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Thermophysical properties evolution of French partly baked bread during freezing
Food Research International 37 (2004) 703–713 www.elsevier.com/locate/foodres
Thermophysical properties evolution of French partly baked bread during freezing Nasser Hamdami b
a,b
, Jean-Yves Monteau
b,*
, Alain Le Bail
b
a Department of Food Science and Technology, The University of Tabriz, 51664 Tabriz, Iran UMR GEPEA (UA CNRS 6144 – SPI), ENITIAA, Rue de la Geraudiere BP 82225, F-44322 Nantes Cedex 03, France
Received 1 October 2003; accepted 26 February 2004
Abstract Few data are available on the thermophysical properties of the frozen partly baked breads. In this paper, thermophysical properties, including apparent and true densities, specific heat, enthalpy and effective thermal conductivity were determined separately for crumb and crust of partly baked bread. Total enthalpy of fusion, unfrozen water and solid specific heat were determined by differential scanning calorimetry. The apparent specific heats were estimated in base of the unfrozen water at )40 °C and initial freezing point. The effective thermal conductivity was measured with a line source probe in the range )35 to 25 °C. Four predictive models of the effective thermal conductivity of porous food were developed (parallel, series, Krischer and Maxwell models). The effective thermal conductivity predicted by Krischer model was in good agreement with the experimental data. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Bread; Thermophysical properties; Porous media; Freezing
1. Introduction Partly baked bread has developed a lot in the past decade. The objective of the part baking is to carry out gelatinization and coagulation of gluten, without reaching the coloring reactions of the crust (Roussel & Chiron, 2002). To retard staling and to extend shelf life of bread, the part baked breads are often frozen. The frozen part baked breads represent half of the volume of frozen breads exported by the French industrialists towards Northern Europe (Millet & Dougin, 1994). Twenty two percent of the industrial bread was part baked frozen bread in 2001 with a growing market share. The study of the heat and mass transfers during freezing, for the assessment of the product behavior under proposed process conditions and for the efficient design of process and equipment, requires accurate values of thermal and physical properties of bread. Many *
Corresponding author. Tel.: +33-251-785-481; fax: +33-251-785467. E-mail address: [email protected] (J.-Y. Monteau). 0963-9969/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodres.2004.02.017
studies on thermophysical properties of bakery products are available in the literature. However, data on thermophysical properties of dough and bakery products during freezing are scarce as compared to other food products, and no published information is available concerning the thermal and physical properties of partly baked bread during freezing. The methods available for measuring and modeling the thermophysical properties of bakery products have been reviewed by different researchers. Rask (1989) reviewed data and prediction models of thermal properties of bakery products. Lind (1991) presented measurement techniques and models of thermal properties of dough during freezing and thawing. More recently, Baik, Marcotte, Sablani, and Castaigne (2001) reviewed measurement techniques, prediction models and published data on thermophysical properties of bakery products. While several modeling approaches have been proposed to predict thermal properties of a material at desired conditions, none of them can be used over a wide range of foods. The most promising approach is based on chemical composition, temperature and physical characteristics. Besides, most structural models neglect
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Nomenclature aw Cp D E feva–con fk H Hfw I L L0 P Q r r R R S T x
water activity specific (sensible) heat (J kg1 °C1 ) diffusivity of water vapor in air, (m2 s1 ) Euler’s constant, 0.5772157 resistance factor against vapor transport structural factor or distribution factor of the Krischer model enthalpy (J kg1 ) enthalpy of water fusion (J kg1 ) current intensity through the heater wire (A) latent heat of fusion (J kg1 ) latent heat of evaporation (J mol1 ) total pressure (Pa) power generated by the probe heater (W m1 ) correlation coefficient distance from the line heat source (m) electric resistance (X m1 ) perfect gas constant, 8.314510 (J mol1 °C1 ) slope of the linear portion of the plot of the temperature vs. In(time) temperature (K) mass fraction (kg/kg product)
Greek letters a thermal diffusivity (m2 s1 ) k thermal conductivity (W m1 °C1 ) interactions between components although they can be significant. The properties that are concerned by this study are the density, the porosity, the unfrozen water mass fraction, the specific heat, the enthalpy, and the thermal conductivity. Two densities can be distinguished, namely the bulk and the true density. For the bulk or apparent density, the pores volume is considered as a part of the material volume. For the second one, the material volume is the volume without the pores (McDonald & Sun, 2001). The bulk density can be determined simply by dividing the mass of the product by its volume. Volume can be measured with various displacement methods (Bakshi & Yoon, 1984; Hwang & Hayakawa, 1980). The volume can also be calculated from sample dimensions if the object has a regular geometry (Christenson, Tong, & Lund, 1989). General models reported in the literature allow the apparent density of any food product to be calculated as a function of the chemical composition, moisture, porosity and temperature (Miles, van Beek, & Veerkamp, 1983). In addition, semi-empirical (Hwang & Hayakawa, 1980) and empirical models (Bakshi & Yoon, 1984) are available. These models describe the variation
keva–con equivalent thermal conductivity due to eva– con phenomenon (W m1 K1 ) h temperature (°C) hi initial freezing point (°C) hr reference temperature ðH ¼ 0Þ (°C) e volume fraction (m3 /m3 product) ea porosity q density (kg m3 ) Subscripts a correspond of pores (voids) air air app apparent u unfrozen water at low temperature (unfreezable water) c continue d dispersed eva–con evaporation–condensation i ice or component i Kri Krischer Max Maxwell pa parallel s solid se series sat saturated t true tw total water w liquid water 0 at 0 °C of the apparent density of baked products, such as cookies and bread rolls, as a function of temperature, moisture and baking time. The true density is usually determined with a pychnometer. If the material is soft, the porosity can be determined from volumes of compressed and non-compressed material (Zanoni, Peri, & Gianotti, 1995). More often it is calculated from the real and apparent densities (Miles et al., 1983). Water can be present in different states in a food during freezing. We arbitrarily choose that 100% of the frozenable water will frozen at a temperature of )40 °C. Therefore, the amount of unfrozen water at this temperature will be named ‘‘unfreezable water’’. The unfreezable water mass fraction can be determined by differential scanning calorimetry (DSC): it is the difference between the total water content and the amount of water detected by the fusion endotherm (Ross, 1978). Another method was proposed by Pham (1987) using enthalpy-temperature data and the Schwartzberg model of the apparent specific heat: the unfreezable water mass fraction was expressed by equaling enthalpy expressions below and above the freezing point.
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Enthalpy and apparent specific heat are two key thermal properties used to solve the non-linear heat diffusion equation when taking into account phase transition. Enthalpy is a state function for which a reference temperature has to be defined ()40 °C is often chosen) (Heldman, 1982; Wang & Kolbe, 1991). Specific heat represents the rate of enthalpy change with the temperature, dH =dh. Since latent heat removal occurs over the freezing temperature domain, it is usual to include the latent heat contribution in the specific heat, which is then called the apparent specific heat, Cpapp . Both experimental and mathematical modeling approaches have been used to determine enthalpy and apparent specific heat of frozen foods. Several methods are used to measure the apparent specific heat and the enthalpy as functions of temperature. These methods are based on experimental results obtained from calorimetric measurements (Lind, 1991; Mannheim, Steinberg, Nelson, & Kendall, 1957; Tocci, Flores, & Mascheroni, 1997). Bakshi and Yoon (1984) developed equations to estimate the specific heat of bread rolls by considering it as a two-component material, water and bread solids. They found the specific heat of bread solids to be lower than the estimated value by Mannheim et al. (1957) (1130.44 to compare with 1557.49 J kg1 °C1 ). Zanoni et al. (1995) showed that the average specific heat of dough and crumb is about 2900 J kg1 °C1 , whereas the average specific heat of the crust is about 1600 J kg1 °C1 . By analyzing the data presented they concluded that moisture is the major variable that influences the specific heat of food products, and that temperature has little effect provided there is no phase change. Thus, there are semi-empirical models describing the variation of the specific heat of baked products with moisture, such as the model of Bakshi and Yoon (1984) for bread rolls, and that of Christenson et al. (1989) for bread, muffins and biscuits. Johnsson and Skj€ oldebrand (1983) setup semi-empirical models for specific heat of bread as functions of moisture and temperature. One of the most important thermal properties is thermal conductivity. Measurement methods of thermal conductivity can be divided in two categories: steadystate methods (SSM) and unsteady state or transient methods (TM). Most researchers recommended TM (Nesvadba, 1982). Among TM, the simplest and most widely used is the line heat source thermal conductivity probe method. Advantages of this method are: (i) a short duration of the experiments (range 5–20 s) and (ii) a reduced temperature rise of the sample (a few °C). By its theory assuming purely conductive–diffusive heat transfer, this method is not appropriate for the determination of thermal conductivity at temperatures slightly below the initial freezing temperatures because of the associated variation of the ice content. The prediction of thermal conductivity values in this tempera-
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ture range using a specific model is sometimes more accurate than measurements (Wang & Kolbe, 1991). Bakshi and Yoon (1984) used the line heat source probe method to measure thermal conductivity of bread products at various moisture contents. They showed that average thermal conductivity of bread dough is about 0.4 W m1 °C1 . Rask, in its review of published data (Rask, 1989), showed that the thermal conductivity for crumb and crust are respectively about 0.3 and 0.05 W m1 °C1 . These values depend on the fact that thermal conductivity is a function of moisture, apparent density and therefore porosity. Thermal conductivity has been presented and modeled as a function of moisture content or process temperature. It has now been recognized that thermal conductivity of foods, including bakery products, is also influenced by the amount of air fraction in the food material. A great variety of more or less complex equations for calculating thermal conductivities exists in the literature. The most well known physical models are the parallel model, the perpendicular (or series) model, the dispersed phase model (or Maxwell model) and the Krischer model (Miles et al., 1983; Rahman, 1995). This research is a part of a study on freezing modeling of the part baked breads. It was designed to collect information about thermal and physical properties of these products during freezing. The specific objectives were: 1. To determine the thermophysical properties of part baked bread as a function of moisture content and temperature. 2. To relate these properties to the samples compositions using different mathematical model. Since there are structural differences between crumb and crust, the properties mentioned above are evaluated separately for each part.
2. Theoretical section This section is intended to document the physical phenomena that determine differences in thermophysical properties between the crumb and the crust, and to give some theoretical elements allowing the prediction of these properties, elements used to obtain the results below. 2.1. Differences between crust and crumb 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 bread dough will thus change with time during baking and the crust will contain less water than the crumb which represents the internal part of the bread (Johnsson & Skj€ oldebrand, 1983; Rask, 1989).
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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. 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 apparent density of bread varies due to both the increase in the product volume and the decrease in the water content during baking. At the end of baking, the crust has low water content and a firm and less porous structure; as a result, its apparent density values are not similar to those for the crumb, which has a higher water content and is more porous (Rask, 1989; Zanoni et al., 1995). Consequently, the other thermal properties are different in the two parts. de Vries, Sluimer, and Bloksma (1989) proposed mathematical models for heat and mass transfer in dough and crumb with consideration of evaporation–condensation mechanism in pores. Evaporation–condensation in the crumb seemed to be a significant mechanism for heat transport in bread in comparison with conductive or radiative heat transfer. Nevertheless this transport might not to be applied to bread crust according to Zanoni and Peri (1993). 2.2. Porosity Using porosity definition and real and apparent densities definition, Eq. (1) can be setup to calculate the porosity (Miles et al., 1983) qapp ea ¼ 1 : ð1Þ qt
Cpapp ðhÞ ¼ CpW ðhÞxW ðhÞ þ Cpi ðhÞxi ðhÞCps ðhÞxs þ L
dxw ðhÞ : dh ð3Þ
The ice content may be estimated with hi xi ¼ ðxtw xu Þ 1 if h < hi ; h xi ¼ 0
if h P hi :
The initial freezing point was defined as the temperature at which the rate of temperature drop of the freezing curve is slowed down (freezing plateau). 2.4. Unfreezable water The unfreezable water at low temperature can be measured by DSC, simply by difference between total water content and the amount of water detected by the fusion endotherm: xu ¼ xtw
Hfw : L
ð2Þ
2.5. Apparent specific heat The apparent specific heat may be calculated by summing specific heats of each component weighed by their mass fractions, and by including energy released by the ice fusion (Miles et al., 1983)
ð5Þ
2.6. Enthalpy The relation between the enthalpy and the apparent specific heat is given by Eq. (6), with H ¼ 0 for the reference temperature hr . Z h Cpapp ðhÞdh: ð6Þ H¼ hr
2.7. Evaporation–condensation phenomenon and thermal conductivity If a temperature gradient is applied to a porous food material, moisture migration as vapor in the pore space occurs. Water evaporates at the high temperature side, diffuses in the pore space according to the vapor pressure gradient caused by the temperature gradient, and condensates at low temperature side (de Vries et al., 1989). Thus latent heat is transported through the pores. By considering the effect of the latent heat transport, the effective thermal conductivity in pores was given by the following equation: ka ðhÞ ¼ kair ðhÞ þ keva–con ðhÞfeva–con ;
2.3. Initial freezing point
ð4Þ
ð7Þ
where keva–con is the equivalent thermal conductivity due to the latent heat transport (evaporation–condensation): keva–con ðT Þ ¼
DðT Þ P dPsat L0 ðT Þaw ðT Þ: RT P aw Psat ðT Þ dT
ð8Þ
This equation is assumed to be applicable to the estimation of the effective thermal conductivity of porous food in our conditions. 2.8. Line heat source probe For pffiffiffiffipoints close to the line heat source such that r=ð2 atÞ P 0:16, the temperature variation initiated by a line heat source is given to better than 1% error (McGinnis, 1987): Q 4at DT ðtÞ ¼ ln 2 E : ð9Þ 4pk r The conductivity may then be determined from the slope S of the straight line DT vs. ln t:
N. Hamdami et al. / Food Research International 37 (2004) 703–713
Q ; 4pS where the power generated by the probe is
k¼
Q ¼ I 2 R:
ð10Þ
2.9. Thermal conductivity models Assuming that the food material is a four-phase system consisting of air, water, ice and solids, the parallel and series models are respectively represented by the following equations (Miles et al., 1983): kpa ðhÞ ¼ ea ðhÞka ðhÞ þ es ðhÞks ðhÞ þ ew ðhÞkw ðhÞ þ ei ðhÞki ðhÞ; ð12Þ kse ðhÞ ¼ 1
ea ðhÞ es ðhÞ ew ðhÞ ei ðhÞ þ þ þ ; ka ðhÞ ks ðhÞ kw ðhÞ ki ðhÞ
ð13Þ
where ki , kw and ks are respectively the thermal conductivities of ice, water and solid (carbohydrate). The volume fraction of any component, ei as a function of temperature is obtained from the following equation ei ðhÞ ¼
qapp xi ðhÞ ; qi
ð14Þ
where xi and qi are respectively the mass fraction (kg/kg product) and the density of the components. Krischer’ s model is based on two extremes in thermal conductivity values, one being derived from the parallel model and the other being derived from the series model, whilst the real value of thermal conductivity should be somewhat in between these two extremes. The distribution factor fk is a weighing factor. kKri ðhÞ ¼
1fk kpa ðhÞ
1 : k þ ksefðhÞ
ð15Þ
The thermal conductivity of a food by the Maxwell equation is defined as (Miles et al., 1983): kMax ¼ kc
2kc þ kd 2ed ðkc kd Þ ; 2kc þ kd þ ed ðkc kd Þ
3. Materials and methods 3.1. Partly baked bread preparation
ð11Þ
707
ð16Þ
where kc and kd are respectively the thermal conductivities of the continuous and discontinuous phase, and ed the volume fraction of the dispersed phase.
Flour was purchased from a local milling plant (Nantes, France). Flour analysis and dough recipe are provided in Table 1. Mixing was done in a spiral mixer (VMI, Montaigu, France) and comprised two steps: a low-speed mixing step (4 min, 100 rpm), and a highspeed mixing step (11 min, 200 rpm). The temperature of the dough after kneading was 23 0.5 °C. The dough was divided into round pieces (140 1 g) and fermented for 30 min at ambient temperature. After first proofing the dough was formed into 30 cm long cylinders and proofed for 90 min at 27 °C and at a relative humidity greater than 90% (final proof). Then, the scarified pieces of dough were pre-baked for 12 min in a convection oven at 150 °C. During the first minutes, water was injected in oven for decreasing the weight loss of samples. The final diameter of the bread cylinders was approximately 57 2 mm. After pre-cooling at 10 °C and at a relative humidity greater than 85% for 40 min, the partly baked breads were packaged in two moisture impermeable films, frozen at )30 °C and stored at )20 °C. 3.2. Sample preparation for analysis In this study, cylindrical breads for density and porosity, crumb samples for unfreezable water and thermal conductivity, and crust slices for unfeezable water, conductivity, density and porosity were used. They were obtained according to the following procedure (Fig. 1(a)): firstly, the frozen partly baked bread was divided in three parts. Then, the cylindrical bread sample was obtained from central part (15 cm long). Finally, the crust was removed from cylindrical bread sample and the interior portion remained as crumb. The socalled crust was characterized by a dense structure with a thickness of about 3 mm. Separating the crust fractions in this way can be done with good reproducibility. All types of sample (bread, crumb and crust) were placed in moisture impermeable polyethylene films. The packaged samples were thawed at 20 °C for 2 h before the experiments.
Table 1 Chemical components of the flour and dough recipe used in experiments Flour component
Content
Method
Dough recipe
Content (g)
Moisture (% DM) Ash content (% DM) Protein content (% DM) Hagberg falling number (s) Zeleny (%)
15.25 0.61 10.80 284 33
NFa ISOb 712 NF V 03720 NF 5 7/MS NF V 03703 NF ISO 5529
Flour Water Salt Compressed yeast Baking aid mix
100 60 2.2 3 0.7
a b
NF, French Standard. ISO, International Standard Organization.
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Fig. 1. (a) Preparation scheme of the samples (part baked bread, crumb and crust samples) and (b) probe positions in the crumb and crust samples.
3.3. Bulk and true densities and porosity Firstly, the cylindrical bread sample was weighed and measurements of apparent volume, of length and of diameter were taken. Secondly, the crumb portion was removed, and the apparent volume and the weight of crust sample were measured. The apparent volumes of bread and crust were measured by rape seed displacement method. Finally, the volume of crumb was calculated by subtraction of the crust volume from bread volume. The true density of samples was measured using a helium pychnometer (AccuPyc 1330, Micromeritics, USA). Eq. (1) was then used to calculate the sample porosities. 3.4. Total water content The total water content of samples was determined in triplicate by drying 5 g of sample in a forced convection oven at 103 °C for 16 h. The samples were cooled in a desiccator and weighed by an analytical balance (sensitivity 0.01 mg). 3.5. Unfreezable water mass fraction The unfreezable water weight fraction was determined using DSC, according to the method presented in theoretical section (Eq. (2)). 3.6. Apparent specific heat and enthalpy A differential scanning calorimeter (DSC 92, Setaram, Caluire, France) was used to evaluate the total enthalpy of the phase change and the specific heat of dry matters of the samples at atmospheric pressure. Samples (100–140 mg) were removed from different locations in crumb and crust, and hermetically closed in aluminum pans. They were frozen in situ in the calorimeter by the way of liquid nitrogen. Experiments were realized five times from )50 °C and up to 40 °C at a heating rate of 2 °C/min. An empty pan was used as a reference. The base line was obtained from a scan realized with two empty pans. Total enthalpy of the phase change was
estimated as the area under the DSC base line and expressed in J kg1 of sample (Tocci et al., 1997). The corresponding total enthalpy of fusion and specific heat were evaluated with the software of the calorimetric apparatus. Because of the span in temperature of the calorimetric peak, the experimental curve was not properly located on the temperature scale. In order to have an acceptable correspondence between the initial freezing point and the apparent specific heat function Cpapp , the apparent specific heat of samples was estimated from the Eq. (3). The temperature dependence of the amount of ice and unfrozen water were taken into account by using Eqs. (4) and (5). The initial freezing point, hi , was deduced from the temperature history of sample. Enthalpy, H , was determined using Eq. (6), with the reference temperature selected as )40 °C. 3.7. Effective thermal conductivity 3.7.1. Thermal conductivity measurement Thermal conductivity was determined with a line source probe, purchased from V. E. Sweat (Texas, A and M University). The thermal conductivity probe was similar to the one described by Sweat and Parmelee (1978). A version of the thermal conductivity measurement system developed by McGinnis (1987) was used to supply power, measure current and record temperatures and voltage (Fig. 2). Firstly, the probe was inserted into the crumb and crust samples according to the Fig. 1(b). To prevent the crust samples compression during conductivity measurement, the crust slices were cut into
Fig. 2. Setup of the thermal conductivity measurement system.
N. Hamdami et al. / Food Research International 37 (2004) 703–713
sub-fractions (30 30 3 mm) and 13 laminates of these sub-fractions were placed in a rectangular container with internal dimension 30 30 40 mm, and packaged in moisture impermeable film to prevent the sample dehydration. Then, the assembly (probe + sample) was kept at a given temperature in an air-freezer (FroilaboS.A., Ozoir, France) having a temperature stability of 0.1 °C. The probe heater was connected to a DC power supply (Redelec 60430, Noailles, France) and a multimeter (Fluke, John Fluke MFG. Co., Inc., USA) to measure the current intensity. The accuracy of the current measurement in the heater circuit was 0.1 mA. The temperature–time and voltage–time data were continuously collected by a digital recorder (Datalog 20, AOIP, Evry, France) which was bi-directionally interfaced with a PC in order to program measurements. The record of voltage was used to find the initial time of the heating. 3.7.2. Thermal conductivity calculation The samples thermal conductivity was calculated using the Eq. (10) where Q is calculated by Eq. (11). To obtain satisfactory linearity of temperature vs. lnðtimeÞ plot, the procedure was standardized by (1) the choice of a power level to increase the temperature up to 10 °C (initial temperature basis), (2) using a duration of 8 s, and (3) by accepting thermal conductivity values measured only when r2 > 0:98. To obtain these conditions, a current value of 0.09–0.17 A was necessary. Seven measurements were made in each sample. For each sample, the conductivity reported is the mean of seven measurements. The thermal conductivity experiments were carried out at selected sample temperature, )35, )30, )25, 1, 15 and 25 °C on the crumb and crust samples, with moisture contents of 45% and 27% (wet basis), respectively. 3.7.3. Calibration The probe calibration was realized by measuring the thermal conductivity of glycerin and of a gel of 0.5% agar and water at selected temperatures between 5 and 25 °C. 3.7.4. Thermal conductivity model development The crumb and crust of bread can be analyzed as a multicomponent three-phase system which, below the initial freezing point, represents a complicated dynamic complex of four fractions, continuously changing their ratios: dry substance (proteins, lipids, carbohydrates, mineral salts, etc.), water, ice crystals and gaseous phase (including air and water vapor). In this study, four physical models, parallel, series, Maxwell and Krischer models, were tested for the thermal conductivity prediction of crumb and crust. The thermal conductivities of ice, water and solid (carbohydrates) are calculated with the following equations (Singh, 1992):
709
ki ðhÞ ¼ 2:2196 6:248 103 h þ 1:0154 104 h2 ; ð17Þ kw ðhÞ ¼ 0:57109 þ 1:7625 103 h 6:7036 106 h2 ; ð18Þ kw h ¼ 0:20141 þ 1:38410 103 h þ 4:3312 106 h2 ; ð19Þ where ka is obtained from the Eq. (7). In all the calculations, the values used for ice, water and solid density were respectively 917, 1000 (Miles et al., 1983), and 1463 1.2 kg m3 (obtained from experiments). The volume fraction of discontinuous phase, ed , is obtained from Eq. (14). For Maxwell model application to porous materials including three or more components, a stepwise procedure is required. At each step the mean thermal conductivity of pairs of components is found. In this study a three-step Maxwell model, developed by Hamdami, Monteau, and Le Bail (2003), was used for thermal conductivity prediction. In the first step, the two phases considered were (1) continuous water phase, (2) discontinuous ice phase. In the second step, the phases were (1) continuous solid phase, (2) discontinuous water–ice phase. Finally, in the third step, the phases were (1) continuous solid–water–ice phase, (2) discontinuous air phase. The model parameters fk and feva–con were estimated by fitting the model calculated values of effective thermal conductivity to experimental ones.
4. Results and discussion 4.1. Density and porosity The weight and apparent volume measurements at room temperature on the partly baked bread samples and their crumb and crust, showed that the crust forms 25.0 1.9% of volume and 37.8 1.9% of weight of the partly baked bread samples. Table 2 gives the experimental apparent and true density values of the different samples (crumb and crust, average of 10 tests). As expected, crust has an apparent and true density greater than those of the crumb, due to the porosity and the total water mass fraction of the crust lower than for the crumb. 4.2. Unfreezable water, apparent specific heat and enthalpy The values of the crumb and crust unfreezable water mass fraction were estimated by application of the Eq. (2) to 10 samples for which total enthalpy of fusion
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Table 2 Apparent and true density, porosity, unfreezable and total water mass fractions of the crumb and crust samples Property
Crust
3
Apparent density (kg m ) True density (kg m3 ) Porosity Unfreezable water mass fraction (kg kg DM1 ) Total water mass fraction (kg/kg product)
Crumb
Mean value
SD
Mean value
SD
332.8 1390 0.760 0.3364 0.273
6.0 5.9 0.017 0.0060 0.025
181.7 1291.5 0.8592 0.413 0.4529
2.6 10.5 0.0030 0.049 0.0032
have been previously measured. Table 2 gives the unfreezable water mass fraction values ðxu Þ in the crumb and crust samples. The difference in the unfreezable water values of the crumb and crust samples can be explained by both physical and chemical changes occurring during the baking process (Lind, 1991). The average initial freezing point of the crumb and crust samples was found to be )5.7 °C 0.2 and )15 to )24 °C, respectively (average of five experiments). The large variation of the initial freezing point of the crust samples was due to the great freezable water content variation of the samples. The following equation gives the specific heat of dry bread as a function of temperature. It was obtained from eight tests of DSC: Cps ðhÞ ¼ 4:582h þ 1138:
ð20Þ
This shows a very good agreement with 1130.44 J kg1 °C1 for bread solids as calculated by Bakshi and Yoon (1984). From the Eqs. (3) and (6), the apparent specific heat and the enthalpy of both frozen and unfrozen products were adequately calculated as a function of temperature while knowing total and unfrozen water content, and initial freezing point. Figs. 3 and 4, show the evolution of the apparent specific heat and enthalpy values as a function of temperature during freezing for a crumb and a crust sample in respect of the given data in Table 2. As shown in
Figs. 3 and 4, because of an important freezable water mass fraction, crumb has a more intense phase change peak and a greater enthalpy than that of crust. When the samples are frozen, the enthalpies for the crust and the crumb are very close. 4.3. Effective thermal conductivity values The values of thermal conductivity measured by the line source probe method were reproducible (2% uncertainty ‘‘experimental standard deviation’’). Fig. 5 shows the effective thermal conductivity values measured for the crumb at two different probe positions (axial and radial) for three positive temperatures: 2.5, 15 and 23 °C. This figure shows that there is not important difference between the results. Thus it can be concluded that the effective thermal conductivity measurements were independent on the probe position. Moreover, it can be noticed that the points are along a straight line. The Figs. 6 and 7 present the thermal conductivity variation vs. temperature for the crumb and the crust. Values given by the models are also represented here. These figures show that effective thermal conductivity is strongly dependent on the porous structure, the freezable water content and the temperature. The effective thermal conductivity above the initial freezing point increases with increasing the temperature due to the increase of the thermal conductivity of the components
Fig. 3. Evolution of the apparent specific heat values for the crumb and crust samples.
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Fig. 4. Evolution of the enthalpy values for the crumb and crust samples.
Fig. 5. Effective thermal conductivity values measured for evolution of the apparent specific heat values for crumb at two different probe positions (radial and axial).
Fig. 6. Experimental and predicted thermal conductivity values for crumb.
(crumb and crust cases) and to the evaporation–condensation effect (crumb case only). In the sub-freezing temperatures, however, the effective thermal conductivity is dependent on freezable water content. If its value is important (crumb case), the effective thermal conductivity increases with decreasing the temperature, due to
the state change to ice. Then, it decreases very slightly. However, if the freezable water content value is less important (crust case), the stage of effective thermal conductivity increase cannot be observed with decreasing the temperature: for all the temperatures, the points are disposed along a straight line.
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Fig. 7. Experimental and predicted thermal conductivity values for crust.
The comparison between the experimental and predicted effective thermal conductivity values show that: (i) Series model gives always under-estimated thermal conductivity values for crumb and crust, (ii) Parallel model gives upper-estimated thermal conductivity values for crumb. However the predicted values approach the experimental ones for the crust, (iii) The predicted effective thermal conductivity values by Maxwell model agree with the experimental ones only for the crumb samples, (iv) The predicted thermal conductivity values
Table 3 Identified values of the resistance factor and structural factor Property
Crumb
Crust
Porosity Total water mass fraction Resistance factor feva–con Structural factor fk
0.85 0.46 0.37 0.27
0.76 0.25 0.09 0.09
by Krischer’s model are in good agreement with the experimental values in both cases. It can be concluded that Krischer’s model is able to correlate the heat transfer in the porous structure of bread crumb and crust better than the others models. These better results are due to the presence of the empirical curve-fitting factor, fk . From Table 3 it can be observed that the identified values of fk and feva–con for the crust samples are less important than for the porous crumb (assuming aw ¼ 1). Generally, the structural factor fk (which stands for the part of the series structure) decreases with an increasing moisture content and a decreasing porosity (Hamdami et al., 2003; Maroulis, Krokida, & Rahman, 2002). The Krischer’s model tends then toward the parallel model. By considering that the crust porosity and moisture were lower than those of the crumb, it can be deduced from Table 3 that the moisture content effect is less important than the porosity effect on the struc-
Fig. 8. Effect of the evaporation–condensation phenomenon on the crumb and crust samples thermal conductivity with xtw ¼ 0:45 and 0.25, and ea ¼ 0:85 and 0.76.
N. Hamdami et al. / Food Research International 37 (2004) 703–713
tural factor. The difference in feva–con for the crumb and crust samples can be explained by the lower value of free water for evaporation and the less porous structure in the crust (Fig. 8 and Table 3). By comparing the predictions of the Krischer’s model with the experimental values, with and without considering the evaporation– condensation phenomenon (Fig. 8), it can be seen that evaporation–condensation plays an important part in heat transfer in crumb compared to the crust. This observation confirms the hypothesis by de Vries et al. (1989) that evaporation–condensation in the crumb results in more rapid heat transfer.
5. Conclusion In this paper, some thermophysical properties, such as porosity, apparent and true densities, specific heat, enthalpy and effective thermal conductivity, of partly baked bread crumb and crust were estimated. The results showed that: (i) The crust forms 25.0 1.9% in volume and 37.8 1.9% in weight of the partly baked bread samples. (ii) The total and unfrozen water mass fractions are respectively 0.45 and 0.23 in crumb, and 0.27 and 0.24 in crust. (iii) The Krischer’s model correlates thermal conductivity data in bread crumb and crust better than the other models (parallel, series and Maxwell models) due to the presence of an extra empirical curve-fitting factor. (iv) In the crust, the measured thermal conductivity lies closer to the parallel model than to the series model compared to the crumb. (v) Evaporation–condensation has a significant part in heat transfer of the crumb. These results could be used to model coupled heat and mass transfer during freezing of the partly baked breads. Acknowledgements Acknowledgements to Jacques Laurenceau, Luc Guihard and Olivier Rioux for technical support. References Baik, O. D., Marcotte, M., Sablani, S. S., & Castaigne, F. (2001). Thermal and physical properties of bakery products. Critical Review in Food Science and Nutrition, 41(5), 321–352. Bakshi, A. S., & Yoon, J. (1984). Thermophysical properties of bread rolls during baking. Lebensmittel Wissenschaft und Technologie, 17, 90–93. Christenson, M. E., Tong, C. H., & Lund, D. B. (1989). Physical properties of baked products as functions of moisture and temperature. Journal of Food Processing and Preservation, 13, 201–217. de Vries, U., Sluimer, P., & Bloksma, A. H. (1989). A quantitative model for heat transport in dough and crumb during baking. In Proceedings of cereal science and technology in Sweden (pp. 174– 188). Ystad, Sweden: Lund University.
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Hamdami, N., Monteau, J.-Y., & Le Bail, A. (2003). Effective thermal conductivity of a high porosity model food at above and subfreezing temperatures. International Journal of Refrigeration, 26(7), 809–816. Heldman, D. R. (1982). Food properties during freezing. Food Technology, 36, 92–96. Hwang, M. P., & Hayakawa, K. (1980). Bulk densities of cookies undergoing commercial baking processes. Journal of Food Science, 45, 1400. Johnsson, C., & Skj€ oldebrand, C. (1983). Thermal properties of bread during baking. In Proceedings of third international congress on engineering and food (pp. 333–341). Dublin: Elsevier Applied Science Publishers. Lind, I. (1991). The measurement and prediction of thermal properties of food during freezing and thawing – A review with particular reference to meat and dough. Journal of Food Engineering, 13, 285– 319. Mannheim, H. C., Steinberg, M. P., Nelson, A. I., & Kendall, T. W. (1957). The specific heat content of bread. Food Technology, 7, 384–388. Maroulis, Z. B., Krokida, M. K., & Rahman, M. S. (2002). A structural generic model to predict the effective thermal conductivity of fruits and vegetables during drying. Journal of Food Engineering, 52(1), 47–52. McDonald, K., & Sun, D.-W. (2001). The formation of pores and their effects in a cooked beef product on the efficiency of vacuum cooling. Journal of Food Engineering, 47, 175–183. McGinnis, D. S. (1987). Automated line-heat source system for the measurement of thermal conductivity and diffusivity. Canadian Agricultural Engineering, 29(2), 201–207. Miles, C. A., van Beek, G., & Veerkamp, C. H. (1983). Calculation of thermophysical properties of foods. In R. Jowitt, F. Escher, B. Hallstrom, H. F. Meffert, W. E. L. Spiess, & G. Vos (Eds.), Physical properties of food (pp. 269–313). London: Applied Science Publishers. Millet, P., & Dougin, Y. (1994). Boulangerie industrielle francßaise. L’^age adulte. Industries des Cereales (April–June), 45–50. Nesvadba, P. (1982). Methods for the measurement of thermal conductivity and diffusivity of foodstuffs. Journal of Food Engineering, 1, 93–115. Pham, Q. T. (1987). Calculation of bound water in frozen food. Journal of Food Science, 52(1), 210–212. Rahman, M. S. (1995). Food properties handbook. Boca Raton, FL: CRC Press. Rask, C. (1989). Thermal properties of dough and bakery products: A review of published data. Journal of Food Engineering, 9, 167–193. Ross, K. D. (1978). Differential scanning calorimetry of nonfreezable water in solute-macromolecule-water systems. Journal of Food Science, 43(6), 1812–1815. Roussel, P., & Chiron, H. (2002). Les pains francßais: Evolution, qualite, production. Vesoul: Mae-Erti Editeurs. Singh, R. P. (1992). Heating and cooling processes for foods. In D. R. Heldman & D. B. Lund (Eds.), Handbook of food engineering (pp. 247–276). New York: Marcel Dekker Inc.. Sweat, V. E., & Parmelee, C. E. (1978). Measurement of thermal conductivity of dairy products and margarines. Journal of Food Process Engineering, 2, 187–197. Tocci, A. M., Flores, E. S. E., & Mascheroni, R. H. (1997). Enthalpy, heat capacity and thermal conductivity of boneless mutton between )40 and +40 °C. Lebensmittel Wissenschaft und Technologie, 30, 184–191. Wang, D. Q., & Kolbe, E. (1991). Thermal properties of surimi analysed using DSC. Journal of Food Science, 56(2), 302–308. Zanoni, B., & Peri, C. (1993). A study of the bread-baking process. I: a phenomenological model. Journal of Food Engineering, 19(4), 389– 398. Zanoni, B., Peri, C., & Gianotti, R. (1995). Determination of the thermal diffusivity of bread as a function of porosity. Journal of Food Engineering, 26(4), 497–510.
Thermophysical properties evolution of French partly baked bread during freezing Nasser Hamdami b
a,b
, Jean-Yves Monteau
b,*
, Alain Le Bail
b
a Department of Food Science and Technology, The University of Tabriz, 51664 Tabriz, Iran UMR GEPEA (UA CNRS 6144 – SPI), ENITIAA, Rue de la Geraudiere BP 82225, F-44322 Nantes Cedex 03, France
Received 1 October 2003; accepted 26 February 2004
Abstract Few data are available on the thermophysical properties of the frozen partly baked breads. In this paper, thermophysical properties, including apparent and true densities, specific heat, enthalpy and effective thermal conductivity were determined separately for crumb and crust of partly baked bread. Total enthalpy of fusion, unfrozen water and solid specific heat were determined by differential scanning calorimetry. The apparent specific heats were estimated in base of the unfrozen water at )40 °C and initial freezing point. The effective thermal conductivity was measured with a line source probe in the range )35 to 25 °C. Four predictive models of the effective thermal conductivity of porous food were developed (parallel, series, Krischer and Maxwell models). The effective thermal conductivity predicted by Krischer model was in good agreement with the experimental data. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Bread; Thermophysical properties; Porous media; Freezing
1. Introduction Partly baked bread has developed a lot in the past decade. The objective of the part baking is to carry out gelatinization and coagulation of gluten, without reaching the coloring reactions of the crust (Roussel & Chiron, 2002). To retard staling and to extend shelf life of bread, the part baked breads are often frozen. The frozen part baked breads represent half of the volume of frozen breads exported by the French industrialists towards Northern Europe (Millet & Dougin, 1994). Twenty two percent of the industrial bread was part baked frozen bread in 2001 with a growing market share. The study of the heat and mass transfers during freezing, for the assessment of the product behavior under proposed process conditions and for the efficient design of process and equipment, requires accurate values of thermal and physical properties of bread. Many *
Corresponding author. Tel.: +33-251-785-481; fax: +33-251-785467. E-mail address: [email protected] (J.-Y. Monteau). 0963-9969/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodres.2004.02.017
studies on thermophysical properties of bakery products are available in the literature. However, data on thermophysical properties of dough and bakery products during freezing are scarce as compared to other food products, and no published information is available concerning the thermal and physical properties of partly baked bread during freezing. The methods available for measuring and modeling the thermophysical properties of bakery products have been reviewed by different researchers. Rask (1989) reviewed data and prediction models of thermal properties of bakery products. Lind (1991) presented measurement techniques and models of thermal properties of dough during freezing and thawing. More recently, Baik, Marcotte, Sablani, and Castaigne (2001) reviewed measurement techniques, prediction models and published data on thermophysical properties of bakery products. While several modeling approaches have been proposed to predict thermal properties of a material at desired conditions, none of them can be used over a wide range of foods. The most promising approach is based on chemical composition, temperature and physical characteristics. Besides, most structural models neglect
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Nomenclature aw Cp D E feva–con fk H Hfw I L L0 P Q r r R R S T x
water activity specific (sensible) heat (J kg1 °C1 ) diffusivity of water vapor in air, (m2 s1 ) Euler’s constant, 0.5772157 resistance factor against vapor transport structural factor or distribution factor of the Krischer model enthalpy (J kg1 ) enthalpy of water fusion (J kg1 ) current intensity through the heater wire (A) latent heat of fusion (J kg1 ) latent heat of evaporation (J mol1 ) total pressure (Pa) power generated by the probe heater (W m1 ) correlation coefficient distance from the line heat source (m) electric resistance (X m1 ) perfect gas constant, 8.314510 (J mol1 °C1 ) slope of the linear portion of the plot of the temperature vs. In(time) temperature (K) mass fraction (kg/kg product)
Greek letters a thermal diffusivity (m2 s1 ) k thermal conductivity (W m1 °C1 ) interactions between components although they can be significant. The properties that are concerned by this study are the density, the porosity, the unfrozen water mass fraction, the specific heat, the enthalpy, and the thermal conductivity. Two densities can be distinguished, namely the bulk and the true density. For the bulk or apparent density, the pores volume is considered as a part of the material volume. For the second one, the material volume is the volume without the pores (McDonald & Sun, 2001). The bulk density can be determined simply by dividing the mass of the product by its volume. Volume can be measured with various displacement methods (Bakshi & Yoon, 1984; Hwang & Hayakawa, 1980). The volume can also be calculated from sample dimensions if the object has a regular geometry (Christenson, Tong, & Lund, 1989). General models reported in the literature allow the apparent density of any food product to be calculated as a function of the chemical composition, moisture, porosity and temperature (Miles, van Beek, & Veerkamp, 1983). In addition, semi-empirical (Hwang & Hayakawa, 1980) and empirical models (Bakshi & Yoon, 1984) are available. These models describe the variation
keva–con equivalent thermal conductivity due to eva– con phenomenon (W m1 K1 ) h temperature (°C) hi initial freezing point (°C) hr reference temperature ðH ¼ 0Þ (°C) e volume fraction (m3 /m3 product) ea porosity q density (kg m3 ) Subscripts a correspond of pores (voids) air air app apparent u unfrozen water at low temperature (unfreezable water) c continue d dispersed eva–con evaporation–condensation i ice or component i Kri Krischer Max Maxwell pa parallel s solid se series sat saturated t true tw total water w liquid water 0 at 0 °C of the apparent density of baked products, such as cookies and bread rolls, as a function of temperature, moisture and baking time. The true density is usually determined with a pychnometer. If the material is soft, the porosity can be determined from volumes of compressed and non-compressed material (Zanoni, Peri, & Gianotti, 1995). More often it is calculated from the real and apparent densities (Miles et al., 1983). Water can be present in different states in a food during freezing. We arbitrarily choose that 100% of the frozenable water will frozen at a temperature of )40 °C. Therefore, the amount of unfrozen water at this temperature will be named ‘‘unfreezable water’’. The unfreezable water mass fraction can be determined by differential scanning calorimetry (DSC): it is the difference between the total water content and the amount of water detected by the fusion endotherm (Ross, 1978). Another method was proposed by Pham (1987) using enthalpy-temperature data and the Schwartzberg model of the apparent specific heat: the unfreezable water mass fraction was expressed by equaling enthalpy expressions below and above the freezing point.
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Enthalpy and apparent specific heat are two key thermal properties used to solve the non-linear heat diffusion equation when taking into account phase transition. Enthalpy is a state function for which a reference temperature has to be defined ()40 °C is often chosen) (Heldman, 1982; Wang & Kolbe, 1991). Specific heat represents the rate of enthalpy change with the temperature, dH =dh. Since latent heat removal occurs over the freezing temperature domain, it is usual to include the latent heat contribution in the specific heat, which is then called the apparent specific heat, Cpapp . Both experimental and mathematical modeling approaches have been used to determine enthalpy and apparent specific heat of frozen foods. Several methods are used to measure the apparent specific heat and the enthalpy as functions of temperature. These methods are based on experimental results obtained from calorimetric measurements (Lind, 1991; Mannheim, Steinberg, Nelson, & Kendall, 1957; Tocci, Flores, & Mascheroni, 1997). Bakshi and Yoon (1984) developed equations to estimate the specific heat of bread rolls by considering it as a two-component material, water and bread solids. They found the specific heat of bread solids to be lower than the estimated value by Mannheim et al. (1957) (1130.44 to compare with 1557.49 J kg1 °C1 ). Zanoni et al. (1995) showed that the average specific heat of dough and crumb is about 2900 J kg1 °C1 , whereas the average specific heat of the crust is about 1600 J kg1 °C1 . By analyzing the data presented they concluded that moisture is the major variable that influences the specific heat of food products, and that temperature has little effect provided there is no phase change. Thus, there are semi-empirical models describing the variation of the specific heat of baked products with moisture, such as the model of Bakshi and Yoon (1984) for bread rolls, and that of Christenson et al. (1989) for bread, muffins and biscuits. Johnsson and Skj€ oldebrand (1983) setup semi-empirical models for specific heat of bread as functions of moisture and temperature. One of the most important thermal properties is thermal conductivity. Measurement methods of thermal conductivity can be divided in two categories: steadystate methods (SSM) and unsteady state or transient methods (TM). Most researchers recommended TM (Nesvadba, 1982). Among TM, the simplest and most widely used is the line heat source thermal conductivity probe method. Advantages of this method are: (i) a short duration of the experiments (range 5–20 s) and (ii) a reduced temperature rise of the sample (a few °C). By its theory assuming purely conductive–diffusive heat transfer, this method is not appropriate for the determination of thermal conductivity at temperatures slightly below the initial freezing temperatures because of the associated variation of the ice content. The prediction of thermal conductivity values in this tempera-
705
ture range using a specific model is sometimes more accurate than measurements (Wang & Kolbe, 1991). Bakshi and Yoon (1984) used the line heat source probe method to measure thermal conductivity of bread products at various moisture contents. They showed that average thermal conductivity of bread dough is about 0.4 W m1 °C1 . Rask, in its review of published data (Rask, 1989), showed that the thermal conductivity for crumb and crust are respectively about 0.3 and 0.05 W m1 °C1 . These values depend on the fact that thermal conductivity is a function of moisture, apparent density and therefore porosity. Thermal conductivity has been presented and modeled as a function of moisture content or process temperature. It has now been recognized that thermal conductivity of foods, including bakery products, is also influenced by the amount of air fraction in the food material. A great variety of more or less complex equations for calculating thermal conductivities exists in the literature. The most well known physical models are the parallel model, the perpendicular (or series) model, the dispersed phase model (or Maxwell model) and the Krischer model (Miles et al., 1983; Rahman, 1995). This research is a part of a study on freezing modeling of the part baked breads. It was designed to collect information about thermal and physical properties of these products during freezing. The specific objectives were: 1. To determine the thermophysical properties of part baked bread as a function of moisture content and temperature. 2. To relate these properties to the samples compositions using different mathematical model. Since there are structural differences between crumb and crust, the properties mentioned above are evaluated separately for each part.
2. Theoretical section This section is intended to document the physical phenomena that determine differences in thermophysical properties between the crumb and the crust, and to give some theoretical elements allowing the prediction of these properties, elements used to obtain the results below. 2.1. Differences between crust and crumb 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 bread dough will thus change with time during baking and the crust will contain less water than the crumb which represents the internal part of the bread (Johnsson & Skj€ oldebrand, 1983; Rask, 1989).
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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. 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 apparent density of bread varies due to both the increase in the product volume and the decrease in the water content during baking. At the end of baking, the crust has low water content and a firm and less porous structure; as a result, its apparent density values are not similar to those for the crumb, which has a higher water content and is more porous (Rask, 1989; Zanoni et al., 1995). Consequently, the other thermal properties are different in the two parts. de Vries, Sluimer, and Bloksma (1989) proposed mathematical models for heat and mass transfer in dough and crumb with consideration of evaporation–condensation mechanism in pores. Evaporation–condensation in the crumb seemed to be a significant mechanism for heat transport in bread in comparison with conductive or radiative heat transfer. Nevertheless this transport might not to be applied to bread crust according to Zanoni and Peri (1993). 2.2. Porosity Using porosity definition and real and apparent densities definition, Eq. (1) can be setup to calculate the porosity (Miles et al., 1983) qapp ea ¼ 1 : ð1Þ qt
Cpapp ðhÞ ¼ CpW ðhÞxW ðhÞ þ Cpi ðhÞxi ðhÞCps ðhÞxs þ L
dxw ðhÞ : dh ð3Þ
The ice content may be estimated with hi xi ¼ ðxtw xu Þ 1 if h < hi ; h xi ¼ 0
if h P hi :
The initial freezing point was defined as the temperature at which the rate of temperature drop of the freezing curve is slowed down (freezing plateau). 2.4. Unfreezable water The unfreezable water at low temperature can be measured by DSC, simply by difference between total water content and the amount of water detected by the fusion endotherm: xu ¼ xtw
Hfw : L
ð2Þ
2.5. Apparent specific heat The apparent specific heat may be calculated by summing specific heats of each component weighed by their mass fractions, and by including energy released by the ice fusion (Miles et al., 1983)
ð5Þ
2.6. Enthalpy The relation between the enthalpy and the apparent specific heat is given by Eq. (6), with H ¼ 0 for the reference temperature hr . Z h Cpapp ðhÞdh: ð6Þ H¼ hr
2.7. Evaporation–condensation phenomenon and thermal conductivity If a temperature gradient is applied to a porous food material, moisture migration as vapor in the pore space occurs. Water evaporates at the high temperature side, diffuses in the pore space according to the vapor pressure gradient caused by the temperature gradient, and condensates at low temperature side (de Vries et al., 1989). Thus latent heat is transported through the pores. By considering the effect of the latent heat transport, the effective thermal conductivity in pores was given by the following equation: ka ðhÞ ¼ kair ðhÞ þ keva–con ðhÞfeva–con ;
2.3. Initial freezing point
ð4Þ
ð7Þ
where keva–con is the equivalent thermal conductivity due to the latent heat transport (evaporation–condensation): keva–con ðT Þ ¼
DðT Þ P dPsat L0 ðT Þaw ðT Þ: RT P aw Psat ðT Þ dT
ð8Þ
This equation is assumed to be applicable to the estimation of the effective thermal conductivity of porous food in our conditions. 2.8. Line heat source probe For pffiffiffiffipoints close to the line heat source such that r=ð2 atÞ P 0:16, the temperature variation initiated by a line heat source is given to better than 1% error (McGinnis, 1987): Q 4at DT ðtÞ ¼ ln 2 E : ð9Þ 4pk r The conductivity may then be determined from the slope S of the straight line DT vs. ln t:
N. Hamdami et al. / Food Research International 37 (2004) 703–713
Q ; 4pS where the power generated by the probe is
k¼
Q ¼ I 2 R:
ð10Þ
2.9. Thermal conductivity models Assuming that the food material is a four-phase system consisting of air, water, ice and solids, the parallel and series models are respectively represented by the following equations (Miles et al., 1983): kpa ðhÞ ¼ ea ðhÞka ðhÞ þ es ðhÞks ðhÞ þ ew ðhÞkw ðhÞ þ ei ðhÞki ðhÞ; ð12Þ kse ðhÞ ¼ 1
ea ðhÞ es ðhÞ ew ðhÞ ei ðhÞ þ þ þ ; ka ðhÞ ks ðhÞ kw ðhÞ ki ðhÞ
ð13Þ
where ki , kw and ks are respectively the thermal conductivities of ice, water and solid (carbohydrate). The volume fraction of any component, ei as a function of temperature is obtained from the following equation ei ðhÞ ¼
qapp xi ðhÞ ; qi
ð14Þ
where xi and qi are respectively the mass fraction (kg/kg product) and the density of the components. Krischer’ s model is based on two extremes in thermal conductivity values, one being derived from the parallel model and the other being derived from the series model, whilst the real value of thermal conductivity should be somewhat in between these two extremes. The distribution factor fk is a weighing factor. kKri ðhÞ ¼
1fk kpa ðhÞ
1 : k þ ksefðhÞ
ð15Þ
The thermal conductivity of a food by the Maxwell equation is defined as (Miles et al., 1983): kMax ¼ kc
2kc þ kd 2ed ðkc kd Þ ; 2kc þ kd þ ed ðkc kd Þ
3. Materials and methods 3.1. Partly baked bread preparation
ð11Þ
707
ð16Þ
where kc and kd are respectively the thermal conductivities of the continuous and discontinuous phase, and ed the volume fraction of the dispersed phase.
Flour was purchased from a local milling plant (Nantes, France). Flour analysis and dough recipe are provided in Table 1. Mixing was done in a spiral mixer (VMI, Montaigu, France) and comprised two steps: a low-speed mixing step (4 min, 100 rpm), and a highspeed mixing step (11 min, 200 rpm). The temperature of the dough after kneading was 23 0.5 °C. The dough was divided into round pieces (140 1 g) and fermented for 30 min at ambient temperature. After first proofing the dough was formed into 30 cm long cylinders and proofed for 90 min at 27 °C and at a relative humidity greater than 90% (final proof). Then, the scarified pieces of dough were pre-baked for 12 min in a convection oven at 150 °C. During the first minutes, water was injected in oven for decreasing the weight loss of samples. The final diameter of the bread cylinders was approximately 57 2 mm. After pre-cooling at 10 °C and at a relative humidity greater than 85% for 40 min, the partly baked breads were packaged in two moisture impermeable films, frozen at )30 °C and stored at )20 °C. 3.2. Sample preparation for analysis In this study, cylindrical breads for density and porosity, crumb samples for unfreezable water and thermal conductivity, and crust slices for unfeezable water, conductivity, density and porosity were used. They were obtained according to the following procedure (Fig. 1(a)): firstly, the frozen partly baked bread was divided in three parts. Then, the cylindrical bread sample was obtained from central part (15 cm long). Finally, the crust was removed from cylindrical bread sample and the interior portion remained as crumb. The socalled crust was characterized by a dense structure with a thickness of about 3 mm. Separating the crust fractions in this way can be done with good reproducibility. All types of sample (bread, crumb and crust) were placed in moisture impermeable polyethylene films. The packaged samples were thawed at 20 °C for 2 h before the experiments.
Table 1 Chemical components of the flour and dough recipe used in experiments Flour component
Content
Method
Dough recipe
Content (g)
Moisture (% DM) Ash content (% DM) Protein content (% DM) Hagberg falling number (s) Zeleny (%)
15.25 0.61 10.80 284 33
NFa ISOb 712 NF V 03720 NF 5 7/MS NF V 03703 NF ISO 5529
Flour Water Salt Compressed yeast Baking aid mix
100 60 2.2 3 0.7
a b
NF, French Standard. ISO, International Standard Organization.
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Fig. 1. (a) Preparation scheme of the samples (part baked bread, crumb and crust samples) and (b) probe positions in the crumb and crust samples.
3.3. Bulk and true densities and porosity Firstly, the cylindrical bread sample was weighed and measurements of apparent volume, of length and of diameter were taken. Secondly, the crumb portion was removed, and the apparent volume and the weight of crust sample were measured. The apparent volumes of bread and crust were measured by rape seed displacement method. Finally, the volume of crumb was calculated by subtraction of the crust volume from bread volume. The true density of samples was measured using a helium pychnometer (AccuPyc 1330, Micromeritics, USA). Eq. (1) was then used to calculate the sample porosities. 3.4. Total water content The total water content of samples was determined in triplicate by drying 5 g of sample in a forced convection oven at 103 °C for 16 h. The samples were cooled in a desiccator and weighed by an analytical balance (sensitivity 0.01 mg). 3.5. Unfreezable water mass fraction The unfreezable water weight fraction was determined using DSC, according to the method presented in theoretical section (Eq. (2)). 3.6. Apparent specific heat and enthalpy A differential scanning calorimeter (DSC 92, Setaram, Caluire, France) was used to evaluate the total enthalpy of the phase change and the specific heat of dry matters of the samples at atmospheric pressure. Samples (100–140 mg) were removed from different locations in crumb and crust, and hermetically closed in aluminum pans. They were frozen in situ in the calorimeter by the way of liquid nitrogen. Experiments were realized five times from )50 °C and up to 40 °C at a heating rate of 2 °C/min. An empty pan was used as a reference. The base line was obtained from a scan realized with two empty pans. Total enthalpy of the phase change was
estimated as the area under the DSC base line and expressed in J kg1 of sample (Tocci et al., 1997). The corresponding total enthalpy of fusion and specific heat were evaluated with the software of the calorimetric apparatus. Because of the span in temperature of the calorimetric peak, the experimental curve was not properly located on the temperature scale. In order to have an acceptable correspondence between the initial freezing point and the apparent specific heat function Cpapp , the apparent specific heat of samples was estimated from the Eq. (3). The temperature dependence of the amount of ice and unfrozen water were taken into account by using Eqs. (4) and (5). The initial freezing point, hi , was deduced from the temperature history of sample. Enthalpy, H , was determined using Eq. (6), with the reference temperature selected as )40 °C. 3.7. Effective thermal conductivity 3.7.1. Thermal conductivity measurement Thermal conductivity was determined with a line source probe, purchased from V. E. Sweat (Texas, A and M University). The thermal conductivity probe was similar to the one described by Sweat and Parmelee (1978). A version of the thermal conductivity measurement system developed by McGinnis (1987) was used to supply power, measure current and record temperatures and voltage (Fig. 2). Firstly, the probe was inserted into the crumb and crust samples according to the Fig. 1(b). To prevent the crust samples compression during conductivity measurement, the crust slices were cut into
Fig. 2. Setup of the thermal conductivity measurement system.
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sub-fractions (30 30 3 mm) and 13 laminates of these sub-fractions were placed in a rectangular container with internal dimension 30 30 40 mm, and packaged in moisture impermeable film to prevent the sample dehydration. Then, the assembly (probe + sample) was kept at a given temperature in an air-freezer (FroilaboS.A., Ozoir, France) having a temperature stability of 0.1 °C. The probe heater was connected to a DC power supply (Redelec 60430, Noailles, France) and a multimeter (Fluke, John Fluke MFG. Co., Inc., USA) to measure the current intensity. The accuracy of the current measurement in the heater circuit was 0.1 mA. The temperature–time and voltage–time data were continuously collected by a digital recorder (Datalog 20, AOIP, Evry, France) which was bi-directionally interfaced with a PC in order to program measurements. The record of voltage was used to find the initial time of the heating. 3.7.2. Thermal conductivity calculation The samples thermal conductivity was calculated using the Eq. (10) where Q is calculated by Eq. (11). To obtain satisfactory linearity of temperature vs. lnðtimeÞ plot, the procedure was standardized by (1) the choice of a power level to increase the temperature up to 10 °C (initial temperature basis), (2) using a duration of 8 s, and (3) by accepting thermal conductivity values measured only when r2 > 0:98. To obtain these conditions, a current value of 0.09–0.17 A was necessary. Seven measurements were made in each sample. For each sample, the conductivity reported is the mean of seven measurements. The thermal conductivity experiments were carried out at selected sample temperature, )35, )30, )25, 1, 15 and 25 °C on the crumb and crust samples, with moisture contents of 45% and 27% (wet basis), respectively. 3.7.3. Calibration The probe calibration was realized by measuring the thermal conductivity of glycerin and of a gel of 0.5% agar and water at selected temperatures between 5 and 25 °C. 3.7.4. Thermal conductivity model development The crumb and crust of bread can be analyzed as a multicomponent three-phase system which, below the initial freezing point, represents a complicated dynamic complex of four fractions, continuously changing their ratios: dry substance (proteins, lipids, carbohydrates, mineral salts, etc.), water, ice crystals and gaseous phase (including air and water vapor). In this study, four physical models, parallel, series, Maxwell and Krischer models, were tested for the thermal conductivity prediction of crumb and crust. The thermal conductivities of ice, water and solid (carbohydrates) are calculated with the following equations (Singh, 1992):
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ki ðhÞ ¼ 2:2196 6:248 103 h þ 1:0154 104 h2 ; ð17Þ kw ðhÞ ¼ 0:57109 þ 1:7625 103 h 6:7036 106 h2 ; ð18Þ kw h ¼ 0:20141 þ 1:38410 103 h þ 4:3312 106 h2 ; ð19Þ where ka is obtained from the Eq. (7). In all the calculations, the values used for ice, water and solid density were respectively 917, 1000 (Miles et al., 1983), and 1463 1.2 kg m3 (obtained from experiments). The volume fraction of discontinuous phase, ed , is obtained from Eq. (14). For Maxwell model application to porous materials including three or more components, a stepwise procedure is required. At each step the mean thermal conductivity of pairs of components is found. In this study a three-step Maxwell model, developed by Hamdami, Monteau, and Le Bail (2003), was used for thermal conductivity prediction. In the first step, the two phases considered were (1) continuous water phase, (2) discontinuous ice phase. In the second step, the phases were (1) continuous solid phase, (2) discontinuous water–ice phase. Finally, in the third step, the phases were (1) continuous solid–water–ice phase, (2) discontinuous air phase. The model parameters fk and feva–con were estimated by fitting the model calculated values of effective thermal conductivity to experimental ones.
4. Results and discussion 4.1. Density and porosity The weight and apparent volume measurements at room temperature on the partly baked bread samples and their crumb and crust, showed that the crust forms 25.0 1.9% of volume and 37.8 1.9% of weight of the partly baked bread samples. Table 2 gives the experimental apparent and true density values of the different samples (crumb and crust, average of 10 tests). As expected, crust has an apparent and true density greater than those of the crumb, due to the porosity and the total water mass fraction of the crust lower than for the crumb. 4.2. Unfreezable water, apparent specific heat and enthalpy The values of the crumb and crust unfreezable water mass fraction were estimated by application of the Eq. (2) to 10 samples for which total enthalpy of fusion
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Table 2 Apparent and true density, porosity, unfreezable and total water mass fractions of the crumb and crust samples Property
Crust
3
Apparent density (kg m ) True density (kg m3 ) Porosity Unfreezable water mass fraction (kg kg DM1 ) Total water mass fraction (kg/kg product)
Crumb
Mean value
SD
Mean value
SD
332.8 1390 0.760 0.3364 0.273
6.0 5.9 0.017 0.0060 0.025
181.7 1291.5 0.8592 0.413 0.4529
2.6 10.5 0.0030 0.049 0.0032
have been previously measured. Table 2 gives the unfreezable water mass fraction values ðxu Þ in the crumb and crust samples. The difference in the unfreezable water values of the crumb and crust samples can be explained by both physical and chemical changes occurring during the baking process (Lind, 1991). The average initial freezing point of the crumb and crust samples was found to be )5.7 °C 0.2 and )15 to )24 °C, respectively (average of five experiments). The large variation of the initial freezing point of the crust samples was due to the great freezable water content variation of the samples. The following equation gives the specific heat of dry bread as a function of temperature. It was obtained from eight tests of DSC: Cps ðhÞ ¼ 4:582h þ 1138:
ð20Þ
This shows a very good agreement with 1130.44 J kg1 °C1 for bread solids as calculated by Bakshi and Yoon (1984). From the Eqs. (3) and (6), the apparent specific heat and the enthalpy of both frozen and unfrozen products were adequately calculated as a function of temperature while knowing total and unfrozen water content, and initial freezing point. Figs. 3 and 4, show the evolution of the apparent specific heat and enthalpy values as a function of temperature during freezing for a crumb and a crust sample in respect of the given data in Table 2. As shown in
Figs. 3 and 4, because of an important freezable water mass fraction, crumb has a more intense phase change peak and a greater enthalpy than that of crust. When the samples are frozen, the enthalpies for the crust and the crumb are very close. 4.3. Effective thermal conductivity values The values of thermal conductivity measured by the line source probe method were reproducible (2% uncertainty ‘‘experimental standard deviation’’). Fig. 5 shows the effective thermal conductivity values measured for the crumb at two different probe positions (axial and radial) for three positive temperatures: 2.5, 15 and 23 °C. This figure shows that there is not important difference between the results. Thus it can be concluded that the effective thermal conductivity measurements were independent on the probe position. Moreover, it can be noticed that the points are along a straight line. The Figs. 6 and 7 present the thermal conductivity variation vs. temperature for the crumb and the crust. Values given by the models are also represented here. These figures show that effective thermal conductivity is strongly dependent on the porous structure, the freezable water content and the temperature. The effective thermal conductivity above the initial freezing point increases with increasing the temperature due to the increase of the thermal conductivity of the components
Fig. 3. Evolution of the apparent specific heat values for the crumb and crust samples.
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Fig. 4. Evolution of the enthalpy values for the crumb and crust samples.
Fig. 5. Effective thermal conductivity values measured for evolution of the apparent specific heat values for crumb at two different probe positions (radial and axial).
Fig. 6. Experimental and predicted thermal conductivity values for crumb.
(crumb and crust cases) and to the evaporation–condensation effect (crumb case only). In the sub-freezing temperatures, however, the effective thermal conductivity is dependent on freezable water content. If its value is important (crumb case), the effective thermal conductivity increases with decreasing the temperature, due to
the state change to ice. Then, it decreases very slightly. However, if the freezable water content value is less important (crust case), the stage of effective thermal conductivity increase cannot be observed with decreasing the temperature: for all the temperatures, the points are disposed along a straight line.
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Fig. 7. Experimental and predicted thermal conductivity values for crust.
The comparison between the experimental and predicted effective thermal conductivity values show that: (i) Series model gives always under-estimated thermal conductivity values for crumb and crust, (ii) Parallel model gives upper-estimated thermal conductivity values for crumb. However the predicted values approach the experimental ones for the crust, (iii) The predicted effective thermal conductivity values by Maxwell model agree with the experimental ones only for the crumb samples, (iv) The predicted thermal conductivity values
Table 3 Identified values of the resistance factor and structural factor Property
Crumb
Crust
Porosity Total water mass fraction Resistance factor feva–con Structural factor fk
0.85 0.46 0.37 0.27
0.76 0.25 0.09 0.09
by Krischer’s model are in good agreement with the experimental values in both cases. It can be concluded that Krischer’s model is able to correlate the heat transfer in the porous structure of bread crumb and crust better than the others models. These better results are due to the presence of the empirical curve-fitting factor, fk . From Table 3 it can be observed that the identified values of fk and feva–con for the crust samples are less important than for the porous crumb (assuming aw ¼ 1). Generally, the structural factor fk (which stands for the part of the series structure) decreases with an increasing moisture content and a decreasing porosity (Hamdami et al., 2003; Maroulis, Krokida, & Rahman, 2002). The Krischer’s model tends then toward the parallel model. By considering that the crust porosity and moisture were lower than those of the crumb, it can be deduced from Table 3 that the moisture content effect is less important than the porosity effect on the struc-
Fig. 8. Effect of the evaporation–condensation phenomenon on the crumb and crust samples thermal conductivity with xtw ¼ 0:45 and 0.25, and ea ¼ 0:85 and 0.76.
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tural factor. The difference in feva–con for the crumb and crust samples can be explained by the lower value of free water for evaporation and the less porous structure in the crust (Fig. 8 and Table 3). By comparing the predictions of the Krischer’s model with the experimental values, with and without considering the evaporation– condensation phenomenon (Fig. 8), it can be seen that evaporation–condensation plays an important part in heat transfer in crumb compared to the crust. This observation confirms the hypothesis by de Vries et al. (1989) that evaporation–condensation in the crumb results in more rapid heat transfer.
5. Conclusion In this paper, some thermophysical properties, such as porosity, apparent and true densities, specific heat, enthalpy and effective thermal conductivity, of partly baked bread crumb and crust were estimated. The results showed that: (i) The crust forms 25.0 1.9% in volume and 37.8 1.9% in weight of the partly baked bread samples. (ii) The total and unfrozen water mass fractions are respectively 0.45 and 0.23 in crumb, and 0.27 and 0.24 in crust. (iii) The Krischer’s model correlates thermal conductivity data in bread crumb and crust better than the other models (parallel, series and Maxwell models) due to the presence of an extra empirical curve-fitting factor. (iv) In the crust, the measured thermal conductivity lies closer to the parallel model than to the series model compared to the crumb. (v) Evaporation–condensation has a significant part in heat transfer of the crumb. These results could be used to model coupled heat and mass transfer during freezing of the partly baked breads. Acknowledgements Acknowledgements to Jacques Laurenceau, Luc Guihard and Olivier Rioux for technical support. References Baik, O. D., Marcotte, M., Sablani, S. S., & Castaigne, F. (2001). Thermal and physical properties of bakery products. Critical Review in Food Science and Nutrition, 41(5), 321–352. Bakshi, A. S., & Yoon, J. (1984). Thermophysical properties of bread rolls during baking. Lebensmittel Wissenschaft und Technologie, 17, 90–93. Christenson, M. E., Tong, C. H., & Lund, D. B. (1989). Physical properties of baked products as functions of moisture and temperature. Journal of Food Processing and Preservation, 13, 201–217. de Vries, U., Sluimer, P., & Bloksma, A. H. (1989). A quantitative model for heat transport in dough and crumb during baking. In Proceedings of cereal science and technology in Sweden (pp. 174– 188). Ystad, Sweden: Lund University.
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