and each of the L-values. The results were presented in a diagram showing that the thermal diffusivity varied between 8 X and 12 X 10ms m*/s. The thermal conductivity of yellow layer cake was investigated by Sweat (1973). The measurement was carried out on samples of different degrees of bakedness and at different locations in the cake. A thermal conductivity probe was used and the samples were cooled at about 28°C before measurement. Density and moisture content were also measured. In order to calculate the thermal diffusivity Sweat estimated the specific heat of the cake by assuming that CP for the non-water fraction was half of that of water.
During baking the specific heat decreased slightly, from 2950 J/kg K in the batter to 2800 J/kg K at the centre of the fully baked cake. There was a marked decrease in density from about 800 kg/m3 to about 300 kg/m3 at times between one-quarter and one-half of the total baking time. During the same period the thermal conductivity decreased and the thermal diffusivity increased. These changes were more marked at the edge of the cake than at the centre. Griffith (1985) determined density, specific heat, thermal conductivity, and thermal diffusivity of a reconstituted corn-based tortilla dough. In these experiments a transient method was used; a copper cylinder was packed with dough of specified moisture content and the cylinder was heated from the outside. The temperature in the centre of
Thermal properties of dough and bakery products
185
the dough and at the surface was measured by thermocouples. Assuming that heat was transferred by conduction in the dough, Griffith calculated the thermal conductivity and the thermal diffusivity from the slope of the time-temperature curve and the temperature difference between the centre and the surface. The specific heat was derived from the density, the thermal conductivity and the thermal diffusivity. The thermal properties were determined at temperatures of 55°C 65°C and 75°C at moisture contents of 50%, 55% and 60% and for heating times of O-08 h, 0.17 h, 0.25 h and 0.33 h. The results of this investigation illustrated the complex influence of time, moisture content and temperature on the properties. The density and the specific heat were found to be independent of the heating time but dependent on the moisture content. In addition, the specific heat depended on the temperature. The thermal conductivity was influenced by the moisture content as well as the temperature and the heating time. The thermal diffusivity increased with prolonged thermal treatment, and was also dependent on the temperature and the moisture content. Since the pattern of the changes was varying both with temperature and moisture content only the ranges of the values are given in Table 2.
DISCUSSION Density The range of the densities tabulated (Table 1 and 2) is very wide, from about 180 kg/m3 for a white bread to about 1290 kg/m3 for a biscuit dough. East European bread is denser than American bread and rye bread is denser than wheat bread. During baking, the density falls with increasing bread volume and decreasing water content. The bulk density of an intact loaf of bread thus decreases with baking time. However, comparing different parts of the bread it is seen that, although the crust may have a less porous structure, due to the lower water content in the crust its density is less than that of the crumb. The difference in density between the dough and the crumb does not depend on the water content but on the volume expansion occurring during baking. Thus the volume expansion of the crumb results in a decrease in the density, the moisture content being substantially unchanged’ (Table 1: Tschubik & Maslow, 1973; Nebelung, 1979; Makljukow & Makljukow, 1983).
186
C. Rask
Specific heat The specific heat of bread and bread dough varies greatly with the water content. From Table 1 it can be seen that the specific heat of dough and crumb, having about the same moisture content, ranges from 2740 J/kg K to 3030 J/kg K, whereas the specific heat of the drier crust is about 1680 J/kg K. The specific heat of dough reported by Ordinanz (1946) is less than that reported by the other authors. Neither the moisture content nor the method of measurement are given by Ordinanz. Table 2 indicates that the specific heats of other bakery products may be of similar magnitude to that of bread. The specific heat of the biscuits and crackers investigated by Hwang and Hayakawa (1979) is comparable with that of a bread crust and yellow cake (Sweat, 1973), and the specific heat of biscuit dough (Kulacki & Kennedy, 1978) is similar to that of a bread dough. The number of products in Table 2, however, is small compared with the great variety occurring. According to Mohsenin ( 1980) the specific heat of various undried foods is greater than that calculated from the specific heat of the dry solid and the moisture content. This is thought to be an effect of bound water which may have a higher specific heat than free water (Freeman, 1942). Pham (1987) reported an amount of bound water of 9% in white bread at a moisture content of 37.3% wet basis, and of 6.4% in wholewheat bread at a moisture content of 42.4% wet basis. The effect of bound water may also have had influence on the measured specific heat in some of the studies reviewed. Mannheim et al. (1957) assumed that the specific heats of the bread solids and of the water were additive and their calculations gave a value of 15 5 8 J/kg K. This is somewhat greater than the specific heat of dry dough calculated according to Polak (1984), of 1260 J/kg K, of a dry crumb according to Johnsson and Skjoldebrand of about 1400 J/kg K, and of bread solids reported by Bakshi and Yoon (1984), of 1130.44 J/kg K. In the study of Johnsson and Skjoldebrand (1984) the experiments were restricted to water contents of not more than 29% on wet basis although bread doughs as well as crumb have moisture contents of about 45-55% (Table 1). Figure 1 shows the specific heat of bread and dough in relation to the moisture content. The values are taken from those publications cited, in which both the specific heat and the moisture content are given. The specific heat calculated according to Bakshi and Yoon (1984) is also plotted in the figure, as is the specific heat of crumb derived from the expression proposed by Johnsson and Skjoidebrand ( 1984). In the latter calculations the moisture content according to Bakshi and Yoon, and an
Thermal properties of dough and bakery products
187
3.6 3.4 3.2
0
1 3-l
l
0
-w
0
2
2.6
-
2.6
-
2.4
-
01 f
3
r 0 F ‘ii x v)
q
/ vv
i; 2.2
Johnsson
-
& Skj6ldebmnd
V
vvvv
XXX XXX
XX
21.6
Bakshi
& Yoon Xx
-
0 dough +dough 0 crumb A crust
0
20 Moisture
Fig. 1.
40 content
(X
wheat ye
60
wb)
Specific heat of dough, crust, crumb and intact bread as a function of moisture content.
assumed increase of the temperature at the centre of the dough were used. Both curves show that, as baking proceeds and water is lost from the bread, there is a decrease in the specific heat value towards that of the crust. Thermal conductivity Linear expressions for calculating the thermal conductivity of many kinds of food have been suggested by several authors. Miles et al. ( 1983) and Mohsenin (1980) have listed some of these and Mete1 et al. ( 1986) has given linear relationships based on moisture content and temperature of yeast doughs (Table 3). From Table 1 it is seen that the thermal conductivity of dough is about O-4 W/m K, compared with that of water of 0.62 W/m K at 32°C (Mohsenin, 1980), whereas the thermal conductivity of the crumb is about O-3 W/m K and that of the crust is about 0.05 W/m K. In Fig. 2 the thermal conductivity versus moisture content is plotted. The figure also shows the change in the thermal conductivity according to Bakshi and Yoon ( 1984) who related thermal conductivity to moisture content and density during baking. This showed a decrease with decreased moisture content as baking proceeded except for the last few minutes when the
C. Rask
0.6
-
0.5
-
0.4
-
0.3
-
0.2
-
0 + 4 A
dough dough crumb ctwst
wheat rye
X Bakshi
0
20
Fig. 2.
k YoonXXXXX
X
X X ’
40
60
Moisture content (X nb) Thermal conductivity versus moisture content.
conductivity increased. A similar decrease, followed by an increase in thermal conductivity, is reported by Kafiev et al. ( 1987) and Neznanova et al. ( 1978). However, dough and bakery products are porous materials in which the degree of porosity and the orientation of the pores must be considered. A plot of thermal conductivity versus density, as in Fig. 3, shows that, the lower the density of a dough or a crumb, the lower the thermal conductivity. The accuracy of models such as that proposed by Bakshi and Yoon (1984) is highly dependent on the accuracy of The authors claimed that their measurement of the density. measurements failed for samples baked for 1 min and 2 min. However, comparison of values estimated from their equation deviate approximately 10 kg/m3 (5%) from those measured after baking times of 7 mm and10min. When measuring thermal conductivity of dough and moist products, moisture migration may occur and should be kept at a minimum. The time of measuring should therefore be as short as possible and a transient method is recommended (Mohsenin, 1980; Nesvadba, 1982; Ohlsson, 1983). Others errors to consider arise from the insertion, of a probe into an unstable structure, as in doughs and partly baked products, since this may rupture the structure close to the probe giving rise to false values.
Thermal properties of dough and bakery products
189
0.8
0.7
-
0.6
-
0.5
-
Unklssboy
et al. V
V$ +
0
0 0
0.4
q
-
++
0
0.3
-
0.2
-
no
0
0
0
Bakshf 0.1
0
0
k Yoon;
-
%I#
I
I
0
0.2
I
I
I
0.4
I
I
0.6 Density
Fig. 3.
wheat rye
AA
A 0
0 dough +dough 0 crumb A crust
(kg/m)xlO
Thermal conductivity
I 0.8
I
I 1
I 1.2
-3
versus density.
The work by Lind ( 1988) shows that at temperatures below the initial freezing point ( - 25°C) the thermal conductivity of non-fermented dough is about 0.9-1.0 W/m K and above the freezing point it is about 0.5 W/m K. To calculate the heat transfer during baking a value for an ‘effective’ thermal conductivity which includes other mechanisms of heat transfer, is needed (Nebelung, 1979; de Vries et al., in press). De Vries et al. calculated the change in temperature of a dough during baking. They assumed a model in which heat is transferred by conduction in the liquid dough phase and by evaporation and condensation in the gas phase. With these assumptions the calculated changes in temperature agreed better with measured values than calculations based on conduction alone. A thermal conductivity of 0.33 W/m K and a heat capacity according to Johnsson and Skjoldebrand (1984) were used. Thermal diffusivity Most of the values reported for thermal diffusivity are derived from density, specific heat and thermal conductivity. The accuracy is therefore dependent on the accuracy of these three properties. Figure 4 shows the thermal diffusivity of bread and dough versus density. As with the other
C. Rask 160 150
-
140 130
-
120
-
110
-
100
-
90
-
60
-
70
qdough
V
;: p;;: A crust V effectb
wheat rya diffusivity
-I
60 50 40 30 20
EJ
10 I 0
I 0.1
I
A
I
0.3
I
I Density
Fig. 4.
1
0.5
I 0.7
I
1 0.9
I
1 1.1
(kg/m)xl$
Thermal diffusivity versus density.
the thermal diffusivity is lower in the crust thermal properties, (3-8 X 10ex m*/s) than in the crumb or in the dough (15-25 X 10e8 m*/s). At temperatures below - 16°C the thermal diffusivity is 40-50 x lop8 m*/s (Lind, 1988). The values of Johnsson and Skjoldebrand of 40.7 X 10Vx m*/s, Kriems and Reinhold of 24-138 x 10ex m*/s, and Tichy of 55.8 x lo-’ m*/s are effective thermal diffusivities which include other mechanisms of heat transfer than pure conduction. Migration of vapor is a probable explanation of the increase in thermal diffusivity noted after the longer times of heating (Griffith, 1985). Other factors influencing the results of Griffith may be structural changes, the water-holding capacity and the length of the heating time. The dough was dried, tied and re-wetted to actual moisture content. The question arises, therefore, as to how this preparation influenced the dough structure and whether this dough had properties comparable with a fresh dough. Dickerson ( 1965) described a similar method of measuring the thermal diffusivity of foods. He claimed that in order to eliminate the initial transient a certain lag time is needed. The following relationship was found:
Thermalproperties of dough and bakery products
191
where a is thermal diffusivity in square inches per minute (1 inch = 2.5 cm), r is time in minutes, and r is radius in inches. In the study by Griffith this criterion was fulfilled only after a heating time of 20 min.
CONCLUSION During baking the dough characteristics change considerably. Attempts have been made to follow the baking in order to evaluate these changes, but so far no complete study has been published. However, as a first estimate, the thermal properties in Figs l-4 and Tables 1 and 2 can be used. If the circumstances call for better accuracy the thermal properties must be measured in each individual case. Another possibility, not discussed in this article, is to calculate the thermal properties by means of a computer program such as COSTHERM (available from M. Kent, Torry Research Station, Aberdeen - ed) (Miles et al., 1983).
ACKNOWLEDGEMENTS The author’s thanks are expressed to Vassilis Gekas who translated most of the Russian articles, and to STU, the National Swedish Board for Technical Development, for financial support.
REFERENCES Auerman, L. Ja. (1977). Technofogie der Brotherstellung. VEB Fachbuchverlag, Leipzig (in German). Bakshi, A. S. & Yoon, J. (1984). Thermophysical properties of bread rolls during baking. Lebensmittel - Wissenschafi und - Technology, 17,90-3. De Vries, U., Sluimer, P. & Bloksma, A. H. (in press). A quantitative model for heat transport in dough and crumb during baking. International Symposium on Cereal Science and Technology in Sweden, 13-16 June 1988, Ystad, Sweden. Dickerson, R. W. Jr. (1965). An apparatus for the measurement of thermal diffusivity of foods. Food Technology, 19,198-204. Freeman, M. E. (1942). Heat capacity and bound water in starch suspension. Archives of Biochemistry, 1,27-39.
Ginsburg, A. S., Gromov, Thermo-physical
Promyshlennost,
M. A., Kracovskaya,
Properties of Food Products Moscow (in Russian).
G. I. & Ukolov, V. S. (1975). and Materials. Pishchevaya
192
C. Rask
Ginsburg, A. S., Gromov, M. A. & Kracovskaya, G. I. (1980). Thermo-physical Properties of Food Products. Pishchevaya Promyshlennost, Moscow (in Russian). Griffith, C. L. (1985). Specific heat, thermal conductivity, density, and thermal diffusivity of Mexican tortillas dough. Journal of Food Science, 50 (5), 1333-7. Gustavsson, S. E., Karawacki, E. & Khan, M. N. (1979). Transient hot-strip method for simultaneously measuring thermal conductivity and thermal diffusivity of solids and fluids. Journal of Physics,D: Applied Physics,Vol. 12. Hwang, M. P. & Hayakawa, K.-I. (1979). A specific heat calorimeter for foods. Journal of Food Science, 44,435-8,448. Hwang, M. P. & Hayakawa, K.-I. ( 1980). Bulk density of cookies undergoing commercial baking processes. Journal of Food Science, 45 (5), 1400-2,1407. Johnsson, C. & Skjoldebrand, C. (1984). Thermal properties of bread during baking. In Engineering of Food, Vol. 1, ed. B. M. McKenna. Elsevier Applied Science Publishers, London. Kafiev, N. M., Lekhter, A. E., Leites, R. Ya., Klokacheva, 0. A., Panin, A. S., Ribakov, A. A. & Didenko, I. A. (1987). Thermophysical characteristics of certain bread dough improvers. MaslozhirovayaPromyshlennost, 1, 20- 1 (in Russian). Kriems, P. & Reinhold, M. (1980a). Das Backen von Mischbrot (V) Warmeubertragung, Temperaturkinetik-. Bicker und Konditor, 34 ( 11), 34 l-6 (in German). Kriems, P. & Reinhold, M. (1980b). Das Backen von Mischbrot (VI) Schlussfolgerungen zur Verbesserung des Backeffektes und der Brotqualitat, Zusammenfassung-. Backer und Konditor, 34 ( 12), 356-9 (in German). Kulacki, F. A. & Kennedy, S. C. (1978). Measurement of the thermo-physical properties of common cookie dough. Journal of Food Science, 43,380-4. Lind, I. (1988). Thawing of minced meat and dough: Thermal data and mathematical modelling. In Progress in Food PreservationProcesses, Vol. 1, 12-14 April, CERIA, Brussels. Lykow, A. W. ( 1955). Experimentelle und Theoretische Grundlagen des Trocknung. VEB Verlagtechnik, Berlin (in German). Makljukow, I. I. & MakIjukow, W. I. (1983). Thermophysikalische Charakteristika fur das Backstiick. In Industrieiifender Backwarenproduktion.Verlag Leicht- und Lebensmittelindustrie, Moskau (in Russian) (Translated by H.-D. Tscheuschner). Mannheim, H. C., Steinberg, M. P., Nelson, A. I. & Kendall, T. W. (1957). The heat content of bread. Food Technology, 7,384-g. Metel, S. N., Mikrukov, V V. & Kasparov, M. N. (1986). Thermophysical characteristics of yeast dough. Izvestiga Vysshikh Uchebnykh Zavedenii, PishcshevayaTeknologiya,4, 107-8 (in Russian). Miles, C. A., Van Beek, G. & Veerkamp, C. H. (1983). Calculations of thermophysical properties of foods. In: Physical Properties of Foods, Vol. 1, ed. R. Jowitt, et al. Applied Science Publishers, London. Mohsenin, N. N. ( 1980). Thermal Properties of Foods and AgriculturalMaterials. Gordon & Breach Science Publishers, New York. Nebelung, M. (1979). Model der Warmeiibertragung in kontinuerlich und
Thermal properties of dough and bakery products
193
diskontinuerlich arbeitenden Kammerofen unter beriicksichtigung von Warmeleitung, Stofftransport und Reaktionen in einem feuchten kapillarporosen Korper (Backprozess). PhD thesis, TU Dresden, DDR. Nesvadba, P. ( 1982). Methods for the measurement of thermal conductivity and diffusivity of foodstuffs. Journal ofFood Engineering, 1,93-l 13. Neznanova, N. A., Panin, A. C., Puchova, L. L. & Skverchak, V. D. (1978). Thermophysical properties of dough and bread from grade I wheat flour during baking. Khlebopekarnaya i Konditerskaya Promyshlennost, 8 13- 14 (in Russian). Ohlsson, T. (1983). The measurement of thermal properties. In Physical Properties of Foods, Vol. 1, ed. R. Jowitt et al. Applied Science Publishers, London. Ordinanz, W. 0. ( 1946). Specific heats of foods in cooking. Food Industries, 18 (12), 101. Pham, Q. T. ( 1987). Calculation of bound water in frozen food. Journal of Food Science, 52 (l), 210-12. Polak, M. (1984). Specific heat capacity of dough. Mlynsko- Pekarensky Prumysl, 30 (2), 42-4 (Czech). Poppendiek, H. F., Randall, R., Breeden, J. A., Chambers, J. E. & Murphy, J. R. ( 1966). Thermal conductivity measurements and predictions for biological fluids and tissues. Cryobiology, 3,318-27. Rao, M. A. & Rizvi, S. S. H. (1986). Engineering Properties of Foods. Marcel Dekker, Inc., New York. Rask, C. (in press). The heat transfer in a convection oven: Influences on some product characteristics. International Symposium on Cereal Science and Technology in Sweden, 13- 16 June 1988, Ystad, Sweden. Riedel, L. (1978). Eine Formel Zur Bereclmung der Enthalpie fettarmer Lebensmittel in Ablrangigkeit von Wassergehalt und Temperatur. Chem Mikrobiol Technol Lebensm,
5,129-33.
Standing, C. N. (1974). Individual heat transfer modes in band oven biscuit baking. Journal of Food Science, 39,267-7 1. Sweat, V. E. ( 1973). Experimental measurement of the thermal conductivity of a yellow cake. Proceedings of the XIIJth International Conference on Thermal Conductivity, University of Missouri-Rolla, Nov. 1973, pp. 213-16. Sweat, V. E. & Haugh, C. G. ( 1974). A thermal conductivity probe for small food samples. Transactions of the ASAE, 17 ( 1). 56-8. Tadano, T. ( 1987). Thermal conductivity of white bread. Bulletin of the College of Agricultural and Veterinary Medicine, (44), 18-22 (in Japanese). Tichy, 0. ( 1974). Matematick’y model sdilem tepla a hmoty pri peceni. Potravinarska a Chladici Technika, 5 (l), 20-7 (in Czech). Tschubik, I. A. & Maslow, A. M. (1973). Wiirmephysikalische Konstanten von Lebensmitteln und Hatbfabrikaten. VEB Fachbuchverlag, Leipzig, p. 28 (in German). Unklesbay, N., Unklesbay, K., Nahaisi, M. & Krause, G. (1981). Thermal conductivity of white bread during convective heat processing. Journal of Food Science, 47,249-53,259.
Wallapapan, K., Sweat, V. E., Diel, K. C. & Engler, C. R. (1986). Thermal properties of porous foods. In Physical and Chemical Properties of Food, ed. M. R. Okos. American Society of Agricultural Engineers, Michigan.
9 (1989) 167-193
Thermal Properties of Dough and Bakery Products: A Review of Published Data Christina Rask Department
of Food Engineering,
University of Lund, PO Box 124, S-22 1 00 Lund, Sweden
(Received 27 April 1988; revised version received 23 January 1989; accepted 6 February 1989)
ABSTRACT To date, no summary of the thermal properties of dough, bread and bakery products is available. This review is therefore an attempt to rectify this situation. The aim has not been to evaluate critically the published studies, but rather to give an overview of the literature in this field to facilitate the estimation of values for the properties of a product of known moisture content and density. The thermal properties covered are specific heat, thermal conductivity and thermal di@sivity. These are tabulated together with the moisture content and the density. The properties of dough and bread are plotted versus moisture content and density. Expressions for calculating the thermal properties are both given in the text and tabulated.
NOTATION a
? B
cP C PDM CP
W
CV H N t
Thermal diffusivity (m”/s) Effective thermal diffusivity (m”/s) Constant Constant Specific heat at constant pressure (J/kg K) Specific heat of dry matter (kJ/kg K) Specific heat of water &J/kg K) Specific heat at constant volume (J/kg K) Bread height (m) Dimensionless time step Temperature (“C) 167
of Food Engineering 0260-8774/89/$03.50 Publishers Ltd, England. Printed in Great Britain
Journal
- 0
1989
Elsevier
Science
168
C. Rask
Mean volume temperature (“C) Temperature (K) Volume ( m3) Volume fraction of air Volume fraction of solid matter Volume fraction of water Moisture content on dry basis (kg/kg) Moisture content on wet basis (kg/kg) Thermal conductivity (W/m K) Thermal conductivity of air (W/m K) Effective thermal conductivity (W/m K) Thermal conductivity of solid matter (W/m K) Time-dependent thermal conductivity (W/m K) Thermal conductivity of water (W/m K) Density (kg/m3) Dimensionless time Time (s) Porosity
INTRODUCTION When dough is exposed to a high temperature in an oven, the temperature of the dough surface rises and water from the outer layer evaporates. The moisture content of a bread dough will thus change with time during baking and the crust will contain less water than the interior, i.e. the crumb. The temperatures in the crust and in the crumb are also quite different. Depending on the oven conditions, the crust can reach a temperature of nearly 200°C. The final temperature in the crumb, however, does not exceed 100°C (Tichy, 1974; Auerman, 1977; Kriems & Reinhold, 1980~3; Johnsson & Skjoldebrand, 1984; Rask, in press). Another characteristic change is the increase in volume of the product. This occurs in the initial stage of baking and is mainly due to the expansion of the gas enclosed in the porous dough structure (Auerman, 1977). The pore size in the crust may be very different from that in the crumb, the crust having a more dense structure than the crumb. Accordingly, the thermal properties are different in the dough, the crumb and the crust, and this should be appreciated when measuring and using thermal properties of ‘bread’. Thermal properties for a number of foods may be found in the literature and some comprehensive collections have been published (e.g.
Thermal properties of dough and bakery products
169
Mohsenin, 1980; Rao & Rizvi, 1986; Wallapapan et al., 1986). These collections contain both data and detailed discussions of measurement techniques. Methods were also discussed by Ohlsson (1983) and by Nesvadba (1982). The latter published a critical review of methods for the determination of thermal conductivity and thermal diffusivity including sources of errors connected to the measurements. Equations for estimation of thermal properties have been published by Miles et al. (1983). Despite this, the information regarding thermal properties of dough and bakery products is scarce. This paper therefore aims to give an overview of the published data on thermal properties of such products and to summarize them for engineering purposes. The review might also be of interest as a base for scientists in their future work. In this review, the products have been divided into two groups namely, bread and other bakery products - and the data are given in Tables 1 and 2. Most of the values are extracted from studies which are briefly discussed in the text. Some of the data, however, originate from published tables in which the methods of measurement have not been reported. Some equations for calculating the properties are summarized in Table 3. The review concludes with a comparison of the tabulated values and values calculated from equations given in the text. For a more detailed description of different methods the reader is referred to the collections mentioned above. The properties covered are specific heat, thermal conductivity and thermal diffusivity. Whenever possible, the moisture content and the density of the product are given. In the publications the moisture content is given either on dry or wet basis. In this collection the moisture content is recalculated where necessary and given on wet basis. The recalculated values are marked in the tables. Another inconsistency in the literature is that in some of the publications (Kulacki & Kennedy, 1978; Unklesbay et al., 198 1; Johnsson & Skjoldebrand, 1984) the amount of added water is reported instead of the moisture content of the product. Of course, this makes an evaluation and a comparison more difficult.
BREAD AND BREAD DOUGH Time dependence In two of the published studies (Unklesbay et al. 1981; Bakshi & Yoon, 1984) the relationship between the bread properties and the baking time was determined by interrupting the baking process after certain time intervals and then measuring the properties. One disadvantage with this
Bread rye/wheat 100/O 10 40 O/l00 10 40
Dough
crust
Dough Bread solids Bread smin 1omin Bread crumb
Product
min min min min
30 100 100 150 35
Temperature CC)
0
34” 41 41
33.4’ 26.9 (
Moisture content (%, wet basis)
290d
430d
202 ‘ 181’
Density (k&n-V
1656’ 1500-1900~~
2560 = 2626 ‘
2151.42’ 1951-77’
05-0.6
0.085’ o-093 L
O-386 0.309 ‘
d
Wlm W
(Jlk W 1130.44
Thermal conductivity
Specific heat
TABLE 1 Moisture Content, Density and Thermal Properties of Dough and Bread
24 52d 43d 138
3.67 ‘
40.7
Thermal diffusivity (m’ls) X I@
Kafiev et al. (1987) Kriems and Reinhold (19806)
Johnsson and SkjGldebrand (1984)
Bakshi and Yoon (1984)
Reference
5
n
0
rye
rye Crumb wheat
rye crust wheat
Dough wheat
Bread solids
CNSt
Bread crumb loaf tin loaf
Dough wheat
Dough
18 18 120-160 l-24
28
- 435 - 285 - 22.0 165 23.0 -38 -28 - 16 19 21
450 500
45.9 h
417 443
750 820
402 340 300
623
1100 1100 1100 1100 1100 1100 1100 1100 1100 1100
44.4 h
0 0
44.4 h 45.9 h
41.8 42.8 0 36.6 35.6-37.0
42
43.5 43.5 43.5 43.5 43.5 46.1 46.1 46.1 46-l 46.1
3000
2800
1680 1680
2800 3000
3190 2975 1470-1680 1558 657
2883
1760 1940 2760 1760 1880 2810 -
0.980 0.500 -
0.28 0.315’ 0.37 0.356 (
0.055 0.055
0.5 0.6
0.298 0.244 0.066-0.43
0.414
-
0.460 1.030 -
0880 -
0.920 -
24.7
22.2
7.85 7.39
23.75 24.34
16-22.3 24.2 2.68
13.3-22.2
43.5 ( 16.3’
14.5’ 53.0
47.8 ( 39.5 ‘
Marmheim et al. (1957) Nebelung (1979)
Makljukow and Makljukow (1983)
Lind (1988)
a 3 g
$-
x
i? a
g q P. 2
9
2
2 2 3
Bread rye/wheat Dough wheat
19.16 19.16
44.8 45.1
Thermal dijjksivity (m2/s) X IOY
55.8 0.314 0327
0.361 0.378
0.6 d
(wlm W
Thermal conductivity
46.7 b 2801 2805
1260’ 2516’
30 O-30 3 24
0 44.4 h
dry wet Bread solids
2720-2850 2850
1600’,d
(Jlkg W
Specific heat
44-4.5 48.5
586 629
(Wm-7
Density
Bread white brown Dough
41.7
Moisture content (%, wet basis)
1880-2180
O-100 O-100
Temperature
(“Cl
contd.
Dough
Dough
Product
Table 1 -
Tschubik and Maslow (1973)
Tichy (1974)
Tadano (1987)
Polak (1984)
Neznanova et al. (1978) Ordinanz (1946)
Reference
F ??
n
420 300
0 0
307.3 284.6 275.1 263.6
545 500
718 701
42.5 45.0
53.6 53.9
“Added amount of water as % of total weight. Talculated from moisture content on dry basis (%). (Calculated. “Estimated from diagram. ‘Volumetric specific heat ( Crp ).
Bread loaf tin loaf Crust loaf tin loaf Bread, white 8 min 16 min 24 min 32 min
rye
1675 1675
2742 2805
3023 3027
0.64 f 0.02
0.72 + 0.04 O-67 f 0.02 0.66 * 0.03
0.055 0.041
0.248 0.232
0.407 0.396
8.00
16.66
18.75 18.75
Unklesbay (1981)
et al.
S-
3Y 2. c % %
3 & :
2
55,65,75
KY)
Temperature
41.5’ 40’ 40’ 39’ 39’ 36.5 ‘ 37.5 ( 34’ 35.5 L 50,55,60
4.1” 8.5”
3.15h 353h 3.87 h 2.72 h 255 h
Moisture content (%, wet basis)
“Added amount of water as % of the total weight. Walculated from moisture content on dry basis (%). “Estimated from diamarn.
Yellow cake batter edge l/4 done centre l/4 done edge l/2 done centre l/2 done edge 314 done centre 314 done edge done centre done Tortilla dough
Biscuit dough AACC hard-sweet Biscuit
Cracker
Biscuit
Product
693.5 815’ 815’ 360’ 290’ 265 ’ 265 ( 285’ 300 ( 1102-1173
1252.3 + 17.6 1286.6 + 8.8
(Wm-‘)
Density
2800 298-317
2950
2940 + 170 2804 f 380
0.223 0.239 0.228 0.147 0.195 0.132 0.135 0.119 0.121 0*0366-0.1079
0.405 f 0.022 0.390 f 0.037 0.07 0.16
(wlm W
(‘I& K)
1875.7 1942.7 1934.3 1595-2 1570.1
Thermal conductivity
Specific heat
10.9 8.6 8.6 21.4 16.1 18.5 16.9 15-O 14.3 10.5-30.8
8-12 8-12
Thermal di@sivity (m’/s) X I@
TABLE 2 Moisture Content, Density and Thermal Properties of Bakery Products Other Than Bread
Griffith (1985)
Kulacki and Kennedy (1978) Standing (1974) Sweat (1973)
Hwang and Hayakawa (1979)
Reference
$ *
n
5
Thermal properties of dough and bakery products
175
method is that after short periods of time in the oven the dough has not stabilized and it therefore collapses easily after being taken out of the oven. This affects the accuracy of determination of the volume and hence the density. Unklesbay et al. (1981) measured the moisture loss, the volume, the bulk density, a porosity ratio and the thermal conductivity of white bread loaves baked in tins. Four loaves, in eight replicates, were baked for 8, 16, 24 and 32 min. As a result of the increase in volume and loss of water, the bulk density decreased during the heating. The decrease was most pronounced between 8 and 16 min of baking. A line heat-source probe, described by Sweat and Haugh ( 1974), was used to measure the thermal conductivity. This measurement was performed on bread cooled for 12 h at 20°C. A slight decrease in the thermal conductivity with increased baking time, from 0.72 W/m K to 0.64 W/m K, was registered. The difference, however, could not be verified statistically. Bakshi and Yoon ( 1984) measured the water content, density, specific heat and thermal conductivity of bread rolls baked for 10 min. Samples were removed during baking and the changes related to time of baking. Both the moisture content and the density decreased with heating time and the time dependence was described by the following relationships: Xwh= 41.53 x IO-“‘“lx’ 5 o = 225 x
10-04095
(Oh)
t (hdm3)
The specific heat was measured by a calorimetric method; an indirect method of mixing developed by Hwang and Hayakawa (1979) who stated that the method could be used even at temperatures above the boiling point of water. Bakshi and Yoon, however, did not report the temperature of the samples at their measurements. According to the authors the specific heat of the bread solids was 1130.44 J/kg K. In this case the definition of bread solids is not clear. For the bread rolls the specific heat was a linear function of the moisture content expressed by: CP = 30.56 X,, + 1130.44
(J/kgK)
The thermal conductivity was measured with a line source probe similar to that used by Unklesbay et al. ( 198 1). The change in the thermal conductivity during baking was related to the change in the density and the moisture content. The following regression equation was derived: il = 0.6792 - 0.0551 X,, + 0.0020 p +
0*0009 Xi,, - 0.000024 X,, p
(W/m K)
White bread
Bread crumb Bread crust
Dough wheat 20-90°C
Johnsson and Skjoldebrand (1984)
Mete1 et al. (1986)
Prodr4ct
Bakshi and Yoon (1984)
Reference
Equations for Calculation
w0673S3r,.
/
= 2272.2 - 4,97 T d= -@23+0.178x lo-‘T I, = 1.38 -0.023X,, ,I=0~31-0~82x10-‘X,,+0~13x10-~T a=(15~41+0134~10-‘T)~10-~ a = (2658 - 0*16X,,) X lo-* a=(16*15-0.113x lo-‘X,,,,+O.l26X lo-‘T)X a=(17*65-0.84x lo-“p-0.49X 10-2X,,+0.89~ p
e++ = o,oooo3 le’ a
C,=1.60(1-X,,)t+X,,CvS+1373(1-X,,) C,=2.62(1-X,,)t+X,,Cv1+1263(1-X,,)
Cr, = 3056X,, + 1130.44 A= 0.6792 - 0.055 1X,,,, + 0.002Op + 0.0009X;, b - O.O00024X,,p
X =41_53 x lO~“‘“lX”’ $225 x 10-ll.u~lYsr
Eql4atiorrs
TABLE 3 of Moisture Content, Density, Thermal Properties of Bakery Products
1Omx lo-*T)x
- O.O00024X,,p
10mx
*
e
a
n
Thermal properties of dough and bakery products
-II
177
178
C. Rask
The thermal conductivity was also represented by Poppendiek et al. ( 1966):
by a model proposed
where V,, l?, and V, are the volume fractions and A,, A,, and ;2, are the thermal conductivities of water, solids and air, respectively. The thermal conductivity of unproofed dough, referred to as bread solids, was 0.386 W/m”C, compared with the calculated value of 0.309 W/m”C. The deviation of the calculated values from the measured thermal conductivity in bread rolls was within 5% except for the first 2 min when the deviation was greater due to the collapse of the dough. Neznanova et al. (1978) and Kafiev et al. (1987) have reported on measurement of volumetric specific heat (Crp) and thermal conductivity in bread during baking. The details of the methods are not given in the articles, but are published elsewhere (Ginsburg et d, 1975, 1980). The results were published as diagrams. The study by Neznanova et al. showed the change in thermal conductivity and volumetric specific heat with time of baking. The experiments were made both in a Brabender oven and an infrared (IR) oven. According to the diagrams the initial value of the thermal conductivity was about 0.5-0.6 W/m K and that of the volumetric specific heat 1.6 x lo3 kJ/m3 K. Both the thermal conductivity and the volumetric specific heat decreased rapidly during the first minutes of baking. The thermal conductivity reached a minimum within 3-4 min and then increased to its initial value at the end of baking. The volumetric specific heat continued to decrease and the final value was about 0.5-0.75 x lo3 kJ/m3 K. The graphs also indicate that the properties measured depended on the type of oven. The baking time, defined by the time elapsed before the crumb reached a temperature of 97-98°C was shorter in the IR oven. Similar changes in volumetric specific heat and thermal conductivity were reported by Kafiev et al. (1987). They investigated the effect of additives, such as diacetyl tartaric acid esters of monoglycerides, and one bread improver named Volzski-2. The moisture content, the density and other dough characteristics were not specified so it is difficult to draw any generally useful conclusions about the changes in the thermal properties from these results.
The influence of temperature and moisture content The effect of temperature on thermal diffusivity was studied by Johnsson and Skjiildebrand ( 1984). By means of thermocouples they measured the temperature at specified locations in white bread during baking. The
Thermal properties of dough and bakery products
179
temperature dependence of the thermal diffusivity was calculated using the Fourier equation. The crust was assumed to be a finite slab and the shape of the interior was assumed to be a cylinder. Since mechanisms other than pure conduction were involved in the heating and contributed to the change in temperature, an effective thermal diffusivity was derived. The effective thermal diffusivity of the crust was expressed as: aeff= AeB’“’ In this expression t,, is the mean volume temperature in accordance with Lykow (1955), while A and B are constants. The values of A and B, determined by regression analysis, were stated to be 0*000031 and -0.067383, respectively, with a correlation coefficient of 0.96. The error in the effective thermal diffusivity due to imprecision in the temperature measurements was 0.1 x 10 - 8 m?/s. No calculation of the error due to the accuracy of thickness measurement was given. The authors stated that, for the interior, this model was valid only at temperatures between 30°C and 6O”C, and for this temperature range a constant thermal diffusivity of 40.7 x lop8 m2/s was given. This calculation model thus failed to show the dependence on temperature of the thermal diffusivity within the bread. To determine the specific heat of the crust and the crumb Johnsson and Skjoldebrand (1984) used differential scanning calorimetry (DSC). The measurements were performed at three different water contents (0, 9 and 17% in the crust, and 0,9 and 29% in the crumb). The samples were heated from 17°C to 127°C at a scanning rate of lO”C/min. The DSC measurements are carried out at constant volume, which is indicated in the following equations obtained by linear regression: crust C, = 2*62( 1 - X,,) t +X,,,,, C,,w+ 1263( 1 -X,,) crumb C, = l-60( 1 - X,,) t +XwbCvw + 1373( 1 - X,,,,)
(J/kgK)
(J/kgK)
The specific heat of water was taken as constant, at 4200 J/kg K. However, according to Polak (1984) the temperature dependence of the specific heat of water can be expressed as: C,W=[4~179-0~000217t+0~000013t~].103
(J/kgK)
At a temperature of 32°C which is in the normal temperature range of a dough after proofing, C’,*calculated from the above expression is 4 185 J/kg K. Mohsenin ( 1980) has given a value of 4179 J/kg K at this temperature. At 100°C the specific heat of water is 42 16 J/kg K (Polak), and 4287 J/kg K (Mohsenin). The specific heat of dried doughs at a temperature t”C can, according to Polak ( 1984) be derived from: C,=[1*114+0-00486tl.10” (J/kgK)
180
C. Rask
The mean value over the temperature from:
range 0°C to PC can be calculated
(J/kgK)
CP=[1~114+0~00243t].103 For moist dough the corresponding c,,=[cp”;~~cpw]
relationship .103
is: (J/kgK)
or C,=[(l
-XV,)
cp,,+xvbCp,l.103
(J/kgK)
The influence of moisture content, temperature and density on the thermal conductivity and the thermal diffusivity has been reported by Mete1 et al. (1986). They investigated yeast doughs within the temperature range 20-90°C. The density varied from 480 kg/m3 to 770 kg/m3 and the moisture content from 39.5% to 45%. The expressions, derived by regression anlaysis, are given in Table 3. The thermal conductivity of the solid phase in white bread was investigated by Tadano (1987). The bread was compressed to obtain different degrees of porosity and then freeze dried. An effective thermal conductivity was determined at 3°C and 24°C both before and after drying. Two different methods were used: a hot-wire method and a stationary parallel-plate method. From the measured effective values the thermal conductivity of bread solids was calculated from various seriesparallel models described in the literature. These calculations gave a thermal conductivity of O-361 W/m K and 0,378 W/m K at 3°C and 24”C, respectively. The specific heat has also been measured at low temperatures. Mannheim et al. (1957) not only determined the specific heat of white and whole-wheat bread solids below and above 0°C but also calculated the ice fraction and enthalpy at different temperatures. The bread sample to be tested was packed into a can and cooled to the test temperature (from + 1°C to - 200°C). The can was then put into the calorimeter, i.e. a Dewar flask. Distilled water was used as heat exchange medium and held at a constant temperature of 24°C. The moisture content of the samples was determined by drying. Assuming that the specific heat of bread solids and water, respectively, contributed to the specific heat of the bread in proportion to their mass fractions, the specific heat of bread solids was calculated from the heat balance at a particular moisture content. Based on the observation that the apparent specific heat was constant in the temperature range - 200°C to - 70°C
Thermal properties of dough and bakery products
181
at 657 J/kg K, it was assumed that at - 70°C all the water present was in a frozen state. At - 40°C the fraction of unfrozen water was 11.2% (white bread) and 16.0% (whole-wheat bread), compared with that reported by Pham (1987) of 36.2% in white bread and of 26.5% in whole-wheat bread. The specific heat, the latent heat of fusion, the ice fraction, the thermal conductivity and the thermal diffusivity of non-fermented doughs during thawing were determined by Lind (1988). Differential scanning calorimetry was used for the determination of the specific heat and the latent heat, whilst the transient hot-strip (THS) method according to Gustavsson et al. (1979) was used for the determination of the two other properties. The THS method was difficult to apply to the measurement of thermal diffusivity of dough. Lind therefore also calculated the thermal diffusivity from specific heat, thermal conductivity and density. The THS method could not be used during the phase transition and, in the region of melting, thermal conductivity and thermal diffusivity were calculated from the ice fraction. At - 40°C 35% of the total water was unfrozen. An equation for calculating the enthalpy of low-fat foods has been published by Riedel(1978). The equation, given in Table 3, was valid in the temperature range - 40°C to + 40°C. Modelling of the baking process Tichy (1974) derived a mathematical model of heat and mass transfer during baking. To be able to simulate the course of the temperature and the changes in water content of bread, Tichy used the finite difference method. From the temperature history of the centre of the bread he calculated an equivalent or effective thermal diffusivity (a,,):
where His the height of the bread in metres, r, is the time in seconds and r* is dimensionless time defined as r* = N X 0.00 1524. N is the dimensionless time step; N= O,..., 160. For a fixed rye and wheat bread of 1500 g, Tichy calcualted a mean effective thermal diffusivity of 55.8 x 10e8 m2/s. The total baking time was 55 mm. The method of Tichy has also been used by Kriems and Reinhold (1980a, 1980b). They calculated an equivalent thermal diffusivity after baking times of 10, 20, 30 and 40 min. The calculations were made for rye bread, wheat bread and for bread made from a mixture of rye and
182
C. Rask
wheat in different proportions and the results were given as a function of time and final density. For all breads investigated, there was only a slight increase in the thermal diffusivity between the 10th and 20th minute. The largest increase occurred between the 20th and 30th minute of baking. The final density was largely dependent on the amount of wheat flour present. The greater the proportion of wheat flour the less was the final density, i.e. the greater was the porosity due to a greater increase in volume during baking. The thermal diffusivity ranged from 0.24 X 10e6 m2/s, for rye bread after a baking time of 10 min, to 1.38 X lo-” m2/s, for the wheat bread after 40 min. Thus the thermal diffusivity increased with decreasing density and increasing baking time. The effective thermal diffusivity was also calculated after storage for 24 h at a temperature of 25°C and found to be 125 x lo-* m2/s. It was not reported how this measurement was made, but the fact that the thermal diffusivity in this case was independent of the density, was regarded as evidence of the contribution to heat transfer by steam in the interior of the dough during heating (compare with Nebelung in the next paragraph). A mathematical model describing the baking process has also been prop&ed by Nebelung ( 1979). He used one model for the oven and one for the product. By combining the two, the baking process could be simulated. For the crumb, Nebelung calculated the thermal conductivity with the porosity ( I,V) as a variable:
Thethermal conductivity of the gas in the pores (A,) was assumed to be equal to that of saturated air at 20°C. The porosity was calculated from the difference between the volume of the crumb and the initial volume of the dough.
w,l_b Vtotal
For bread made with wheat flour Nebelung found a porosity of 0.226 and a thermal conductivity of O-315 W/m K. Corresponding values for rye bread were: porosity 0.221 and thermal conductivity 0.356 W/m K. Nebelung stated that during baking the heat was not transferred by conduction alone. Heat transfer by evaporation and condensation of steam must also be taken into account, resulting in an effective thermal conductivity, Leff, consisting of one constant term, Adough,and one timerelated term, jlvap,the latter depending on the evaporation of water in the dough. The effective diffusivity, a,,, was calculated for the whole baking
Thermal properties of dough and bakery products
183
according to:
It was assumed that the mean value of the specific heat was constant while the mean density changed during baking. In this model, &, and hence also jleff were dependent on the external heat transfer. This means that the thermal diffusivity was dependent on both the properties of the product and the conditions in the oven. Nebelung showed this for two different kinds of oven: a laboratory oven and a tunnel oven with several temperature zones. Nebelung ( 1974) has also published thermal property values for dough, crust and crumb. These are mean values taken mainly from the East European literature. The values are listed in Table 1 together with the thermal conductivities of white bread and rye bread calculated from Nebelung’s model.
OTHER BAKERY PRODUCTS Hwang and Hayakawa (1979) have developed a method for measuring the specific heat of highly hygroscopic foods, or samples at a temperature above 100°C. Among the materials tested were crackers and biscuits. The results can be found in Table 2. Hwang and Hayakawa (1980) also developed a method to estimate the bulk density of cookies during baking. Samples were collected from 11 locations in a multi-zone band oven at a local bakery. When corrected for shrinkage, both during and after baking, the density during baking could be correlated to temperature and water content. The following relationship was found for the three different kinds of cookies examined: ~=[Boo+B,~T+B~,Xdb+B,lT.Xdh].lO~
(kg/m3)
The values of the constants ‘B’ had to be determined for each of the cookies. The validity of the relationship has not been tested for other products. To determine the heat transfer in a band oven, Standing (1974) estimated the thermal conductivity in biscuits by measuring the temperature at two locations, 2 and 5 mm from their base. During these measurements the biscuits were heated by conduction from a hot plate. The plate temperature was varied from 159°C to 208°C and the thermal
184
C. Rask
conductivity was calculated from a heat balance over the hot plate and the biscuit. Thus the calculated conductivity included the resistance to heat transfer between the plate and the surface of the product. The thermal conductivity was greater 5 mm from the base (0.16 W/m K) than at a distance of 2 mm (O-07 W/m K). The experiments also indicated that the conductivity decreased at higher plate temperatures. Kulacki and Kennedy (1978) measured the density, the specific heat, the thermal conductivity and the thermal diffusivity of two commercial biscuit doughs (AACC dough and hard-sweet dough). The density was derived by weighing a known volume of dough. The determination was carried out at 25°C and the results appear in Table 2. The specific heat was measured using the method of mixtures at three different temperatures. The tabulated values are the averages of the three values. The thermal conductivity was determined by a single-plate method and was measured at several temperatures in the interval 24-64°C. Because of an unexplainable decrease in the conductivity at the higher temperatures the tabulated values are mean values valid for the lower temperatures only. The thermal diffusivity was calculated from p, CP and each of the L-values. The results were presented in a diagram showing that the thermal diffusivity varied between 8 X and 12 X 10ms m*/s. The thermal conductivity of yellow layer cake was investigated by Sweat (1973). The measurement was carried out on samples of different degrees of bakedness and at different locations in the cake. A thermal conductivity probe was used and the samples were cooled at about 28°C before measurement. Density and moisture content were also measured. In order to calculate the thermal diffusivity Sweat estimated the specific heat of the cake by assuming that CP for the non-water fraction was half of that of water.
During baking the specific heat decreased slightly, from 2950 J/kg K in the batter to 2800 J/kg K at the centre of the fully baked cake. There was a marked decrease in density from about 800 kg/m3 to about 300 kg/m3 at times between one-quarter and one-half of the total baking time. During the same period the thermal conductivity decreased and the thermal diffusivity increased. These changes were more marked at the edge of the cake than at the centre. Griffith (1985) determined density, specific heat, thermal conductivity, and thermal diffusivity of a reconstituted corn-based tortilla dough. In these experiments a transient method was used; a copper cylinder was packed with dough of specified moisture content and the cylinder was heated from the outside. The temperature in the centre of
Thermal properties of dough and bakery products
185
the dough and at the surface was measured by thermocouples. Assuming that heat was transferred by conduction in the dough, Griffith calculated the thermal conductivity and the thermal diffusivity from the slope of the time-temperature curve and the temperature difference between the centre and the surface. The specific heat was derived from the density, the thermal conductivity and the thermal diffusivity. The thermal properties were determined at temperatures of 55°C 65°C and 75°C at moisture contents of 50%, 55% and 60% and for heating times of O-08 h, 0.17 h, 0.25 h and 0.33 h. The results of this investigation illustrated the complex influence of time, moisture content and temperature on the properties. The density and the specific heat were found to be independent of the heating time but dependent on the moisture content. In addition, the specific heat depended on the temperature. The thermal conductivity was influenced by the moisture content as well as the temperature and the heating time. The thermal diffusivity increased with prolonged thermal treatment, and was also dependent on the temperature and the moisture content. Since the pattern of the changes was varying both with temperature and moisture content only the ranges of the values are given in Table 2.
DISCUSSION Density The range of the densities tabulated (Table 1 and 2) is very wide, from about 180 kg/m3 for a white bread to about 1290 kg/m3 for a biscuit dough. East European bread is denser than American bread and rye bread is denser than wheat bread. During baking, the density falls with increasing bread volume and decreasing water content. The bulk density of an intact loaf of bread thus decreases with baking time. However, comparing different parts of the bread it is seen that, although the crust may have a less porous structure, due to the lower water content in the crust its density is less than that of the crumb. The difference in density between the dough and the crumb does not depend on the water content but on the volume expansion occurring during baking. Thus the volume expansion of the crumb results in a decrease in the density, the moisture content being substantially unchanged’ (Table 1: Tschubik & Maslow, 1973; Nebelung, 1979; Makljukow & Makljukow, 1983).
186
C. Rask
Specific heat The specific heat of bread and bread dough varies greatly with the water content. From Table 1 it can be seen that the specific heat of dough and crumb, having about the same moisture content, ranges from 2740 J/kg K to 3030 J/kg K, whereas the specific heat of the drier crust is about 1680 J/kg K. The specific heat of dough reported by Ordinanz (1946) is less than that reported by the other authors. Neither the moisture content nor the method of measurement are given by Ordinanz. Table 2 indicates that the specific heats of other bakery products may be of similar magnitude to that of bread. The specific heat of the biscuits and crackers investigated by Hwang and Hayakawa (1979) is comparable with that of a bread crust and yellow cake (Sweat, 1973), and the specific heat of biscuit dough (Kulacki & Kennedy, 1978) is similar to that of a bread dough. The number of products in Table 2, however, is small compared with the great variety occurring. According to Mohsenin ( 1980) the specific heat of various undried foods is greater than that calculated from the specific heat of the dry solid and the moisture content. This is thought to be an effect of bound water which may have a higher specific heat than free water (Freeman, 1942). Pham (1987) reported an amount of bound water of 9% in white bread at a moisture content of 37.3% wet basis, and of 6.4% in wholewheat bread at a moisture content of 42.4% wet basis. The effect of bound water may also have had influence on the measured specific heat in some of the studies reviewed. Mannheim et al. (1957) assumed that the specific heats of the bread solids and of the water were additive and their calculations gave a value of 15 5 8 J/kg K. This is somewhat greater than the specific heat of dry dough calculated according to Polak (1984), of 1260 J/kg K, of a dry crumb according to Johnsson and Skjoldebrand of about 1400 J/kg K, and of bread solids reported by Bakshi and Yoon (1984), of 1130.44 J/kg K. In the study of Johnsson and Skjoldebrand (1984) the experiments were restricted to water contents of not more than 29% on wet basis although bread doughs as well as crumb have moisture contents of about 45-55% (Table 1). Figure 1 shows the specific heat of bread and dough in relation to the moisture content. The values are taken from those publications cited, in which both the specific heat and the moisture content are given. The specific heat calculated according to Bakshi and Yoon (1984) is also plotted in the figure, as is the specific heat of crumb derived from the expression proposed by Johnsson and Skjoidebrand ( 1984). In the latter calculations the moisture content according to Bakshi and Yoon, and an
Thermal properties of dough and bakery products
187
3.6 3.4 3.2
0
1 3-l
l
0
-w
0
2
2.6
-
2.6
-
2.4
-
01 f
3
r 0 F ‘ii x v)
q
/ vv
i; 2.2
Johnsson
-
& Skj6ldebmnd
V
vvvv
XXX XXX
XX
21.6
Bakshi
& Yoon Xx
-
0 dough +dough 0 crumb A crust
0
20 Moisture
Fig. 1.
40 content
(X
wheat ye
60
wb)
Specific heat of dough, crust, crumb and intact bread as a function of moisture content.
assumed increase of the temperature at the centre of the dough were used. Both curves show that, as baking proceeds and water is lost from the bread, there is a decrease in the specific heat value towards that of the crust. Thermal conductivity Linear expressions for calculating the thermal conductivity of many kinds of food have been suggested by several authors. Miles et al. ( 1983) and Mohsenin (1980) have listed some of these and Mete1 et al. ( 1986) has given linear relationships based on moisture content and temperature of yeast doughs (Table 3). From Table 1 it is seen that the thermal conductivity of dough is about O-4 W/m K, compared with that of water of 0.62 W/m K at 32°C (Mohsenin, 1980), whereas the thermal conductivity of the crumb is about O-3 W/m K and that of the crust is about 0.05 W/m K. In Fig. 2 the thermal conductivity versus moisture content is plotted. The figure also shows the change in the thermal conductivity according to Bakshi and Yoon ( 1984) who related thermal conductivity to moisture content and density during baking. This showed a decrease with decreased moisture content as baking proceeded except for the last few minutes when the
C. Rask
0.6
-
0.5
-
0.4
-
0.3
-
0.2
-
0 + 4 A
dough dough crumb ctwst
wheat rye
X Bakshi
0
20
Fig. 2.
k YoonXXXXX
X
X X ’
40
60
Moisture content (X nb) Thermal conductivity versus moisture content.
conductivity increased. A similar decrease, followed by an increase in thermal conductivity, is reported by Kafiev et al. ( 1987) and Neznanova et al. ( 1978). However, dough and bakery products are porous materials in which the degree of porosity and the orientation of the pores must be considered. A plot of thermal conductivity versus density, as in Fig. 3, shows that, the lower the density of a dough or a crumb, the lower the thermal conductivity. The accuracy of models such as that proposed by Bakshi and Yoon (1984) is highly dependent on the accuracy of The authors claimed that their measurement of the density. measurements failed for samples baked for 1 min and 2 min. However, comparison of values estimated from their equation deviate approximately 10 kg/m3 (5%) from those measured after baking times of 7 mm and10min. When measuring thermal conductivity of dough and moist products, moisture migration may occur and should be kept at a minimum. The time of measuring should therefore be as short as possible and a transient method is recommended (Mohsenin, 1980; Nesvadba, 1982; Ohlsson, 1983). Others errors to consider arise from the insertion, of a probe into an unstable structure, as in doughs and partly baked products, since this may rupture the structure close to the probe giving rise to false values.
Thermal properties of dough and bakery products
189
0.8
0.7
-
0.6
-
0.5
-
Unklssboy
et al. V
V$ +
0
0 0
0.4
q
-
++
0
0.3
-
0.2
-
no
0
0
0
Bakshf 0.1
0
0
k Yoon;
-
%I#
I
I
0
0.2
I
I
I
0.4
I
I
0.6 Density
Fig. 3.
wheat rye
AA
A 0
0 dough +dough 0 crumb A crust
(kg/m)xlO
Thermal conductivity
I 0.8
I
I 1
I 1.2
-3
versus density.
The work by Lind ( 1988) shows that at temperatures below the initial freezing point ( - 25°C) the thermal conductivity of non-fermented dough is about 0.9-1.0 W/m K and above the freezing point it is about 0.5 W/m K. To calculate the heat transfer during baking a value for an ‘effective’ thermal conductivity which includes other mechanisms of heat transfer, is needed (Nebelung, 1979; de Vries et al., in press). De Vries et al. calculated the change in temperature of a dough during baking. They assumed a model in which heat is transferred by conduction in the liquid dough phase and by evaporation and condensation in the gas phase. With these assumptions the calculated changes in temperature agreed better with measured values than calculations based on conduction alone. A thermal conductivity of 0.33 W/m K and a heat capacity according to Johnsson and Skjoldebrand (1984) were used. Thermal diffusivity Most of the values reported for thermal diffusivity are derived from density, specific heat and thermal conductivity. The accuracy is therefore dependent on the accuracy of these three properties. Figure 4 shows the thermal diffusivity of bread and dough versus density. As with the other
C. Rask 160 150
-
140 130
-
120
-
110
-
100
-
90
-
60
-
70
qdough
V
;: p;;: A crust V effectb
wheat rya diffusivity
-I
60 50 40 30 20
EJ
10 I 0
I 0.1
I
A
I
0.3
I
I Density
Fig. 4.
1
0.5
I 0.7
I
1 0.9
I
1 1.1
(kg/m)xl$
Thermal diffusivity versus density.
the thermal diffusivity is lower in the crust thermal properties, (3-8 X 10ex m*/s) than in the crumb or in the dough (15-25 X 10e8 m*/s). At temperatures below - 16°C the thermal diffusivity is 40-50 x lop8 m*/s (Lind, 1988). The values of Johnsson and Skjoldebrand of 40.7 X 10Vx m*/s, Kriems and Reinhold of 24-138 x 10ex m*/s, and Tichy of 55.8 x lo-’ m*/s are effective thermal diffusivities which include other mechanisms of heat transfer than pure conduction. Migration of vapor is a probable explanation of the increase in thermal diffusivity noted after the longer times of heating (Griffith, 1985). Other factors influencing the results of Griffith may be structural changes, the water-holding capacity and the length of the heating time. The dough was dried, tied and re-wetted to actual moisture content. The question arises, therefore, as to how this preparation influenced the dough structure and whether this dough had properties comparable with a fresh dough. Dickerson ( 1965) described a similar method of measuring the thermal diffusivity of foods. He claimed that in order to eliminate the initial transient a certain lag time is needed. The following relationship was found:
Thermalproperties of dough and bakery products
191
where a is thermal diffusivity in square inches per minute (1 inch = 2.5 cm), r is time in minutes, and r is radius in inches. In the study by Griffith this criterion was fulfilled only after a heating time of 20 min.
CONCLUSION During baking the dough characteristics change considerably. Attempts have been made to follow the baking in order to evaluate these changes, but so far no complete study has been published. However, as a first estimate, the thermal properties in Figs l-4 and Tables 1 and 2 can be used. If the circumstances call for better accuracy the thermal properties must be measured in each individual case. Another possibility, not discussed in this article, is to calculate the thermal properties by means of a computer program such as COSTHERM (available from M. Kent, Torry Research Station, Aberdeen - ed) (Miles et al., 1983).
ACKNOWLEDGEMENTS The author’s thanks are expressed to Vassilis Gekas who translated most of the Russian articles, and to STU, the National Swedish Board for Technical Development, for financial support.
REFERENCES Auerman, L. Ja. (1977). Technofogie der Brotherstellung. VEB Fachbuchverlag, Leipzig (in German). Bakshi, A. S. & Yoon, J. (1984). Thermophysical properties of bread rolls during baking. Lebensmittel - Wissenschafi und - Technology, 17,90-3. De Vries, U., Sluimer, P. & Bloksma, A. H. (in press). A quantitative model for heat transport in dough and crumb during baking. International Symposium on Cereal Science and Technology in Sweden, 13-16 June 1988, Ystad, Sweden. Dickerson, R. W. Jr. (1965). An apparatus for the measurement of thermal diffusivity of foods. Food Technology, 19,198-204. Freeman, M. E. (1942). Heat capacity and bound water in starch suspension. Archives of Biochemistry, 1,27-39.
Ginsburg, A. S., Gromov, Thermo-physical
Promyshlennost,
M. A., Kracovskaya,
Properties of Food Products Moscow (in Russian).
G. I. & Ukolov, V. S. (1975). and Materials. Pishchevaya
192
C. Rask
Ginsburg, A. S., Gromov, M. A. & Kracovskaya, G. I. (1980). Thermo-physical Properties of Food Products. Pishchevaya Promyshlennost, Moscow (in Russian). Griffith, C. L. (1985). Specific heat, thermal conductivity, density, and thermal diffusivity of Mexican tortillas dough. Journal of Food Science, 50 (5), 1333-7. Gustavsson, S. E., Karawacki, E. & Khan, M. N. (1979). Transient hot-strip method for simultaneously measuring thermal conductivity and thermal diffusivity of solids and fluids. Journal of Physics,D: Applied Physics,Vol. 12. Hwang, M. P. & Hayakawa, K.-I. (1979). A specific heat calorimeter for foods. Journal of Food Science, 44,435-8,448. Hwang, M. P. & Hayakawa, K.-I. ( 1980). Bulk density of cookies undergoing commercial baking processes. Journal of Food Science, 45 (5), 1400-2,1407. Johnsson, C. & Skjoldebrand, C. (1984). Thermal properties of bread during baking. In Engineering of Food, Vol. 1, ed. B. M. McKenna. Elsevier Applied Science Publishers, London. Kafiev, N. M., Lekhter, A. E., Leites, R. Ya., Klokacheva, 0. A., Panin, A. S., Ribakov, A. A. & Didenko, I. A. (1987). Thermophysical characteristics of certain bread dough improvers. MaslozhirovayaPromyshlennost, 1, 20- 1 (in Russian). Kriems, P. & Reinhold, M. (1980a). Das Backen von Mischbrot (V) Warmeubertragung, Temperaturkinetik-. Bicker und Konditor, 34 ( 11), 34 l-6 (in German). Kriems, P. & Reinhold, M. (1980b). Das Backen von Mischbrot (VI) Schlussfolgerungen zur Verbesserung des Backeffektes und der Brotqualitat, Zusammenfassung-. Backer und Konditor, 34 ( 12), 356-9 (in German). Kulacki, F. A. & Kennedy, S. C. (1978). Measurement of the thermo-physical properties of common cookie dough. Journal of Food Science, 43,380-4. Lind, I. (1988). Thawing of minced meat and dough: Thermal data and mathematical modelling. In Progress in Food PreservationProcesses, Vol. 1, 12-14 April, CERIA, Brussels. Lykow, A. W. ( 1955). Experimentelle und Theoretische Grundlagen des Trocknung. VEB Verlagtechnik, Berlin (in German). Makljukow, I. I. & MakIjukow, W. I. (1983). Thermophysikalische Charakteristika fur das Backstiick. In Industrieiifender Backwarenproduktion.Verlag Leicht- und Lebensmittelindustrie, Moskau (in Russian) (Translated by H.-D. Tscheuschner). Mannheim, H. C., Steinberg, M. P., Nelson, A. I. & Kendall, T. W. (1957). The heat content of bread. Food Technology, 7,384-g. Metel, S. N., Mikrukov, V V. & Kasparov, M. N. (1986). Thermophysical characteristics of yeast dough. Izvestiga Vysshikh Uchebnykh Zavedenii, PishcshevayaTeknologiya,4, 107-8 (in Russian). Miles, C. A., Van Beek, G. & Veerkamp, C. H. (1983). Calculations of thermophysical properties of foods. In: Physical Properties of Foods, Vol. 1, ed. R. Jowitt, et al. Applied Science Publishers, London. Mohsenin, N. N. ( 1980). Thermal Properties of Foods and AgriculturalMaterials. Gordon & Breach Science Publishers, New York. Nebelung, M. (1979). Model der Warmeiibertragung in kontinuerlich und
Thermal properties of dough and bakery products
193
diskontinuerlich arbeitenden Kammerofen unter beriicksichtigung von Warmeleitung, Stofftransport und Reaktionen in einem feuchten kapillarporosen Korper (Backprozess). PhD thesis, TU Dresden, DDR. Nesvadba, P. ( 1982). Methods for the measurement of thermal conductivity and diffusivity of foodstuffs. Journal ofFood Engineering, 1,93-l 13. Neznanova, N. A., Panin, A. C., Puchova, L. L. & Skverchak, V. D. (1978). Thermophysical properties of dough and bread from grade I wheat flour during baking. Khlebopekarnaya i Konditerskaya Promyshlennost, 8 13- 14 (in Russian). Ohlsson, T. (1983). The measurement of thermal properties. In Physical Properties of Foods, Vol. 1, ed. R. Jowitt et al. Applied Science Publishers, London. Ordinanz, W. 0. ( 1946). Specific heats of foods in cooking. Food Industries, 18 (12), 101. Pham, Q. T. ( 1987). Calculation of bound water in frozen food. Journal of Food Science, 52 (l), 210-12. Polak, M. (1984). Specific heat capacity of dough. Mlynsko- Pekarensky Prumysl, 30 (2), 42-4 (Czech). Poppendiek, H. F., Randall, R., Breeden, J. A., Chambers, J. E. & Murphy, J. R. ( 1966). Thermal conductivity measurements and predictions for biological fluids and tissues. Cryobiology, 3,318-27. Rao, M. A. & Rizvi, S. S. H. (1986). Engineering Properties of Foods. Marcel Dekker, Inc., New York. Rask, C. (in press). The heat transfer in a convection oven: Influences on some product characteristics. International Symposium on Cereal Science and Technology in Sweden, 13- 16 June 1988, Ystad, Sweden. Riedel, L. (1978). Eine Formel Zur Bereclmung der Enthalpie fettarmer Lebensmittel in Ablrangigkeit von Wassergehalt und Temperatur. Chem Mikrobiol Technol Lebensm,
5,129-33.
Standing, C. N. (1974). Individual heat transfer modes in band oven biscuit baking. Journal of Food Science, 39,267-7 1. Sweat, V. E. ( 1973). Experimental measurement of the thermal conductivity of a yellow cake. Proceedings of the XIIJth International Conference on Thermal Conductivity, University of Missouri-Rolla, Nov. 1973, pp. 213-16. Sweat, V. E. & Haugh, C. G. ( 1974). A thermal conductivity probe for small food samples. Transactions of the ASAE, 17 ( 1). 56-8. Tadano, T. ( 1987). Thermal conductivity of white bread. Bulletin of the College of Agricultural and Veterinary Medicine, (44), 18-22 (in Japanese). Tichy, 0. ( 1974). Matematick’y model sdilem tepla a hmoty pri peceni. Potravinarska a Chladici Technika, 5 (l), 20-7 (in Czech). Tschubik, I. A. & Maslow, A. M. (1973). Wiirmephysikalische Konstanten von Lebensmitteln und Hatbfabrikaten. VEB Fachbuchverlag, Leipzig, p. 28 (in German). Unklesbay, N., Unklesbay, K., Nahaisi, M. & Krause, G. (1981). Thermal conductivity of white bread during convective heat processing. Journal of Food Science, 47,249-53,259.
Wallapapan, K., Sweat, V. E., Diel, K. C. & Engler, C. R. (1986). Thermal properties of porous foods. In Physical and Chemical Properties of Food, ed. M. R. Okos. American Society of Agricultural Engineers, Michigan.