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Thermophysical properties of processed meat and poultry products
Available online at www.sciencedirect.com
Journal of Food Engineering 88 (2008) 315–322 www.elsevier.com/locate/jfoodeng
Thermophysical properties of processed meat and poultry products Miche`le Marcotte a,*, Ali R. Taherian a, Yousef Karimi a,b a
Food Research and Development Centre, Agriculture and Agri-Food Canada, 3600 Casavant Blvd West. St. Hyacinthe, Quebec, Canada J2S 8E3 b Department of Food Science and Agricultural Chemistry, McGill University, Macdonald Campus, 21,111 Lakeshore Road, Ste Anne de Bellevue, Quebec, Canada H9X 3V9 Received 6 September 2007; received in revised form 7 February 2008; accepted 13 February 2008 Available online 10 March 2008
Abstract Thermophysical properties of various meat and poultry emulsions were evaluated at four temperatures (20, 40, 60 and 80 °C). Thermal conductivities (0.26–0.48 W m1 K1) increased linearly with temperature between 20 and 60 °C. Between 60 and 80 °C, it remained constant for most products except bologna. Curves for thermal conductivity as a function of temperature could be roughly grouped into two different categories: products containing meat particles and those containing meat emulsions. The application of various models was investigated for thermal conductivity prediction. It was found that a three phase structural based Kirscher model had the potential for predicting thermal conductivities with acceptable accuracy. Densities decreased slightly as a function of temperature from 20 to 40 °C. A transition phase was observed from 40 to 60 °C, which was followed by a decrease from 60 to 80 °C. There was a decrease of about 50 kg m3 between the density of a raw product at room temperature (at maximum 1070 kg m3) and the product heated to 80 °C (at minimum 970 kg m3), due to the gelation or setting of the structure. After a transition period from 10 to 30 °C, the heat capacity increased linearly from 30 to 80 °C, and ranged from 2850 to 3380 J kg1 °C1, respectively. Densities and heat capacities were strongly influenced by the carbohydrate content (i.e. as the carbohydrate content increased the density decreased). The salt content adversely affected thermal conductivity and thermal diffusivity values. However, these parameters increased with moisture content. Ó 2008 Published by Elsevier Ltd. Keywords: Meat and poultry emulsions; Meat and poultry products; Thermal conductivity; Thermophysical properties; Modeling; Correlation matrix
1. Introduction Thermophysical properties (specific heat, thermal conductivity, thermal diffusivity and density) of food are important parameters in describing various thermal processes, optimizing the design and the operation of heating, cooking, freezing and cooling systems (Karunakar et al., 1998). Thermal properties are also essential for the modeling and evaluation of food processing operations involving heat transfer, especially when energy costs, food quality and safety are the main considerations. These properties are especially important to ensure food safety
*
Corresponding author. Tel.: +1 450 768 3295; fax: +1 450 773 2888. E-mail address: [email protected] (M. Marcotte).
0260-8774/$ - see front matter Ó 2008 Published by Elsevier Ltd. doi:10.1016/j.jfoodeng.2008.02.016
(Unklesbay et al., 1999). As an example, the temperature at the core of a typical sausage must be above a certain level (72 °C) by the end of heating and below certain temperature (15 °C) at the end of cooling in order to achieve microbiological stability of the product (Akterian, 1997). Therefore, there is a need to evaluate the heating characteristics of the products, known as thermophysical properties. There are many methods available to measure thermophysical properties such as guarded hot plate method, differential scanning calorimeter (DSC) attachment method, capped column test device, line heat source probe method, temperature history and transient hot strip (THS) method (Baik et al., 2001). While the first three mentioned methods are applied at steady state, the last two methods are applied for transient conditions.
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Nomenclature Cp E f I k m N O Q Rth r2
specific heat at constant pressure (kJ m3 o 1 C ) predicted value a distribution factor current (mA) thermal conductivity (W m1 K1) slope of the linear part of the temperature vs. ln (time) graph number of samples experimental value heat flux (W m1) probe resistance (m1) coefficient of determination
Thermal conductivity is highly temperature dependent especially over a temperature range where a phase change occurs. According to Karunakar et al. (1998), at a low temperature range (0–40 °C), the thermal conductivity does not exhibit very significant difference between various temperatures. At high temperatures (>50 °C), it increases gradually as the temperature increases (Pan and Singh, 2001). Both thermal conductivity and heat capacity are known to increase with moisture content increase (Shmalko et al., 1996). Water content will affect the heat capacity more than other components, the lower heat capacity values generally occur with the lower moisture content values (Unklesbay et al., 1999). Thermal conductivity and density of foods vary with temperature during thermal processing due to the changes in texture and/or composition (Karunakar et al., 1998). A decrease in density values will become important due to its effect on other thermal properties (Mohsenin, 1980). Most changes in meat products occur during heating, shrinkage, tissue hardening, moisture loss, fat loss and discoloration, and are caused by the changes in muscle protein denaturation (Pan and Singh, 2001). All these changes in the meat will affect the thermophysical properties. Mathematical models can be used to study and understand the relationship between thermophysical properties of complex food systems and temperature. For the prediction of the thermal conductivities, a large number of models have been suggested in the literature (Gonzo, 2002; Wang et al., 2006; Carson, 2006), used for composite or heterogeneous materials based on composition. Most of the proposed models are highly material based and contain material-specific parameters. Although, some models are considered to have a more general applicability, their parameters are still empirically determined. Generic models have been proposed by some scientists (Gonzo, 2002; Wang et al., 2006; Carson, 2006), where a set of equations, usually based on a conceptual ‘parent’ model, are derived. These models are developed so that they can account for variations in composition and struc-
SD T
Standard error temperature
Greek symbols a thermal diffusivity (m2 s1) U volume fraction q density (kg m3) Subscripts a air i component i s solid w water
ture, even though they often contain empirical parameters. The selection of the appropriate model for a given food product is not an easy task. As reported by Carson et al. (2006), there is a huge disagreement between thermal conductivity values predicted from various models. It can be concluded that, to-date, no single model or prediction procedure has been found with a universal applicability. Therefore, it must be evaluated on a case-by case basis. In recent decades, there have been many published research work on experimental values of thermophysical properties of foods and mathematical models to represent these data (Polley et al., 1980; Sanz et al., 1987; Lind, 1991; Karunakar et al., 1998; Baik et al., 2001; Gonzo, 2002; Wang et al., 2006; Carson, 2006). However, there is very little work done on food emulsions. The overall goal of this study was to measure thermophysical properties of various commercial meat and poultry emulsions as a function of temperature. A more specific objective was also to investigate the ability of mathematical models to predict the thermal conductivity of these emulsions. 2. Materials and methods 2.1. Products Five types of meat products were used: fine emulsion of bologna and wieners, coarse emulsion of pepperoni, turkey emulsion and flaky ham. Turkey emulsions and the flaky ham contained muscle parts. Raw products were collected from a typical industrial plant and measurements were made the day after. The products were kept at 4 °C cold room until they were analyzed. All experiments were performed three times and with three different batches of products. Thermophysical properties of meat and poultry emulsions were gathered at different temperatures from raw product to cooked product temperature. The composition of meat and poultry emulsions studied is listed in Table 1.
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Having the slope, it was possible to calculate the thermal conductivity using the following equations:
Table 1 Composition of various meat and poultry emulsions (%) Food emulsion
Moisture
Fat
Salt
Ash
Protein
Carbohydrate
Q ¼ Rth I 2
Bologna Pepperoni Wieners Turkey Ham
61.59 57.26 60.51 74.88 72.70
20.31 21.72 20.9 1.67 6.35
2.39 2.53 2.43 1.54 2.78
4.22 3.48 4.19 6.69 7.08
11.49 12.32 12.4 15.46 11.62
2.39 5.22 2.00 1.30 2.25
k¼
Q 4pm
ð1Þ ð2Þ
where Q is the heat flux (W m1), Rth the probe resistance (X m1), k the thermal conductivity (W m1 K1), I the current (mA) and m the slope of the linear part of the temperature vs. ln (time) graph.
2.2. Thermal conductivity measurements
2.3. Density measurement
Thermal conductivity measurements of various meat samples were performed using the probe method based on the line-heat source approach developed by Sweat (1974). In the probe method, there was a heater wire insulated over its length and a thermocouple at the center of this length. The probe was 38 mm long with an outside diameter of 0.66 mm. It consisted of a constantan heater wire and a chromel–constantan thermocouple (type E) (Sweat, 1995). The probe was connected to a power supply (Hewlett-Packard, 6236B) and to a multimeter (TES 2610 multimeter) in order to read the current more precisely; the multimeter was set to read in mA DC. The thermocouple wires were connected to a data acquisition system (Data Shuttle by Strawberry Tree) connected to a computer (Baik et al., 1999). The software ‘‘Workbench for Windows version 3” was used to convert the analog signal of the thermocouple into a digital signal, to set the acquisition rate at 1 reading every 2 s. The probe had a theoretical internal resistance of 226.67 X m1. It was calibrated with glycerol. Values obtained were within 10% of the literature value of 0.284 W m1 K1 at 20 °C. Constant temperature baths set in increments of 20 °C were used for the experiments: water baths at 20 °C, 40 °C and 60 °C, and an 80 °C oil bath to prevent evaporation. A copper cylinder (12.7 cm height and 2.54 cm inside diameter with a maximum wall thickness of 0.159 cm) with a high thermal conductivity was used. Emulsions samples were inserted using a syringe, whereas the turkey and the flaky ham were introduced by hand. A rubber cover was placed at both ends of the cylinder to insulate them and maintain heat flow only from the side of the cylinder. An infinite cylinder was assumed for thermal conductivity calculations. Three cylinders were placed in each of the four temperature controlled water bath. When the core temperature of the samples reached equilibrium with the water bath, the top rubber cover was replaced by a thinner one and the probe was inserted in a small hole made at the center. The probe was placed at the core of the sample. The data acquisition was switched on for 8 s to record the initial temperature. Then the power was turned on to pass a current of 200 mA for 2 min of data acquisition before being stopped. The thermal conductivity was calculated by plotting the temperature versus the natural logarithm of the time and taking the slope of the linear part of this graph.
Densities were determined from the mass of the samples inserted in the copper cylinder and the volume of the cylinders, which were pre-determined for six cylinders and the average value was considered. The mass of the samples was measured at the end of the treatment to verify if there was any weight change during the treatment. The density was calculated as the ratio of the final mass of the sample to its volume. 2.4. Heat capacity A modulated differential scanning calorimeter (MDSC 2910, TA Instruments Inc., New Castle, DE) was used with a nitrogen cooling system. MDSC has the ability for application of two independent heating rates, isothermal and modulated, which is an advantage over conventional DSC that carries only isothermal. This allowed determination of the heat capacity at various temperatures. At the start, the cell constant of the instrument was evaluated by running an experiment with Sapphire (Al2O3). The ratio of the experimental heat capacity to the theoretical heat capacity of Sapphire gave a cell constant of 1.935. A minimum mass of 200 g product was then homogenized using a ‘‘Polytron” (Polytron, PT 10–35 by Kinematica) in order to get a representative sample, especially for coarse emulsion, turkey and ham, and to fill up the experimental container which was small in capacity. A sample of 10–13 mg was placed in the aluminium pan which was then hermetically sealed using an encapsulating press from TA Instruments Inc. An empty pan that had been previously weight-matched with the sample pan was also sealed for reference. The method consisted of equilibrating the sample at 5 °C, starting the modulation for a 60-second period with an amplitude of ±1 °C, keeping it isothermal for 5 min, and heating the sample at a rate of 2.0 °C/min from 5 °C to 90 °C. Helium was used as a purging gas at a flow of 25 ml min1. The instrument automatically gave heat capacity curves from 5 to 90 °C. Furthermore, the heat capacities (Cp) of the emulsions were related to temperature (T) using following linear regression equation: C p ¼ a þ bT
ð3Þ
where a is the intercept and b the slope of the regression line.
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2.5. Thermal diffusivity calculation The thermal diffusivity values were calculated from the experimental values of density, thermal conductivity and specific heat using the following equation: k a¼ qC p
ð4Þ
where a is the thermal diffusivity (m2 s1), k the thermal conductivity (W m1 K1), q is density (kg m3), Cp is specific heat at constant pressure (kJ m3 °C1).
Table 3 Thermal conductivity of food components as a function of temperature (40 °C < T < (150 °C) Component
Thermal conductivity (W m1 K1)
Protein Fat Carbohydrate ash Ash Water Air
1.7880 101 + 1.1958 103 T 2.7178 106 T 1.8071 101 2.7604 104 T 1.7749 107 T 2.0141 101 + 1.3874 103 T 4.3312 106 T
2 2
3.2962 101 + 1.4011 103 T 2.9069 106 T 2 5.7109 101 + 1.7625 103 T – 6.7036 106 T 2 2.3820 102 + 6.75 105 T
Adapted from Ramaswawy and Marcotte (2006).
2.6. Thermal conductivity modeling A generic three phase model, known as Kirscher’s model (Maroulis et al., 2002; Wang et al., 2006), was selected and used in this study. Kirscher’s model is one of the most widely used, and it is basically a combination of the prediction of the Series and Parallel models (Carson et al., 2006) containing a weighting parameter (f) (also named distribution factor) which has to be adjusted for different food systems. The model was formulated as follows: 1 þ kfse Þ
ð5Þ
k p ¼ /s k s þ /w k w þ /a k a
ð6Þ
ke ¼
k se ¼
ð1f kp
1 /s ks
ð7Þ
þ /kww þ /kaa
where kw, ks, ka are the thermal conductivities of water, solids and air, respectively, f is a distribution factor and Uw, Us, Ua are the volume fractions of water, solids and air, respectively. Thermal conductivities of pure food components are available in the literature as a function of temperatures. The volume fractions (Uw, Us, Ua) are dependent on the material state. Since the compositions of meat and poultry emulsions were determined and presented on a weight basis, the volume fraction of each component was evaluated using its density. The densities of various components, as a function of temperature, are shown in Table 2 (Ramaswamy and Marcotte, 2006). The thermal conductivity of the solid phase was calculated by combining the thermal conductivity of each individual component (i.e., protein, carbohydrate, ash, and fat) using the procedure suggested by Table 2 Density of food components (40 °C < T < (150 °C)
as
a
function
of
temperature
Component
Density (kg m3)
Protein Fat Carbohydrate Ash Water Air
1329.9–0.5184 T 925.59–0.41757 T 1599.1–0.31046 T 2423.8–0.28063 T 997.18 + 3.1439 103 T – 3.7574 103 T 1.2847–3.2358 103 T
Adapted from Ramaswamy and Marcotte (2006).
2
Carson et al. (2006). The component thermal conductivity was determined using the functions presented in Table 3. Since the Kirscher’s weighing factor was not available for meat and poultry emulsions, it was adjusted to get the best model performance i.e. by matching predicted and experimental values. In order to examine the performance of the applied model, the correlation between thermal conductivity values predicted by the model and those calculated from the experimental data were evaluated using the coefficient of determination (r2), standard errors and standard percentage errors. The standard error was obtained by the following equation: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P ðEi Oi Þ ð8Þ SD ¼ N where Ei is the estimated value of thermal conductivity; Oi is its observed (experimental) value; and N is the number of samples. The relative standard error is defined as the ratio of standard error to the average experimental value of thermal conductivity and expressed as a percentage. 3. Results and discussion 3.1. Thermal conductivity As shown in Fig. 1, the thermal conductivity values increased with temperature for all products. For a fine bologna emulsion, the thermal conductivity increased from 0.304 ± 0.028 W m1 K1 at 22 °C to 0.459 ± 0.100 W m1 K1 at 80 °C; and for a fine wieners emulsion, the values varied from 0.281 ± 0.022 to 0.415 ± 0.066 W m1 K1. For a coarse pepperoni emulsion, the thermal conductivity varied between 0.272 ± 0.019 to 0.402 ± 0.044 W m1 K1 from 22 to 79 °C. In the case of products containing muscle parts, it was found that the thermal conductivity of turkey product varied between 0.332 ± 0.040 and 0.482 ± 0.086 W m1 K1; and that for the ham product varied from 0.339 ± 0.037 to 0.437 ± 0.058 W m1 K1. Measurements were performed using samples from three different production batches. Average values are reported since there was a good agreement between the results of these batches. Two sets of measurements were performed on each batch of products to establish repeat-
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0.50
Thermal Conductivity (W m -1 K-1)
0.45
0.40
0.35
Bologna Ham Pepperoni Turkey Wieners
0.30
0.25
0.20 20
30
40
50
60
70
80
90
Temperature (ºC)
Fig. 1. Thermal conductivity of meat and poultry emulsions.
a small increase in the volume of the sample during the heating stage of the emulsions. At the start of heating, a slight increase in density, associated with all the tested emulsions, was observed which may be due to the fat content changing phase from solid to liquid. Nevertheless, the densities decreased slightly with temperature in general (Fig. 2). For each product, the density of the final product heated to 80 °C was lower by approximately 50 kg m3 when compared with the initial raw product kept at room temperature. The density of the raw pepperoni and ham products were 1031 and 1037 kg m3 and for the cooked products were 969 and 1014 kg m3, respectively.
ability. Differences between values were found to be of the same order of magnitude as the measurements undertaken on two individual batches indicating that our methodology was highly repeatable. The observed differences between batches were probably due to variation in the composition of each batch, which may occur during production of each batch at industrial level. 3.2. Density The density changes observed during cooking were very small. There was no significant mass loss for these products. Gelation or setting of the solid structure caused
1080
1060
Density (kg m-3)
1040
1020
1000
Bologna Pepperoni Wieners Turkey Ham
980
960 20
30
40
50
60
70
Temperature (ºC)
Fig. 2. Density of meat and poultry emulsions.
80
90
320
M. Marcotte et al. / Journal of Food Engineering 88 (2008) 315–322 3500
3400
Heat capacity (J kg-1 k-1)
3300
3200
3100
3000
2900 Bologna Pepperoni Wieners TURKEY Ham
2800
2700 0
10
20
30
40
50
60
70
80
90
Temperature (°C)
Fig. 3. Heat capacity of meat and poultry emulsions.
3.3. Heat capacity
Table 4 Correlation of heat capacity with temperature for various emulsions
It is well known that the heat capacity varies with temperature, which was also confirmed by our results shown in Fig. 3. The heat capacity values of meat emulsions at constant pressure increased linearly between 35 °C and 82 °C with a gradient of 4.34 J kg1 K1. Amongst the emulsions studied, the lowest heat capacity was found for the Pepperoni emulsion: 2812 J kg1 K1 at 10 °C and 3027 J kg1 K1 at 82 °C. This emulsion showed a peak of 3160 J kg1 K1 at 26 °C. For the bologna emulsion, the heat capacity was found to be around 2933 J kg1 K1 at 10 °C and 3191 J kg1 K1 at 82 °C. The heat capacity curve for this emulsion also indicated a maximum value of 3055 J kg1 K1 at 20 °C. The minimum was 2933 J kg1 K1 at 10 °C. The heat capacity curve for wieners had a similar shape compared to bologna, but the values were approximately 150 J kg1 K1 higher over the curve length. For the turkey product, the curve was almost linear over the entire range of temperatures studied, i.e. 10 to 82 °C with a slope of 3.9 J kg1 K1 and an ordinate of 3050 J kg1 K1. The ham product had a maximum heat capacity of 3287 J kg1 K1 at 82 °C and a minimum of 3031 J kg1 K1 at 10 °C, this curve also included a peak at 20 °C (3224 J kg1 K1). The average standard deviation for all curves was 115.5 J kg1 K1. It has been reported that the composition of product (i.e. fat, protein, water and salt contents) will influence the values of these properties (Zhang et al., 2007). The peak values observed varied directly with fat content, suggesting that samples containing higher fat content absorb more thermal energy for changing the fat from solid to liquid state. In order to be able to predict heat capacity of the emulsions, the values of heat capacity were related to the temperature in the range 34–82 °C. Table 4 shows the
Emulsion
Heat capacity (J kg1 K1)
r2
Bologna Pepperoni Wieners Turkey Ham
2836.8 + 4.306 2719.1 + 3.760 2962.4 + 4.282 3003.3 + 4.567 2940.3 + 4.234
0.996 0.978 0.990 0.998 0.996
T T T T T
regression parameters along with the coefficient of determination (r2) values. High values of r2 indicate that heat capacity and temperature are noticeably related. 3.4. Thermal diffusivity Thermal diffusivity is another property that changes with temperature (Fig. 4), since it is related to all three thermophysical properties described above: conductivity, heat capacity and density. The thermal diffusivity curves were very similar to thermal conductivity curves because other properties are not as sensitive to temperature. The thermal diffusivity values of the emulsions varied from 8.30 108 m2 s1 (for pepperoni and wieners) at room temperature to 1.36 107 m2 s1 (for pepperoni) at 80 °C. 3.5. Correlation between composition and thermophysical properties Values of thermophysical properties were measured for a variety of meat and poultry emulsions. Significant differences were found that may be attributed to the meat and poultry compositions. Average values of thermophysical properties were therefore, correlated to the chemical composition. Table 5 shows the correlation matrix. A strong proportional relationship would be indicated by a value
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1.600E-07
1.500E-07
Thermal diffusivity (m2 s-1)
1.400E-07
1.300E-07
1.200E-07
1.100E-07 Bologna Pepperoni Wieners Turkey Ham
1.000E-07
9.000E-08
8.000E-08 20
30
40
50
60
70
80
90
Temperature (ºC)
Fig. 4. Thermal diffusivity of meat and poultry emulsions. Table 5 Correlation matrix for thermophysical properties vs. emulsion composition
k q Cp a Moisture (%) Fat (%) Salt (%) Protein (%) Carbohydrate (%)
k
q
Cp
a
Moisture (%)
Fat (%)
Salt (%)
Protein (%)
Carbohydrate (%)
1.000 0.383 0.744 0.959 0.960 0.978 0.652 0.776 0.655
1.000 0.734 0.155 0.530 0.387 0.099 0.055 0.828
1.000 0.525 0.743 0.668 0.488 0.491 0.972
1.000 0.899 0.957 0.638 0.799 0.419
1.000 0.986 0.450 0.569 0.678
1.000 0.503 0.654 0.580
1.000 0.927 0.471
1.000 0.393
1.000
close to 1 or 1; and a value close to 0 indicates weak correlation. From a compositional point of view, the proportion of moisture was inversely correlated to the amount of fat. The proportion of salt was also inversely related to the percentage of protein in these products. The density and the heat capacity were strongly influenced by carbohydrate content (i.e. as the carbohydrate content increased, the density decreased). As the moisture content increased, the thermal conductivity and diffusivity increased. As the fat content increased, the value of k and a decreased. Contrary to the expectations, the proportion of salt did not have any significant effect on the density, heat capacity, thermal conductivity and diffusivity. This was probably due to the limited amount of salt (approximately 2%) added to the emulsions. The proportion of proteins did not significantly influence these properties as correlation coefficients were smaller than 0.9. 3.6. Thermal conductivity modeling Meat and poultry emulsions can be considered to be porous media containing a significant amount of gas (usu-
ally air) on a volume basis. These products are therefore, three phase systems containing air (a), water (w), and solids (s). To predict an effective thermal conductivity of the meat or poultry emulsions, the applicability of various two phase-based models such as: Series model, Parallel model, Kopelman model, Maxwell model, Levy’s model, EMT model (Carson et al., 2005) was investigated. None of these models was found to be adequate (results not shown). The thermal conductivities of the food products were calculated using Kirscher’s model (Eqs. (5)–(7)). The distribution factor f was adjusted for each product so that predicted and experimental values matched. The f values vary from 0.35 (for pepperoni) to 0.45 (for Bologna and turkey). These values are much lower than the value of 0.743 reported for dried apple by Maroulis et al. (2002) where the samples had very low moisture content. However they are comparable with the values reported by Hamdami et al. (2003). The value of the distribution factor depends on the moisture content and decrease with the increase in moisture content as has been reported by Hamdami et al. (2003). A comparison of predicted and experimental thermal conductivities demonstrated a good agreement. Statistical parameters of the comparison are summarized in
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Table 6 Comparison of statistical parameters for predicting thermal conductivities using Kirscher’s model along with the weighting factor (f) Food emulsion
Weighting parameter (f)
Coefficient of determination (r2)
Standard error
Relative standard error (%)
Bologna Pepperoni Wieners Turkey Ham
0.45 0.35 0.40 0.45 0.40
0.916 0.984 0.986 0.993 0.906
0.0234 0.0047 0.0043 0.0033 0.0187
4.89 1.39 1.24 2.10 3.43
Table 6. Low values of the standard error along with the high r2 values for all products indicated that the model performed well, where the highest and lowest values of r2 were 0.993 and 0.906 for turkey and ham, respectively. The relative standard error was less than 5% for all products. 4. Conclusions Thermophysical properties are important because of their influence on the thermal exchanges between smokehouses or cookers and meat and poultry emulsions, since the long cooking–cooling process relies heavily on conduction heating. It is also important to identify the movement of heat through the product since proper cooking–cooling cycles are generally established using core temperature measurement that must reach a pre-determined legal requirement at the end of the process. Results of this paper have shown that there are significant differences between thermophysical properties of various emulsions. The correlation matrix revealed that these differences may be attributed to the composition of the emulsions. To predict the thermal conductivity of the product different models were applied and it was found that a generic three phase structure based model is best suited to predict thermal conductivities. Therefore, it is possible to formulate meat and poultry emulsions with optimal thermophysical properties in order to maximize efficiency of cooking-cooling cycles. Moreover, these properties can also be used as an input for modeling of heat transfer during the cooking–cooling process. Acknowledgments The authors would like to thank the Canadian Meat Council for their support. References Akterian, S.G., 1997. Control strategy using functions of sensitivity for thermal processing of sausages. Journal of Food Engineering 31, 449– 455.
Baik, O.D., Sablani, S.S., Marcotte, M., Castaigne, F., 1999. Modeling the thermal properties of a cup cake during baking. Journal of Food Science 64, 295–299. Baik, O.D., Marcotte, M., Sablani, S.S., Castaigne, F., 2001. Thermal and physical properties of bakery products – a review. Critical Review in Food Science CRC 41 (5), 321–352. Carson, J.K., 2006. Review of effective thermal conductivity models for foods. International Journal of Refrigeration 29, 958–967. Carson, J.K., Lovatt, S.J., Tanner, D.J., Cleland, A.C., 2005. Thermal conductivity bounds for isotropic, porous materials. International Journal of Heat and Mass Transfer 48, 2150–2158. Carson, J.K., Lovatt, S.J., Tanner, D.J., Cleland, A.C., 2006. Predicting the effective thermal conductivity of unfrozen, porous foods. Journal of Food Engineering 75, 297–307. Gonzo, E.E., 2002. Estimating correlations for the effective thermal conductivity of granular materials. Chemical Engineering Journal 90, 299–302. 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, 809–816. Karunakar, B., Mishra, S.K., Bandyopadhyay, S., 1998. Specific heat and thermal conductivity of shrimp meat. Journal of Food Engineering 37, 345–351. 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. 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. Mohsenin, N.N., 1980. Thermal Properties of Foods and Agricultural Materials. Gordon and Breach Science Publishers, New York. Pan, Z., Singh, R.P., 2001. Physical and thermal properties of ground beef during cooking. Food Science and Technology 34, 437–444. Polley, S.L., Synder, 0.P., Kotnour, P., 1980. A compilation of thermal properties of foods. Food Technology 34 (1l), 76–94. Ramaswamy, H., Marcotte, M., 2006. Food processing. In: Principles and Applications. Taylor & Francis Publishers, Boca Raton, Florida (pp. 62–66). Sanz, P.D., Alonso, M.D., Mascheroni, R.H., 1987. Thermophysical properties of meat products: general bibliography and experimental values. Transactions of ASAE 30 (l), 283–289. Shmalko, M.E., Morawicki, R.O., Ramallo, L.A., 1996. Simultaneous determination of specific heat and thermal conductivity using the finite-difference method. Journal of Food Engineering 31, 531– 540. Sweat, V.E., 1974. Experimental values of thermal conductivity of selected fruits and vegetables. Journal of Food Science 39, 1080–1083. Sweat, V.E., 1995. Thermal properties of foods. In: Rao, M.A., Rizvi, S.S.H. (Eds.), Engineering Properties of Foods. Marcel Dekker, NY– Basel, pp. 99–138. Unklesbay, N., Unklesbay, K., Clarke, A.D., 1999. Thermal properties of restructured beef snack sticks throughout smokehouse processing. Food Science and Technology 32, 527–534. Wang, J.F., Carson, J.K., North, M.F., Cleland, D.J., 2006. A new approach to the modeling of the effective thermal conductivity of heterogeneous materials. International Journal of Heat and Mass Transfer 49 (17–18), 3075–3083. Zhang, L., Lyng, J.G., Brunton, N.P., 2007. The effect of fat, water and salt on the thermal and dielectric properties of meat batter and its temperature following microwave or radio frequency heating. Journal of Food Engineering 80 (1), 142–151.
Journal of Food Engineering 88 (2008) 315–322 www.elsevier.com/locate/jfoodeng
Thermophysical properties of processed meat and poultry products Miche`le Marcotte a,*, Ali R. Taherian a, Yousef Karimi a,b a
Food Research and Development Centre, Agriculture and Agri-Food Canada, 3600 Casavant Blvd West. St. Hyacinthe, Quebec, Canada J2S 8E3 b Department of Food Science and Agricultural Chemistry, McGill University, Macdonald Campus, 21,111 Lakeshore Road, Ste Anne de Bellevue, Quebec, Canada H9X 3V9 Received 6 September 2007; received in revised form 7 February 2008; accepted 13 February 2008 Available online 10 March 2008
Abstract Thermophysical properties of various meat and poultry emulsions were evaluated at four temperatures (20, 40, 60 and 80 °C). Thermal conductivities (0.26–0.48 W m1 K1) increased linearly with temperature between 20 and 60 °C. Between 60 and 80 °C, it remained constant for most products except bologna. Curves for thermal conductivity as a function of temperature could be roughly grouped into two different categories: products containing meat particles and those containing meat emulsions. The application of various models was investigated for thermal conductivity prediction. It was found that a three phase structural based Kirscher model had the potential for predicting thermal conductivities with acceptable accuracy. Densities decreased slightly as a function of temperature from 20 to 40 °C. A transition phase was observed from 40 to 60 °C, which was followed by a decrease from 60 to 80 °C. There was a decrease of about 50 kg m3 between the density of a raw product at room temperature (at maximum 1070 kg m3) and the product heated to 80 °C (at minimum 970 kg m3), due to the gelation or setting of the structure. After a transition period from 10 to 30 °C, the heat capacity increased linearly from 30 to 80 °C, and ranged from 2850 to 3380 J kg1 °C1, respectively. Densities and heat capacities were strongly influenced by the carbohydrate content (i.e. as the carbohydrate content increased the density decreased). The salt content adversely affected thermal conductivity and thermal diffusivity values. However, these parameters increased with moisture content. Ó 2008 Published by Elsevier Ltd. Keywords: Meat and poultry emulsions; Meat and poultry products; Thermal conductivity; Thermophysical properties; Modeling; Correlation matrix
1. Introduction Thermophysical properties (specific heat, thermal conductivity, thermal diffusivity and density) of food are important parameters in describing various thermal processes, optimizing the design and the operation of heating, cooking, freezing and cooling systems (Karunakar et al., 1998). Thermal properties are also essential for the modeling and evaluation of food processing operations involving heat transfer, especially when energy costs, food quality and safety are the main considerations. These properties are especially important to ensure food safety
*
Corresponding author. Tel.: +1 450 768 3295; fax: +1 450 773 2888. E-mail address: [email protected] (M. Marcotte).
0260-8774/$ - see front matter Ó 2008 Published by Elsevier Ltd. doi:10.1016/j.jfoodeng.2008.02.016
(Unklesbay et al., 1999). As an example, the temperature at the core of a typical sausage must be above a certain level (72 °C) by the end of heating and below certain temperature (15 °C) at the end of cooling in order to achieve microbiological stability of the product (Akterian, 1997). Therefore, there is a need to evaluate the heating characteristics of the products, known as thermophysical properties. There are many methods available to measure thermophysical properties such as guarded hot plate method, differential scanning calorimeter (DSC) attachment method, capped column test device, line heat source probe method, temperature history and transient hot strip (THS) method (Baik et al., 2001). While the first three mentioned methods are applied at steady state, the last two methods are applied for transient conditions.
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Nomenclature Cp E f I k m N O Q Rth r2
specific heat at constant pressure (kJ m3 o 1 C ) predicted value a distribution factor current (mA) thermal conductivity (W m1 K1) slope of the linear part of the temperature vs. ln (time) graph number of samples experimental value heat flux (W m1) probe resistance (m1) coefficient of determination
Thermal conductivity is highly temperature dependent especially over a temperature range where a phase change occurs. According to Karunakar et al. (1998), at a low temperature range (0–40 °C), the thermal conductivity does not exhibit very significant difference between various temperatures. At high temperatures (>50 °C), it increases gradually as the temperature increases (Pan and Singh, 2001). Both thermal conductivity and heat capacity are known to increase with moisture content increase (Shmalko et al., 1996). Water content will affect the heat capacity more than other components, the lower heat capacity values generally occur with the lower moisture content values (Unklesbay et al., 1999). Thermal conductivity and density of foods vary with temperature during thermal processing due to the changes in texture and/or composition (Karunakar et al., 1998). A decrease in density values will become important due to its effect on other thermal properties (Mohsenin, 1980). Most changes in meat products occur during heating, shrinkage, tissue hardening, moisture loss, fat loss and discoloration, and are caused by the changes in muscle protein denaturation (Pan and Singh, 2001). All these changes in the meat will affect the thermophysical properties. Mathematical models can be used to study and understand the relationship between thermophysical properties of complex food systems and temperature. For the prediction of the thermal conductivities, a large number of models have been suggested in the literature (Gonzo, 2002; Wang et al., 2006; Carson, 2006), used for composite or heterogeneous materials based on composition. Most of the proposed models are highly material based and contain material-specific parameters. Although, some models are considered to have a more general applicability, their parameters are still empirically determined. Generic models have been proposed by some scientists (Gonzo, 2002; Wang et al., 2006; Carson, 2006), where a set of equations, usually based on a conceptual ‘parent’ model, are derived. These models are developed so that they can account for variations in composition and struc-
SD T
Standard error temperature
Greek symbols a thermal diffusivity (m2 s1) U volume fraction q density (kg m3) Subscripts a air i component i s solid w water
ture, even though they often contain empirical parameters. The selection of the appropriate model for a given food product is not an easy task. As reported by Carson et al. (2006), there is a huge disagreement between thermal conductivity values predicted from various models. It can be concluded that, to-date, no single model or prediction procedure has been found with a universal applicability. Therefore, it must be evaluated on a case-by case basis. In recent decades, there have been many published research work on experimental values of thermophysical properties of foods and mathematical models to represent these data (Polley et al., 1980; Sanz et al., 1987; Lind, 1991; Karunakar et al., 1998; Baik et al., 2001; Gonzo, 2002; Wang et al., 2006; Carson, 2006). However, there is very little work done on food emulsions. The overall goal of this study was to measure thermophysical properties of various commercial meat and poultry emulsions as a function of temperature. A more specific objective was also to investigate the ability of mathematical models to predict the thermal conductivity of these emulsions. 2. Materials and methods 2.1. Products Five types of meat products were used: fine emulsion of bologna and wieners, coarse emulsion of pepperoni, turkey emulsion and flaky ham. Turkey emulsions and the flaky ham contained muscle parts. Raw products were collected from a typical industrial plant and measurements were made the day after. The products were kept at 4 °C cold room until they were analyzed. All experiments were performed three times and with three different batches of products. Thermophysical properties of meat and poultry emulsions were gathered at different temperatures from raw product to cooked product temperature. The composition of meat and poultry emulsions studied is listed in Table 1.
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Having the slope, it was possible to calculate the thermal conductivity using the following equations:
Table 1 Composition of various meat and poultry emulsions (%) Food emulsion
Moisture
Fat
Salt
Ash
Protein
Carbohydrate
Q ¼ Rth I 2
Bologna Pepperoni Wieners Turkey Ham
61.59 57.26 60.51 74.88 72.70
20.31 21.72 20.9 1.67 6.35
2.39 2.53 2.43 1.54 2.78
4.22 3.48 4.19 6.69 7.08
11.49 12.32 12.4 15.46 11.62
2.39 5.22 2.00 1.30 2.25
k¼
Q 4pm
ð1Þ ð2Þ
where Q is the heat flux (W m1), Rth the probe resistance (X m1), k the thermal conductivity (W m1 K1), I the current (mA) and m the slope of the linear part of the temperature vs. ln (time) graph.
2.2. Thermal conductivity measurements
2.3. Density measurement
Thermal conductivity measurements of various meat samples were performed using the probe method based on the line-heat source approach developed by Sweat (1974). In the probe method, there was a heater wire insulated over its length and a thermocouple at the center of this length. The probe was 38 mm long with an outside diameter of 0.66 mm. It consisted of a constantan heater wire and a chromel–constantan thermocouple (type E) (Sweat, 1995). The probe was connected to a power supply (Hewlett-Packard, 6236B) and to a multimeter (TES 2610 multimeter) in order to read the current more precisely; the multimeter was set to read in mA DC. The thermocouple wires were connected to a data acquisition system (Data Shuttle by Strawberry Tree) connected to a computer (Baik et al., 1999). The software ‘‘Workbench for Windows version 3” was used to convert the analog signal of the thermocouple into a digital signal, to set the acquisition rate at 1 reading every 2 s. The probe had a theoretical internal resistance of 226.67 X m1. It was calibrated with glycerol. Values obtained were within 10% of the literature value of 0.284 W m1 K1 at 20 °C. Constant temperature baths set in increments of 20 °C were used for the experiments: water baths at 20 °C, 40 °C and 60 °C, and an 80 °C oil bath to prevent evaporation. A copper cylinder (12.7 cm height and 2.54 cm inside diameter with a maximum wall thickness of 0.159 cm) with a high thermal conductivity was used. Emulsions samples were inserted using a syringe, whereas the turkey and the flaky ham were introduced by hand. A rubber cover was placed at both ends of the cylinder to insulate them and maintain heat flow only from the side of the cylinder. An infinite cylinder was assumed for thermal conductivity calculations. Three cylinders were placed in each of the four temperature controlled water bath. When the core temperature of the samples reached equilibrium with the water bath, the top rubber cover was replaced by a thinner one and the probe was inserted in a small hole made at the center. The probe was placed at the core of the sample. The data acquisition was switched on for 8 s to record the initial temperature. Then the power was turned on to pass a current of 200 mA for 2 min of data acquisition before being stopped. The thermal conductivity was calculated by plotting the temperature versus the natural logarithm of the time and taking the slope of the linear part of this graph.
Densities were determined from the mass of the samples inserted in the copper cylinder and the volume of the cylinders, which were pre-determined for six cylinders and the average value was considered. The mass of the samples was measured at the end of the treatment to verify if there was any weight change during the treatment. The density was calculated as the ratio of the final mass of the sample to its volume. 2.4. Heat capacity A modulated differential scanning calorimeter (MDSC 2910, TA Instruments Inc., New Castle, DE) was used with a nitrogen cooling system. MDSC has the ability for application of two independent heating rates, isothermal and modulated, which is an advantage over conventional DSC that carries only isothermal. This allowed determination of the heat capacity at various temperatures. At the start, the cell constant of the instrument was evaluated by running an experiment with Sapphire (Al2O3). The ratio of the experimental heat capacity to the theoretical heat capacity of Sapphire gave a cell constant of 1.935. A minimum mass of 200 g product was then homogenized using a ‘‘Polytron” (Polytron, PT 10–35 by Kinematica) in order to get a representative sample, especially for coarse emulsion, turkey and ham, and to fill up the experimental container which was small in capacity. A sample of 10–13 mg was placed in the aluminium pan which was then hermetically sealed using an encapsulating press from TA Instruments Inc. An empty pan that had been previously weight-matched with the sample pan was also sealed for reference. The method consisted of equilibrating the sample at 5 °C, starting the modulation for a 60-second period with an amplitude of ±1 °C, keeping it isothermal for 5 min, and heating the sample at a rate of 2.0 °C/min from 5 °C to 90 °C. Helium was used as a purging gas at a flow of 25 ml min1. The instrument automatically gave heat capacity curves from 5 to 90 °C. Furthermore, the heat capacities (Cp) of the emulsions were related to temperature (T) using following linear regression equation: C p ¼ a þ bT
ð3Þ
where a is the intercept and b the slope of the regression line.
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2.5. Thermal diffusivity calculation The thermal diffusivity values were calculated from the experimental values of density, thermal conductivity and specific heat using the following equation: k a¼ qC p
ð4Þ
where a is the thermal diffusivity (m2 s1), k the thermal conductivity (W m1 K1), q is density (kg m3), Cp is specific heat at constant pressure (kJ m3 °C1).
Table 3 Thermal conductivity of food components as a function of temperature (40 °C < T < (150 °C) Component
Thermal conductivity (W m1 K1)
Protein Fat Carbohydrate ash Ash Water Air
1.7880 101 + 1.1958 103 T 2.7178 106 T 1.8071 101 2.7604 104 T 1.7749 107 T 2.0141 101 + 1.3874 103 T 4.3312 106 T
2 2
3.2962 101 + 1.4011 103 T 2.9069 106 T 2 5.7109 101 + 1.7625 103 T – 6.7036 106 T 2 2.3820 102 + 6.75 105 T
Adapted from Ramaswawy and Marcotte (2006).
2.6. Thermal conductivity modeling A generic three phase model, known as Kirscher’s model (Maroulis et al., 2002; Wang et al., 2006), was selected and used in this study. Kirscher’s model is one of the most widely used, and it is basically a combination of the prediction of the Series and Parallel models (Carson et al., 2006) containing a weighting parameter (f) (also named distribution factor) which has to be adjusted for different food systems. The model was formulated as follows: 1 þ kfse Þ
ð5Þ
k p ¼ /s k s þ /w k w þ /a k a
ð6Þ
ke ¼
k se ¼
ð1f kp
1 /s ks
ð7Þ
þ /kww þ /kaa
where kw, ks, ka are the thermal conductivities of water, solids and air, respectively, f is a distribution factor and Uw, Us, Ua are the volume fractions of water, solids and air, respectively. Thermal conductivities of pure food components are available in the literature as a function of temperatures. The volume fractions (Uw, Us, Ua) are dependent on the material state. Since the compositions of meat and poultry emulsions were determined and presented on a weight basis, the volume fraction of each component was evaluated using its density. The densities of various components, as a function of temperature, are shown in Table 2 (Ramaswamy and Marcotte, 2006). The thermal conductivity of the solid phase was calculated by combining the thermal conductivity of each individual component (i.e., protein, carbohydrate, ash, and fat) using the procedure suggested by Table 2 Density of food components (40 °C < T < (150 °C)
as
a
function
of
temperature
Component
Density (kg m3)
Protein Fat Carbohydrate Ash Water Air
1329.9–0.5184 T 925.59–0.41757 T 1599.1–0.31046 T 2423.8–0.28063 T 997.18 + 3.1439 103 T – 3.7574 103 T 1.2847–3.2358 103 T
Adapted from Ramaswamy and Marcotte (2006).
2
Carson et al. (2006). The component thermal conductivity was determined using the functions presented in Table 3. Since the Kirscher’s weighing factor was not available for meat and poultry emulsions, it was adjusted to get the best model performance i.e. by matching predicted and experimental values. In order to examine the performance of the applied model, the correlation between thermal conductivity values predicted by the model and those calculated from the experimental data were evaluated using the coefficient of determination (r2), standard errors and standard percentage errors. The standard error was obtained by the following equation: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P ðEi Oi Þ ð8Þ SD ¼ N where Ei is the estimated value of thermal conductivity; Oi is its observed (experimental) value; and N is the number of samples. The relative standard error is defined as the ratio of standard error to the average experimental value of thermal conductivity and expressed as a percentage. 3. Results and discussion 3.1. Thermal conductivity As shown in Fig. 1, the thermal conductivity values increased with temperature for all products. For a fine bologna emulsion, the thermal conductivity increased from 0.304 ± 0.028 W m1 K1 at 22 °C to 0.459 ± 0.100 W m1 K1 at 80 °C; and for a fine wieners emulsion, the values varied from 0.281 ± 0.022 to 0.415 ± 0.066 W m1 K1. For a coarse pepperoni emulsion, the thermal conductivity varied between 0.272 ± 0.019 to 0.402 ± 0.044 W m1 K1 from 22 to 79 °C. In the case of products containing muscle parts, it was found that the thermal conductivity of turkey product varied between 0.332 ± 0.040 and 0.482 ± 0.086 W m1 K1; and that for the ham product varied from 0.339 ± 0.037 to 0.437 ± 0.058 W m1 K1. Measurements were performed using samples from three different production batches. Average values are reported since there was a good agreement between the results of these batches. Two sets of measurements were performed on each batch of products to establish repeat-
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319
0.50
Thermal Conductivity (W m -1 K-1)
0.45
0.40
0.35
Bologna Ham Pepperoni Turkey Wieners
0.30
0.25
0.20 20
30
40
50
60
70
80
90
Temperature (ºC)
Fig. 1. Thermal conductivity of meat and poultry emulsions.
a small increase in the volume of the sample during the heating stage of the emulsions. At the start of heating, a slight increase in density, associated with all the tested emulsions, was observed which may be due to the fat content changing phase from solid to liquid. Nevertheless, the densities decreased slightly with temperature in general (Fig. 2). For each product, the density of the final product heated to 80 °C was lower by approximately 50 kg m3 when compared with the initial raw product kept at room temperature. The density of the raw pepperoni and ham products were 1031 and 1037 kg m3 and for the cooked products were 969 and 1014 kg m3, respectively.
ability. Differences between values were found to be of the same order of magnitude as the measurements undertaken on two individual batches indicating that our methodology was highly repeatable. The observed differences between batches were probably due to variation in the composition of each batch, which may occur during production of each batch at industrial level. 3.2. Density The density changes observed during cooking were very small. There was no significant mass loss for these products. Gelation or setting of the solid structure caused
1080
1060
Density (kg m-3)
1040
1020
1000
Bologna Pepperoni Wieners Turkey Ham
980
960 20
30
40
50
60
70
Temperature (ºC)
Fig. 2. Density of meat and poultry emulsions.
80
90
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M. Marcotte et al. / Journal of Food Engineering 88 (2008) 315–322 3500
3400
Heat capacity (J kg-1 k-1)
3300
3200
3100
3000
2900 Bologna Pepperoni Wieners TURKEY Ham
2800
2700 0
10
20
30
40
50
60
70
80
90
Temperature (°C)
Fig. 3. Heat capacity of meat and poultry emulsions.
3.3. Heat capacity
Table 4 Correlation of heat capacity with temperature for various emulsions
It is well known that the heat capacity varies with temperature, which was also confirmed by our results shown in Fig. 3. The heat capacity values of meat emulsions at constant pressure increased linearly between 35 °C and 82 °C with a gradient of 4.34 J kg1 K1. Amongst the emulsions studied, the lowest heat capacity was found for the Pepperoni emulsion: 2812 J kg1 K1 at 10 °C and 3027 J kg1 K1 at 82 °C. This emulsion showed a peak of 3160 J kg1 K1 at 26 °C. For the bologna emulsion, the heat capacity was found to be around 2933 J kg1 K1 at 10 °C and 3191 J kg1 K1 at 82 °C. The heat capacity curve for this emulsion also indicated a maximum value of 3055 J kg1 K1 at 20 °C. The minimum was 2933 J kg1 K1 at 10 °C. The heat capacity curve for wieners had a similar shape compared to bologna, but the values were approximately 150 J kg1 K1 higher over the curve length. For the turkey product, the curve was almost linear over the entire range of temperatures studied, i.e. 10 to 82 °C with a slope of 3.9 J kg1 K1 and an ordinate of 3050 J kg1 K1. The ham product had a maximum heat capacity of 3287 J kg1 K1 at 82 °C and a minimum of 3031 J kg1 K1 at 10 °C, this curve also included a peak at 20 °C (3224 J kg1 K1). The average standard deviation for all curves was 115.5 J kg1 K1. It has been reported that the composition of product (i.e. fat, protein, water and salt contents) will influence the values of these properties (Zhang et al., 2007). The peak values observed varied directly with fat content, suggesting that samples containing higher fat content absorb more thermal energy for changing the fat from solid to liquid state. In order to be able to predict heat capacity of the emulsions, the values of heat capacity were related to the temperature in the range 34–82 °C. Table 4 shows the
Emulsion
Heat capacity (J kg1 K1)
r2
Bologna Pepperoni Wieners Turkey Ham
2836.8 + 4.306 2719.1 + 3.760 2962.4 + 4.282 3003.3 + 4.567 2940.3 + 4.234
0.996 0.978 0.990 0.998 0.996
T T T T T
regression parameters along with the coefficient of determination (r2) values. High values of r2 indicate that heat capacity and temperature are noticeably related. 3.4. Thermal diffusivity Thermal diffusivity is another property that changes with temperature (Fig. 4), since it is related to all three thermophysical properties described above: conductivity, heat capacity and density. The thermal diffusivity curves were very similar to thermal conductivity curves because other properties are not as sensitive to temperature. The thermal diffusivity values of the emulsions varied from 8.30 108 m2 s1 (for pepperoni and wieners) at room temperature to 1.36 107 m2 s1 (for pepperoni) at 80 °C. 3.5. Correlation between composition and thermophysical properties Values of thermophysical properties were measured for a variety of meat and poultry emulsions. Significant differences were found that may be attributed to the meat and poultry compositions. Average values of thermophysical properties were therefore, correlated to the chemical composition. Table 5 shows the correlation matrix. A strong proportional relationship would be indicated by a value
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321
1.600E-07
1.500E-07
Thermal diffusivity (m2 s-1)
1.400E-07
1.300E-07
1.200E-07
1.100E-07 Bologna Pepperoni Wieners Turkey Ham
1.000E-07
9.000E-08
8.000E-08 20
30
40
50
60
70
80
90
Temperature (ºC)
Fig. 4. Thermal diffusivity of meat and poultry emulsions. Table 5 Correlation matrix for thermophysical properties vs. emulsion composition
k q Cp a Moisture (%) Fat (%) Salt (%) Protein (%) Carbohydrate (%)
k
q
Cp
a
Moisture (%)
Fat (%)
Salt (%)
Protein (%)
Carbohydrate (%)
1.000 0.383 0.744 0.959 0.960 0.978 0.652 0.776 0.655
1.000 0.734 0.155 0.530 0.387 0.099 0.055 0.828
1.000 0.525 0.743 0.668 0.488 0.491 0.972
1.000 0.899 0.957 0.638 0.799 0.419
1.000 0.986 0.450 0.569 0.678
1.000 0.503 0.654 0.580
1.000 0.927 0.471
1.000 0.393
1.000
close to 1 or 1; and a value close to 0 indicates weak correlation. From a compositional point of view, the proportion of moisture was inversely correlated to the amount of fat. The proportion of salt was also inversely related to the percentage of protein in these products. The density and the heat capacity were strongly influenced by carbohydrate content (i.e. as the carbohydrate content increased, the density decreased). As the moisture content increased, the thermal conductivity and diffusivity increased. As the fat content increased, the value of k and a decreased. Contrary to the expectations, the proportion of salt did not have any significant effect on the density, heat capacity, thermal conductivity and diffusivity. This was probably due to the limited amount of salt (approximately 2%) added to the emulsions. The proportion of proteins did not significantly influence these properties as correlation coefficients were smaller than 0.9. 3.6. Thermal conductivity modeling Meat and poultry emulsions can be considered to be porous media containing a significant amount of gas (usu-
ally air) on a volume basis. These products are therefore, three phase systems containing air (a), water (w), and solids (s). To predict an effective thermal conductivity of the meat or poultry emulsions, the applicability of various two phase-based models such as: Series model, Parallel model, Kopelman model, Maxwell model, Levy’s model, EMT model (Carson et al., 2005) was investigated. None of these models was found to be adequate (results not shown). The thermal conductivities of the food products were calculated using Kirscher’s model (Eqs. (5)–(7)). The distribution factor f was adjusted for each product so that predicted and experimental values matched. The f values vary from 0.35 (for pepperoni) to 0.45 (for Bologna and turkey). These values are much lower than the value of 0.743 reported for dried apple by Maroulis et al. (2002) where the samples had very low moisture content. However they are comparable with the values reported by Hamdami et al. (2003). The value of the distribution factor depends on the moisture content and decrease with the increase in moisture content as has been reported by Hamdami et al. (2003). A comparison of predicted and experimental thermal conductivities demonstrated a good agreement. Statistical parameters of the comparison are summarized in
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Table 6 Comparison of statistical parameters for predicting thermal conductivities using Kirscher’s model along with the weighting factor (f) Food emulsion
Weighting parameter (f)
Coefficient of determination (r2)
Standard error
Relative standard error (%)
Bologna Pepperoni Wieners Turkey Ham
0.45 0.35 0.40 0.45 0.40
0.916 0.984 0.986 0.993 0.906
0.0234 0.0047 0.0043 0.0033 0.0187
4.89 1.39 1.24 2.10 3.43
Table 6. Low values of the standard error along with the high r2 values for all products indicated that the model performed well, where the highest and lowest values of r2 were 0.993 and 0.906 for turkey and ham, respectively. The relative standard error was less than 5% for all products. 4. Conclusions Thermophysical properties are important because of their influence on the thermal exchanges between smokehouses or cookers and meat and poultry emulsions, since the long cooking–cooling process relies heavily on conduction heating. It is also important to identify the movement of heat through the product since proper cooking–cooling cycles are generally established using core temperature measurement that must reach a pre-determined legal requirement at the end of the process. Results of this paper have shown that there are significant differences between thermophysical properties of various emulsions. The correlation matrix revealed that these differences may be attributed to the composition of the emulsions. To predict the thermal conductivity of the product different models were applied and it was found that a generic three phase structure based model is best suited to predict thermal conductivities. Therefore, it is possible to formulate meat and poultry emulsions with optimal thermophysical properties in order to maximize efficiency of cooking-cooling cycles. Moreover, these properties can also be used as an input for modeling of heat transfer during the cooking–cooling process. Acknowledgments The authors would like to thank the Canadian Meat Council for their support. References Akterian, S.G., 1997. Control strategy using functions of sensitivity for thermal processing of sausages. Journal of Food Engineering 31, 449– 455.
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