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Real-time estimation of slowest heating point temperature and residual cooking time by coupling multipoint temperature measurement and mathematical modelling: Application to meat cooking automation
Food Control 23 (2012) 412e418
Contents lists available at ScienceDirect
Food Control journal homepage: www.elsevier.com/locate/foodcont
Real-time estimation of slowest heating point temperature and residual cooking time by coupling multipoint temperature measurement and mathematical modelling: Application to meat cooking automation Massimiliano Rinaldi*, Emma Chiavaro, Roberto Massini Dipartimento di Ingegneria Industriale, Università degli Studi di Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 May 2011 Received in revised form 28 July 2011 Accepted 2 August 2011
In this work, an innovative procedure for real-time heat transfer modelling and dimensional change estimation during meat cooking was presented. By using a multipoint temperature probe, a punctual calculation of slowest heating point (SHP) temperature was obtained at each time from the radial temperature distribution inside the product. Experimental temperature data from the multipoint probe was combined with a mathematical algorithm previously validated to perform a real-time estimation of SHP temperature and residual cooking time on the basis of the data stored at each instant. The developed procedure and algorithm were validated by cooking pork loin and roast beef samples at 180 and 200 C both under natural and forced convection regimes. Real-time predicted cooking time and SHP endpoint temperature values were very close to those experimentally obtained: at the 85% of the cooking process, the maximum percentage errors for SHP endpoint temperature and cooking time prediction were 1.72 and 1.67%, respectively. In addition, SHP location inside the meat samples was also obtained at each time instant and used to estimate dimensional changes during cooking: calculated final characteristic dimensions were very similar to those experimentally obtained for all cooking trials. The developed approach could be useful for the automatic cooking operations planning in food-service with microbial safety assurance. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Cooking Meat Thermal diffusivity Heat transfer modelling
1. Introduction Cooking represents an important step both for industrial and domestic processing of meat products that are commonly made safe and desirable by this process. Otherwise, many food-borne diseases are generated by the adoption of poor hygienic practices and insufficient heat treatment during cooking of meat as it causes only a partial destruction of pathogenic microorganisms (Santos, Zaritzky, & Califano, 2008). Consumers empirically base the evaluation of cooking point of food by their experience and judgement or, alternatively, by cooking times reported on labels; but these methods generally cause misleading among them. A recent study (USDA, 2003a) revealed that consumers typically judge if meat is cooked or not on the basis of their own opinion on colour level reached by meal preparation. The same study also demonstrated that the change of colour in beef meat may happen before the safety temperature was reached in the product slowest heating point (SHP), with a great hazard for * Corresponding author. Tel.: þ39 (0)521 905846; fax: þ39 (0)521 905705. E-mail address: [email protected] (M. Rinaldi). 0956-7135/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodcont.2011.08.009
consumer health. For this reason, the United States Department of Agriculture since 2001 launched a campaign to encourage consumers to cook food to a safe internal temperature (Medeiros, Hillers, Kendall, & Mason, 2001) and then promoted “Thermy” and “Is It Done Yet?” campaigns (USDA, 2003b and 2006) with the aim to increase consumer use of thermometers during domestic food processing and cooking. Moreover, the same Organization provided a detailed list of endpoint temperatures that can be considered safe (USDA, 2007) as well as Food and Drug Administration distributed a summary chart for minimum cooking food temperatures and holding times for several meat products (FDA, 2009). Likewise, European Commission, after a survey on consumers concerning safety of foodstuff in 1997, launched the “2000e2001 food safety education campaign” (EC, 2000) in which coordinators decided to give consumers advice on food hygiene on cleanliness in the kitchen, uninterrupted refrigeration, correct use of microwave ovens and, in particular, cooking temperature and cooking time for certain types of meat. However, the use of thermometers during cooking operation cannot give a complete guarantee for consumer safety to chefs and
M. Rinaldi et al. / Food Control 23 (2012) 412e418
food-service industry professionals, as their positioning could deeply affect the temperature measurements and the exact location of SHP is hardly findable. In fact, SHP position is strictly related to meat size and shape, cooking function and, frequently, to dimensional change that occurs during cooking process (Tornberg, 2005). The application of mathematical models to predict temperature distribution during food and meat cooking in particular, was one of the several approaches recently proposed to overcome this limit. However, mathematical models require the knowledge of several product-specific parameters, such as product weight, raw dimensions and thermal properties, as well as of treatment temperature profile. Chen, Marks, and Murphy (1999) developed a 2-D axisymmetric finite element model to simulate heat and mass transfer during convection cooking of regularly shaped chicken patties with given actual oven air temperature and neglected shrinkage. Obuz, Powell, and Dikeman (2002) working on simulation of forced-air convection cooking of cylindrical beef roasts by means of the finite-difference method without shrinkage reported that the model should be refined to better simulate temperature histories. In a further study (Obuz, Dikeman, Erickson, Hunt, & Herald, 2004) the same author presented a predicting model for steaks but the simulated profiles were over-predicted in the first part of the cooking procedure, probably because thermal properties and oven temperature were considered constant during the cooking cycle. Bottani and Volpi (2009) developed an analytical model for the prediction of cooking time of meat products in industrial steam ovens but also in this case size reduction was neglected and treatment temperature given. This fact limits the use of mathematical model by itself to the theoretical design of cooking processes by food scientists (Santos, Zaritzky, & Califano, 2010). The use of thermometers with multiple sensible points proposed by Pittia, Furlanetto, Maifreni, Tassan Mangina, and Dalla Rosa (2008) may give the advantage of a deep simplification of the positioning operation also reducing endpoint temperature measurement errors, but in itself cannot give a prediction of SHP temperature profile evolution for the cooking process design and control. The aim of this work was to propose an innovative approach for meat cooking automation combining both the use of a multipoint thermometer and a real-time dimensional estimation on the basis of heat transfer modelling to predict cooking times and endpoint temperature at the SHP. 2. Materials and methods 2.1. Samples and cooking procedure Several cuts of pork (loin) and beef (roast beef) of different size and weight (Table 1) were obtained from a local supermarket at
413
72 h from animal slaughter. Samples were stored at 4 C, removed from the refrigerator and immediately cooked. Raw and cooked dimensions (measured by means of a calliper) as well as raw weights, cooking times and cooking losses are reported in Table 1. Samples were considered as elliptic cylinders with minimum radius (rmin), maximum radius (rmax) and lenght. Proximate composition for pork loin (water 72.5%, protein 23.2%, fat 3.5%, and ash 1.1%) and roast beef (water 73.2%, protein 22.1%, fat 3.6%, and ash 1.1%) was confirmed by using standard methods (AOAC, 2002). Four samples both for loin and beef were cooked in an electrical oven (Whirlpool Dynamic Multi 5 AKP 253/IX, MI, USA), preheated for at least 40 min, at two constant temperatures (180 and 220 C) with both natural (NC) and forced convection (FC) functions. Samples were placed on a square oven paper sheet (15 15 cm) on the oven tray. Pork loin cooking tests were considered completed when the thermal centre had reached 70 C, as stated by FDA (2009) for whole meat roasts. On the other hand, beef samples were cooked to a medium rare degree of doneness (USDA, 2007) until a thermal centre temperature of 62.8 C was reached. 2.2. Cooking temperature measurements and multipoint probe insertions Cooking temperatures were recorded by means of a self-made multipoint temperature probe (MP), which was connected to a multimeter acquisition system (Yokogawa Electric Corporation, Tokio, Japan). The temperature probe (total length 104 mm and diameter 2 mm) was set up by using 6 wire thermocouples (K-type; Ni/Al-Ni/Cr) having their measuring points placed at a distance of 13 mm between themselves and leaving the same distance from both the needle ends. In addition, sample SHP temperatures were also monitored by using 3 wire (SP) thermocouples (K-type; Ni/Al-Ni/Cr; diameter of 0.9 mm) connected to the same aforesaid acquisition system. SP sensible points were positioned with regards to be as near as possible to SHP on the basis of the raw product dimensions, whereas MP was positioned with regards to cross sample geometrical centre. Both for multipoint probe and single thermocouples, an acquisition rate of 2 s was used and time-temperature data were collected in an ExcelÒ ASCII worksheet. Preliminary tests at 180 C with forced convection (FC) function were carried out both on pork and beef samples in order to find the best way of multipoint probe insertion. The multipoint probe was inserted in the meat sample just before cooking, taking care to cross the geometrical centre of the product, with four different insertion modes (Fig. 1): perpendicular to the oven tray and to the muscle fibres (vertical), parallel to the oven tray and perpendicular to the muscle fibres (lateral), parallel to the oven tray and to the muscle fibres (horizontal) and with a 45 angle with respect to the oven
Table 1 Pork loin and roast beef samples: raw and cooked parameters. Pork loin
FC180 FC220 NC180 NC220
Raw Cooked Raw Cooked Raw Cooked Raw Cooked
Roast beef
rmin (cm)
rmax (cm)
h (cm)
weight (g)
5.0 6.0 4.9 5.9 5.5 5.9 5.0 6.4
11.8 11.1 12.4 12.4 10.6 10.4 12.3 11.3
14.0 11.1 13.3 11.5 14.6 11.0 15.5 13.2
830.0 710.1 780.0 639.8 758.0 633.2 997.8 767.5
tc (min)
WL (%)
rmin (cm)
rmax (cm)
h (cm)
weight (g)
93
14.5
79
18.0
95
16.5
114
23.1
5.0 7.1 4.8 7.4 4.7 7.9 4.8 8.0
15.0 13.8 12.3 11.8 16.0 14.9 14.7 14.0
8.3 10.0 15.0 10.2 12.3 8.4 12.2 6.9
698.4 576.1 977.3 764.2 901.2 733.0 851.3 707.8
Abbreviations: FC, forced convection; NC, natural convection; tc, cooking time; WL, weight loss.
tc (min)
WL (%)
75.0
17.5
113
21.8
97
18.7
86
16.8
414
M. Rinaldi et al. / Food Control 23 (2012) 412e418
Fig. 1. Four different multipoint probe insertion modes.
tray and to the muscle fibres (diagonal). For all the samples considered in this work, at least one sensible point of the multipoint sensor was positioned out of the sample recording temperature near meat surface. For all the cooking tests, the multipoint probe completely crossed the sample in order to reach the end of its stroke with the meat surface touching the probe base.
At each acquisition time (2 s), temperature recorded by at least four multipoint probe sensors (MP1, MP1, MP3 and MP4) was plotted against meat section height and a parabolic regression was performed: SHP location and actual sample lowest temperature were calculated as the minimum of the interpolated functions and expressed as the distance from the meat bottom. By assuming that heat transfers within the meat is only by conduction and that the SHP is located at geometrical centre as consequence, the sample characteristic dimension (sample radius) at each time interval was considered to be equal to the calculated SHP location. Meat samples were approximated to cylinders with estimated characteristic dimension as radius and two-fold characteristic dimension as length, as observed in preliminary tests and confirmed in validation ones. At each time interval characteristic dimension was estimated from experimental temperature data and then used for the heat transfer modelling. For all cooking trials, final cooked sample dimension was measured by means of a calliper and compared with the estimated one.
the sample length was considered to be two-fold the estimated radius; (iv) the problem is axisymmetric; (v) conduction was considered as the only heat transfer mechanism within the meat. At each time interval, real-time apparent thermal diffusivity functions estimation was performed as previously reported by Rinaldi, Chiavaro, and Massini (2010) by using the experimental temperature data from the multipoint probe. Then, these apparent functions and the estimated samples characteristic dimension (cylinder radius) were used to predict the SHP temperature evolution. Sample shape approximations were carried out by considering that multipoint probe crossed the thermal centre and was placed along minimum radius in vertical insertion which represents the characteristic dimension and is the most important one in conductive heat transfer. Sample length was approximated on the basis of preliminary tests dimension measurements in which resulted about two-fold radius during cooking cycle. In addition, apparent thermal diffusivity functions fitted experimental temperature data from multipoint probe recorded during the cooking cycle and balanced shape approximation, as consequence. Finally, apparent thermal diffusivity estimation algorithm as well as temperature prediction one used the same dimensional approximations. Treatment temperature used to predict cooking time was obtained by extrapolating the last thirty experimental oven temperature values recorded by the multipoint measuring point placed out of the sample and near its surface. Model validation tests were carried out by means of the cooking procedures previously described.
2.4. Model development and validation for real-time estimation of cooking time
2.5. Statistical analysis
Heat transfer modelling was performed by considering assumptions as follows: (i) meat samples were homogeneous and cylindrical bodies; (ii) the estimated characteristic dimension at each time interval was considered equal to the sample radius; (iii)
Means and standard deviations (SD) were calculated with STATISTICA (release 5.5, Statsoft Inc., Tulsa, Oklahoma, USA) statistical software. STATISTICA was also used to perform Student t-tests (p < 0.05) and regression analysis.
2.3. Real-time sample characteristic dimension and SHP temperature estimation
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3. Results and discussion 3.1. Multipoint probe insertions and temperature measurements In whole muscle, thermal conductivity is reported to be slightly higher for conduction perpendicular to fibre orientation than for parallel conduction (Obuz et al., 2002) and in this study four types of multipoint probe insertion were evaluated to select the one that could offer the best results for the cooking time estimation procedure. FC cooking procedure at 180 C was chosen for these preliminary tests. Fig. 2 shows the temperature differences between the measuring point with the lowest temperature (MPlow), corresponding to the SHP, and each of the other three measuring points (MP1, MP2 and MP3) differently positioned within the pork loins for each type of insertion. Vertical (Fig. 2, A) insertion mode allowed obtaining the highest temperature differences as multipoint probe crossed the sample along the minimum radius (Table 1) and conductively heat transfer mechanism was observed; similar results were obtained for the roast beef samples (data not shown). Since thermal diffusivity estimation, SHP location and MP slowest temperature (MPlow) calculation were based on recorded data the temperature differences among measuring points must be as high as possible. Thus, the vertical multipoint insertion mode (perpendicular to the oven tray and to the muscle fibres) was used for the cooking automation model development and validation both for pork loin and roast beef. Mean SHP temperatures measured by means of wire thermoSP ), for both cooking couples inserted in each meat sample (SHPmeas procedures (FC and S) at 180 and 220 C, were compared to those MP ): absolute errors were measured by the multipoint probe (SHPmeas
415
obtained and reported in Table 2. In addition, SHP temperatures MP ) and were also calculated by using multipoint probe data (SHPcal compared to others and reported in Table 2. Final temperature comparison was carried out by considering the lowest multipoint probe measuring point and the lowest values recorded by the three thermocouples. High variability in SHP temperature measurement was obtained for measurements with single thermocouples, despite great attention was put in positioning the measuring point: this fact was probably due to the continuous change of meat dimensions that occurred during cooking due to protein denaturation and water loss (Trout, 1988). Multipoint probe allowed measuring the meat SHP final temperature with higher accuracy than single point ones both for pork loin and roast beef samples, as previously reported (Pittia et al., 2008). All the obtained mean temperature differences (Table 2) were very high and unacceptable for food safety. In addition, the single thermocouples always overestimated final SHP temperatures both for pork and beef samples, resulting in serious biological hazards for the consumers. MP and SHP MP (Table 2) Temperature differences between SHPmeas cal presented a mean value of about 0.25 C; these differences were so small because, in the worst case, SHP maximum distance from one of the multipoint probe measuring points was 6.5 mm. 3.2. Real-time estimation procedure validation The developed procedure, which combine a mathematical model previously validated (Rinaldi et al., 2010) and a multipoint probe for the temperature measurement, was validated by means of several cooking trials carried out both on beef and pork samples: endpoint temperature, cooking time and characteristic dimension
Fig. 2. Temperature differences with four multipoint probe insertions for pork samples: A, Vertical; B, Horizontal; C, Diagonal; D, Lateral. MPlow: sensible point with the lowest temperature.
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Table 2 Mean final temperature differences between single (SP) and multipoint probe (MP) at SHP for FC and S trials at 180 and 220 C.
Pork loin Roast beef
Desired TSHP
SP MP ) ( C) (SHPmeas SHPmeas
SP MP ) ( C) (SHPmeas SHPcal
70.0 C 62.8 C
2.81 (2.10) 2.50 (1.34)
0.25 (0.06) 0.28 (0.02)
n ¼ 3, standard deviation given in parenthesis. SC : SHP temperature measured by means of single thermocouple. SHPmeas MP : SHP temperature measured by means of multipoint probe. SHPmeas
were real-time predicted at each time interval (2 s) and compared to those experimentally measured. Percentage errors calculated comparing both estimated cooking time and end-point SHP temperature with those experimentally obtained for pork loins are reported in Fig. 3 for each cooking temperature (180 and 220 C) and oven function (FC and NC). Prediction errors were higher at the beginning of the cooking trials and then decreased for all the tests as expected. At the 45% of the cooking process, the maximum percentage errors for SHP endpoint temperature and cooking time prediction were 6.31 and 7.55%, respectively. At 65% of cooking, values of 3.21 and 4.68% were reached for SHP endpoint temperature and cooking time, respectively while at the 85%, errors diminished to reach values of 1.72 and 1.67%, respectively. This result could be a combination of two effects: in the first part of the cooking process, heating rate of the product was very high leading to a fast increase of sample temperatures as well as of thermal diffusivity. Moreover, since proposed thermal diffusivity and characteristic dimension calculations were based on the experimental temperature data from the
multipoint probe, model accuracy became higher as the amount of data recorded by means of the multipoint probe increased. Same percentage errors for beef samples are shown in Fig. 4: values were slightly higher than those obtained for pork, probably due to the higher dimensional changes of roast beef samples in comparison with pork, as shown in Table 1. Obtained percentage estimation errors are in the ranges of previous studies: Santos et al. (2010) reported a mean relative error of the predicted temperature of 3.3% for black sausages heated in a stirred thermostatic bath in the temperature range from 60 to 90 C; Goñi and Salvadori (2010) obtained an average absolute error of 3.9% for cooking time prediction of semitendinosus muscles cooked in a domestic electrical oven with set oven temperatures ranging from about 170 to about 220 C. SHP locations within the meat samples were continuously estimated and reported in Fig. 5A for pork loin and 5B for roast beef samples. SHP location continuously changed for pork loin during the cooking process, as muscle fibres changed their dimensions (Barbera & Tassone, 2006). As shown in Fig. 5A, dimensional changes were higher in the last part of the cooking process and started to occur for all cooking trials at about 40 % of the total cooking time corresponding to a SHP temperature of about 40 C (not shown) whereas outer layers of the samples presented an experimentally recorded temperature differences of about 10e15 C compared to SHP (Fig. 2). The temperature at which dimensional change intensified obtained in this work was in agree with Micklandery, Peshlovy, Purslow, and Engelseny (2002) and Palka and Daun (1999) which reported a range between 50 and 60 C for shrinkage parallel to the myofibrils and collagen denaturation and with Bendall and Restall
Fig. 3. Pork loin percentage errors for final SHP temperature and cooking time. FC Forced Convection; S Static.
M. Rinaldi et al. / Food Control 23 (2012) 412e418
417
Fig. 4. Roast beef percentage errors for final SHP temperature and cooking time. FC Forced Convection; S Static.
(1983) which reported that shrinkage begins when the outer part of the meat reached 64e65 C. Roast beef SHP locations showed the same trend of the pork loin samples: a significant dimensional change began after the 40% of the total cooking time (Fig. 5B). Obtained dimensional changes (Table 1) were similar to those reported by Goñi and Salvadori (2010) for beef semitendinosus cooked at similar oven temperatures. Thus, this last part of cooking could represent the most critical phase for the microbiological inactivation. In those cooking stages, single thermocouples may also probably change their position leading to great errors for final SHP temperature with serious
Fig. 5. SHP location real-time estimation (expressed as cm from the oven tray). A pork loin; B roast beef.
Fig. 6. Measured and estimated final characteristic dimensions for pork and beef samples.
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M. Rinaldi et al. / Food Control 23 (2012) 412e418
microbiological hazards for consumers. The proposed approach which combined multipoint probe and mathematical modelling may probably allow managing cooking procedure by assuring microbial safety. Finally, estimated characteristic dimensions were very close to those measured at the end of the cooking process both for pork loin and roast beef although meat samples presented irregular geometries (Fig. 6), quite different to respect the cylindrical shape assumed for the mathematic simulation. 4. Conclusions A real-time procedure for heat transfer modelling was developed and validated for pork and beef cooking by coupling a multipoint probe for the temperature measurement and a finitedifference algorithm previously applied to meat cooking. This approach appeared to be useful for the real-time estimation of characteristic dimension and slowest heating point (SHP) location without measuring the initial product dimensions, as well as for the prediction of final cooking time and SHP temperature. In conclusion, this procedure could be used for a real-time management of cooking time by varying the treatment temperature and modelling the SHP temperature profile in order to reach the safe cooking temperature for meat in a desired time. Further studies will consider cooking procedures in which treatment temperature continuously varies and/or residual heat within the oven chamber will be recovered and used to cook: the developed real-time model could help to define the exact time at which the heating can be stopped in order to save energy reaching safe temperatures at SHP. Acknowledgements The authors gratefully acknowledge Angelica Di Gianvito for her technical assistance in performing part of the experiments. References AOAC. (2002). Official methods of analysis (16th ed.). Arlington, VA: Associaton of Official Analytical Chemists. Barbera, S., & Tassone, S. (2006). Meat cooking shrinkage: measurement of a new meat quality parameter. Meat Science, 73(3), 467e474. Bendall, J. R., & Restall, D. J. (1983). The cooking of single myofibres, small myofibre bundles and muscle strips from beef M. psoas and M. Sternomandibularis muscles at varying heating rates and temperatures. Meat Science, 8(2), 93e117.
Bottani, E., & Volpi, A. (2009). An analytical model for cooking automation in industrial steam ovens. Journal of Food Engineering, 90(2), 153e160. Chen, H., Marks, B. P., & Murphy, R. Y. (1999). Modeling coupled heat and mass transfer for convection cooking of chicken patties. Journal of Food Engineering, 42, 139e146. European Community, European Commission, Directorate General for Health and Consumers (2000). [Internet document] URL: http://ec.europa.eu/dgs/health_ consumer/events/event35_en.pdf [Accessed 26.07.11]. FDA. Food Code. (2009). Recommendations of the United States Public Health Service, Food and Drug Administration. National Technical Information Service Publication. PB2009e112613. Goñi, S. M., & Salvadori, V. O. (2010). Prediction of cooking times and weight losses during meat roasting. Journal of Food Engineering, 100(1), 1e11. Medeiros, L. C., Hillers, V. N., Kendall, P. A., & Mason, A. (2001). Food safety education: what should we be teaching to consumers? Journal of Nutrition Education, 33(2), 108e113. Micklandery, E., Peshlovy, B., Purslow, P. P., & Engelseny, S. B. (2002). NMR-cooking: monitoring the changes in meat during cooking by low-field 1H-NMR. Trends in Food Science & Technology, 13(9e10), 341e346. Obuz, E., Powell, T. E., & Dikeman, M. E. (2002). Simulation of cooking cylindrical beef roasts. LWT - Food Science and Technology, 35, 637e644. Obuz, E., Dikeman, M. E., Erickson, L. E., Hunt, M. C., & Herald, T. J. (2004). Predicting temperature profiles to determine degree of doneness for beef biceps femoris and longissimus lumborum steaks. Meat Science, 67(1), 101e107. Palka, K., & Daun, H. (1999). Changes in texture, cooking losses, and myofibrillar structure of bovine M-semitendinosus during heating. Meat Science, 51(3), 237e243. Pittia, P., Furlanetto, R., Maifreni, M., Tassan Mangina, F., & Dalla Rosa, M. (2008). Safe cooking optimisation by F-value computation in a semi-automatic oven. Food Control, 19(7), 688e697. Rinaldi, M., Chiavaro, E., & Massini, R. (2010). Apparent thermal diffusivity estimation for the heat transfer modelling of pork loin under air/steam cooking treatments. International Journal of Food Science & Technology, 45(9), 1909e1917. Santos, M. V., Zaritzky, N., & Califano, A. (2008). Modeling heat transfer and inactivation of Escherichia coli O157:H7 in precooked meat products in Argentina using the finite element method. Meat Science, 79(3), 595e602. Santos, M. V., Zaritzky, N., & Califano, A. (2010). A control strategy to assure safety conditions in the thermal treatment of meat products using a numerical algorithms. Food Control, 21(2), 191e197. Tornberg, E. (2005). Effects of heat on meat proteins e Implications on structure and quality of meat products. Meat Science, 70(3), 493e508. Trout, G. R. (1988). Techniques for measuring water binding capacity in muscle foods-a review of methodology. Meat Science, 23(4), 232e252. United States Department of Agriculture Food Safety and Inspection Service. (2007). Cooking for groups: A volunteer’s guide to food safety. [Internet document] URL: http://www.fsis.usda.gov/Fact_Sheets/Cooking_for_Groups_index/ [Accessed 26.07.11]. United States Department of Agriculture Food Safety and Inspection Service. (2003a). Color of cooked ground beef as it relates to doneness. [Internet document] URL: http://www.fsis.usda.gov/Factsheets/Color_of_Cooked_Ground_ Beef/index.asp [Accessed 26.07.11]. United States Department of Agriculture Food Safety and Inspection Service. (2003b). Is it done yet. [Internet document] URL: http://www.IsItDoneYet.gov [Accessed 26.07.11]. United States Department of Agriculture Food Safety and Inspection Service. (2006). Thermy. [Internet document] URL: http://www.fsis.usda.gov/Thermy [Accessed 26.07.11].
Contents lists available at ScienceDirect
Food Control journal homepage: www.elsevier.com/locate/foodcont
Real-time estimation of slowest heating point temperature and residual cooking time by coupling multipoint temperature measurement and mathematical modelling: Application to meat cooking automation Massimiliano Rinaldi*, Emma Chiavaro, Roberto Massini Dipartimento di Ingegneria Industriale, Università degli Studi di Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 May 2011 Received in revised form 28 July 2011 Accepted 2 August 2011
In this work, an innovative procedure for real-time heat transfer modelling and dimensional change estimation during meat cooking was presented. By using a multipoint temperature probe, a punctual calculation of slowest heating point (SHP) temperature was obtained at each time from the radial temperature distribution inside the product. Experimental temperature data from the multipoint probe was combined with a mathematical algorithm previously validated to perform a real-time estimation of SHP temperature and residual cooking time on the basis of the data stored at each instant. The developed procedure and algorithm were validated by cooking pork loin and roast beef samples at 180 and 200 C both under natural and forced convection regimes. Real-time predicted cooking time and SHP endpoint temperature values were very close to those experimentally obtained: at the 85% of the cooking process, the maximum percentage errors for SHP endpoint temperature and cooking time prediction were 1.72 and 1.67%, respectively. In addition, SHP location inside the meat samples was also obtained at each time instant and used to estimate dimensional changes during cooking: calculated final characteristic dimensions were very similar to those experimentally obtained for all cooking trials. The developed approach could be useful for the automatic cooking operations planning in food-service with microbial safety assurance. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Cooking Meat Thermal diffusivity Heat transfer modelling
1. Introduction Cooking represents an important step both for industrial and domestic processing of meat products that are commonly made safe and desirable by this process. Otherwise, many food-borne diseases are generated by the adoption of poor hygienic practices and insufficient heat treatment during cooking of meat as it causes only a partial destruction of pathogenic microorganisms (Santos, Zaritzky, & Califano, 2008). Consumers empirically base the evaluation of cooking point of food by their experience and judgement or, alternatively, by cooking times reported on labels; but these methods generally cause misleading among them. A recent study (USDA, 2003a) revealed that consumers typically judge if meat is cooked or not on the basis of their own opinion on colour level reached by meal preparation. The same study also demonstrated that the change of colour in beef meat may happen before the safety temperature was reached in the product slowest heating point (SHP), with a great hazard for * Corresponding author. Tel.: þ39 (0)521 905846; fax: þ39 (0)521 905705. E-mail address: [email protected] (M. Rinaldi). 0956-7135/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodcont.2011.08.009
consumer health. For this reason, the United States Department of Agriculture since 2001 launched a campaign to encourage consumers to cook food to a safe internal temperature (Medeiros, Hillers, Kendall, & Mason, 2001) and then promoted “Thermy” and “Is It Done Yet?” campaigns (USDA, 2003b and 2006) with the aim to increase consumer use of thermometers during domestic food processing and cooking. Moreover, the same Organization provided a detailed list of endpoint temperatures that can be considered safe (USDA, 2007) as well as Food and Drug Administration distributed a summary chart for minimum cooking food temperatures and holding times for several meat products (FDA, 2009). Likewise, European Commission, after a survey on consumers concerning safety of foodstuff in 1997, launched the “2000e2001 food safety education campaign” (EC, 2000) in which coordinators decided to give consumers advice on food hygiene on cleanliness in the kitchen, uninterrupted refrigeration, correct use of microwave ovens and, in particular, cooking temperature and cooking time for certain types of meat. However, the use of thermometers during cooking operation cannot give a complete guarantee for consumer safety to chefs and
M. Rinaldi et al. / Food Control 23 (2012) 412e418
food-service industry professionals, as their positioning could deeply affect the temperature measurements and the exact location of SHP is hardly findable. In fact, SHP position is strictly related to meat size and shape, cooking function and, frequently, to dimensional change that occurs during cooking process (Tornberg, 2005). The application of mathematical models to predict temperature distribution during food and meat cooking in particular, was one of the several approaches recently proposed to overcome this limit. However, mathematical models require the knowledge of several product-specific parameters, such as product weight, raw dimensions and thermal properties, as well as of treatment temperature profile. Chen, Marks, and Murphy (1999) developed a 2-D axisymmetric finite element model to simulate heat and mass transfer during convection cooking of regularly shaped chicken patties with given actual oven air temperature and neglected shrinkage. Obuz, Powell, and Dikeman (2002) working on simulation of forced-air convection cooking of cylindrical beef roasts by means of the finite-difference method without shrinkage reported that the model should be refined to better simulate temperature histories. In a further study (Obuz, Dikeman, Erickson, Hunt, & Herald, 2004) the same author presented a predicting model for steaks but the simulated profiles were over-predicted in the first part of the cooking procedure, probably because thermal properties and oven temperature were considered constant during the cooking cycle. Bottani and Volpi (2009) developed an analytical model for the prediction of cooking time of meat products in industrial steam ovens but also in this case size reduction was neglected and treatment temperature given. This fact limits the use of mathematical model by itself to the theoretical design of cooking processes by food scientists (Santos, Zaritzky, & Califano, 2010). The use of thermometers with multiple sensible points proposed by Pittia, Furlanetto, Maifreni, Tassan Mangina, and Dalla Rosa (2008) may give the advantage of a deep simplification of the positioning operation also reducing endpoint temperature measurement errors, but in itself cannot give a prediction of SHP temperature profile evolution for the cooking process design and control. The aim of this work was to propose an innovative approach for meat cooking automation combining both the use of a multipoint thermometer and a real-time dimensional estimation on the basis of heat transfer modelling to predict cooking times and endpoint temperature at the SHP. 2. Materials and methods 2.1. Samples and cooking procedure Several cuts of pork (loin) and beef (roast beef) of different size and weight (Table 1) were obtained from a local supermarket at
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72 h from animal slaughter. Samples were stored at 4 C, removed from the refrigerator and immediately cooked. Raw and cooked dimensions (measured by means of a calliper) as well as raw weights, cooking times and cooking losses are reported in Table 1. Samples were considered as elliptic cylinders with minimum radius (rmin), maximum radius (rmax) and lenght. Proximate composition for pork loin (water 72.5%, protein 23.2%, fat 3.5%, and ash 1.1%) and roast beef (water 73.2%, protein 22.1%, fat 3.6%, and ash 1.1%) was confirmed by using standard methods (AOAC, 2002). Four samples both for loin and beef were cooked in an electrical oven (Whirlpool Dynamic Multi 5 AKP 253/IX, MI, USA), preheated for at least 40 min, at two constant temperatures (180 and 220 C) with both natural (NC) and forced convection (FC) functions. Samples were placed on a square oven paper sheet (15 15 cm) on the oven tray. Pork loin cooking tests were considered completed when the thermal centre had reached 70 C, as stated by FDA (2009) for whole meat roasts. On the other hand, beef samples were cooked to a medium rare degree of doneness (USDA, 2007) until a thermal centre temperature of 62.8 C was reached. 2.2. Cooking temperature measurements and multipoint probe insertions Cooking temperatures were recorded by means of a self-made multipoint temperature probe (MP), which was connected to a multimeter acquisition system (Yokogawa Electric Corporation, Tokio, Japan). The temperature probe (total length 104 mm and diameter 2 mm) was set up by using 6 wire thermocouples (K-type; Ni/Al-Ni/Cr) having their measuring points placed at a distance of 13 mm between themselves and leaving the same distance from both the needle ends. In addition, sample SHP temperatures were also monitored by using 3 wire (SP) thermocouples (K-type; Ni/Al-Ni/Cr; diameter of 0.9 mm) connected to the same aforesaid acquisition system. SP sensible points were positioned with regards to be as near as possible to SHP on the basis of the raw product dimensions, whereas MP was positioned with regards to cross sample geometrical centre. Both for multipoint probe and single thermocouples, an acquisition rate of 2 s was used and time-temperature data were collected in an ExcelÒ ASCII worksheet. Preliminary tests at 180 C with forced convection (FC) function were carried out both on pork and beef samples in order to find the best way of multipoint probe insertion. The multipoint probe was inserted in the meat sample just before cooking, taking care to cross the geometrical centre of the product, with four different insertion modes (Fig. 1): perpendicular to the oven tray and to the muscle fibres (vertical), parallel to the oven tray and perpendicular to the muscle fibres (lateral), parallel to the oven tray and to the muscle fibres (horizontal) and with a 45 angle with respect to the oven
Table 1 Pork loin and roast beef samples: raw and cooked parameters. Pork loin
FC180 FC220 NC180 NC220
Raw Cooked Raw Cooked Raw Cooked Raw Cooked
Roast beef
rmin (cm)
rmax (cm)
h (cm)
weight (g)
5.0 6.0 4.9 5.9 5.5 5.9 5.0 6.4
11.8 11.1 12.4 12.4 10.6 10.4 12.3 11.3
14.0 11.1 13.3 11.5 14.6 11.0 15.5 13.2
830.0 710.1 780.0 639.8 758.0 633.2 997.8 767.5
tc (min)
WL (%)
rmin (cm)
rmax (cm)
h (cm)
weight (g)
93
14.5
79
18.0
95
16.5
114
23.1
5.0 7.1 4.8 7.4 4.7 7.9 4.8 8.0
15.0 13.8 12.3 11.8 16.0 14.9 14.7 14.0
8.3 10.0 15.0 10.2 12.3 8.4 12.2 6.9
698.4 576.1 977.3 764.2 901.2 733.0 851.3 707.8
Abbreviations: FC, forced convection; NC, natural convection; tc, cooking time; WL, weight loss.
tc (min)
WL (%)
75.0
17.5
113
21.8
97
18.7
86
16.8
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Fig. 1. Four different multipoint probe insertion modes.
tray and to the muscle fibres (diagonal). For all the samples considered in this work, at least one sensible point of the multipoint sensor was positioned out of the sample recording temperature near meat surface. For all the cooking tests, the multipoint probe completely crossed the sample in order to reach the end of its stroke with the meat surface touching the probe base.
At each acquisition time (2 s), temperature recorded by at least four multipoint probe sensors (MP1, MP1, MP3 and MP4) was plotted against meat section height and a parabolic regression was performed: SHP location and actual sample lowest temperature were calculated as the minimum of the interpolated functions and expressed as the distance from the meat bottom. By assuming that heat transfers within the meat is only by conduction and that the SHP is located at geometrical centre as consequence, the sample characteristic dimension (sample radius) at each time interval was considered to be equal to the calculated SHP location. Meat samples were approximated to cylinders with estimated characteristic dimension as radius and two-fold characteristic dimension as length, as observed in preliminary tests and confirmed in validation ones. At each time interval characteristic dimension was estimated from experimental temperature data and then used for the heat transfer modelling. For all cooking trials, final cooked sample dimension was measured by means of a calliper and compared with the estimated one.
the sample length was considered to be two-fold the estimated radius; (iv) the problem is axisymmetric; (v) conduction was considered as the only heat transfer mechanism within the meat. At each time interval, real-time apparent thermal diffusivity functions estimation was performed as previously reported by Rinaldi, Chiavaro, and Massini (2010) by using the experimental temperature data from the multipoint probe. Then, these apparent functions and the estimated samples characteristic dimension (cylinder radius) were used to predict the SHP temperature evolution. Sample shape approximations were carried out by considering that multipoint probe crossed the thermal centre and was placed along minimum radius in vertical insertion which represents the characteristic dimension and is the most important one in conductive heat transfer. Sample length was approximated on the basis of preliminary tests dimension measurements in which resulted about two-fold radius during cooking cycle. In addition, apparent thermal diffusivity functions fitted experimental temperature data from multipoint probe recorded during the cooking cycle and balanced shape approximation, as consequence. Finally, apparent thermal diffusivity estimation algorithm as well as temperature prediction one used the same dimensional approximations. Treatment temperature used to predict cooking time was obtained by extrapolating the last thirty experimental oven temperature values recorded by the multipoint measuring point placed out of the sample and near its surface. Model validation tests were carried out by means of the cooking procedures previously described.
2.4. Model development and validation for real-time estimation of cooking time
2.5. Statistical analysis
Heat transfer modelling was performed by considering assumptions as follows: (i) meat samples were homogeneous and cylindrical bodies; (ii) the estimated characteristic dimension at each time interval was considered equal to the sample radius; (iii)
Means and standard deviations (SD) were calculated with STATISTICA (release 5.5, Statsoft Inc., Tulsa, Oklahoma, USA) statistical software. STATISTICA was also used to perform Student t-tests (p < 0.05) and regression analysis.
2.3. Real-time sample characteristic dimension and SHP temperature estimation
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3. Results and discussion 3.1. Multipoint probe insertions and temperature measurements In whole muscle, thermal conductivity is reported to be slightly higher for conduction perpendicular to fibre orientation than for parallel conduction (Obuz et al., 2002) and in this study four types of multipoint probe insertion were evaluated to select the one that could offer the best results for the cooking time estimation procedure. FC cooking procedure at 180 C was chosen for these preliminary tests. Fig. 2 shows the temperature differences between the measuring point with the lowest temperature (MPlow), corresponding to the SHP, and each of the other three measuring points (MP1, MP2 and MP3) differently positioned within the pork loins for each type of insertion. Vertical (Fig. 2, A) insertion mode allowed obtaining the highest temperature differences as multipoint probe crossed the sample along the minimum radius (Table 1) and conductively heat transfer mechanism was observed; similar results were obtained for the roast beef samples (data not shown). Since thermal diffusivity estimation, SHP location and MP slowest temperature (MPlow) calculation were based on recorded data the temperature differences among measuring points must be as high as possible. Thus, the vertical multipoint insertion mode (perpendicular to the oven tray and to the muscle fibres) was used for the cooking automation model development and validation both for pork loin and roast beef. Mean SHP temperatures measured by means of wire thermoSP ), for both cooking couples inserted in each meat sample (SHPmeas procedures (FC and S) at 180 and 220 C, were compared to those MP ): absolute errors were measured by the multipoint probe (SHPmeas
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obtained and reported in Table 2. In addition, SHP temperatures MP ) and were also calculated by using multipoint probe data (SHPcal compared to others and reported in Table 2. Final temperature comparison was carried out by considering the lowest multipoint probe measuring point and the lowest values recorded by the three thermocouples. High variability in SHP temperature measurement was obtained for measurements with single thermocouples, despite great attention was put in positioning the measuring point: this fact was probably due to the continuous change of meat dimensions that occurred during cooking due to protein denaturation and water loss (Trout, 1988). Multipoint probe allowed measuring the meat SHP final temperature with higher accuracy than single point ones both for pork loin and roast beef samples, as previously reported (Pittia et al., 2008). All the obtained mean temperature differences (Table 2) were very high and unacceptable for food safety. In addition, the single thermocouples always overestimated final SHP temperatures both for pork and beef samples, resulting in serious biological hazards for the consumers. MP and SHP MP (Table 2) Temperature differences between SHPmeas cal presented a mean value of about 0.25 C; these differences were so small because, in the worst case, SHP maximum distance from one of the multipoint probe measuring points was 6.5 mm. 3.2. Real-time estimation procedure validation The developed procedure, which combine a mathematical model previously validated (Rinaldi et al., 2010) and a multipoint probe for the temperature measurement, was validated by means of several cooking trials carried out both on beef and pork samples: endpoint temperature, cooking time and characteristic dimension
Fig. 2. Temperature differences with four multipoint probe insertions for pork samples: A, Vertical; B, Horizontal; C, Diagonal; D, Lateral. MPlow: sensible point with the lowest temperature.
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Table 2 Mean final temperature differences between single (SP) and multipoint probe (MP) at SHP for FC and S trials at 180 and 220 C.
Pork loin Roast beef
Desired TSHP
SP MP ) ( C) (SHPmeas SHPmeas
SP MP ) ( C) (SHPmeas SHPcal
70.0 C 62.8 C
2.81 (2.10) 2.50 (1.34)
0.25 (0.06) 0.28 (0.02)
n ¼ 3, standard deviation given in parenthesis. SC : SHP temperature measured by means of single thermocouple. SHPmeas MP : SHP temperature measured by means of multipoint probe. SHPmeas
were real-time predicted at each time interval (2 s) and compared to those experimentally measured. Percentage errors calculated comparing both estimated cooking time and end-point SHP temperature with those experimentally obtained for pork loins are reported in Fig. 3 for each cooking temperature (180 and 220 C) and oven function (FC and NC). Prediction errors were higher at the beginning of the cooking trials and then decreased for all the tests as expected. At the 45% of the cooking process, the maximum percentage errors for SHP endpoint temperature and cooking time prediction were 6.31 and 7.55%, respectively. At 65% of cooking, values of 3.21 and 4.68% were reached for SHP endpoint temperature and cooking time, respectively while at the 85%, errors diminished to reach values of 1.72 and 1.67%, respectively. This result could be a combination of two effects: in the first part of the cooking process, heating rate of the product was very high leading to a fast increase of sample temperatures as well as of thermal diffusivity. Moreover, since proposed thermal diffusivity and characteristic dimension calculations were based on the experimental temperature data from the
multipoint probe, model accuracy became higher as the amount of data recorded by means of the multipoint probe increased. Same percentage errors for beef samples are shown in Fig. 4: values were slightly higher than those obtained for pork, probably due to the higher dimensional changes of roast beef samples in comparison with pork, as shown in Table 1. Obtained percentage estimation errors are in the ranges of previous studies: Santos et al. (2010) reported a mean relative error of the predicted temperature of 3.3% for black sausages heated in a stirred thermostatic bath in the temperature range from 60 to 90 C; Goñi and Salvadori (2010) obtained an average absolute error of 3.9% for cooking time prediction of semitendinosus muscles cooked in a domestic electrical oven with set oven temperatures ranging from about 170 to about 220 C. SHP locations within the meat samples were continuously estimated and reported in Fig. 5A for pork loin and 5B for roast beef samples. SHP location continuously changed for pork loin during the cooking process, as muscle fibres changed their dimensions (Barbera & Tassone, 2006). As shown in Fig. 5A, dimensional changes were higher in the last part of the cooking process and started to occur for all cooking trials at about 40 % of the total cooking time corresponding to a SHP temperature of about 40 C (not shown) whereas outer layers of the samples presented an experimentally recorded temperature differences of about 10e15 C compared to SHP (Fig. 2). The temperature at which dimensional change intensified obtained in this work was in agree with Micklandery, Peshlovy, Purslow, and Engelseny (2002) and Palka and Daun (1999) which reported a range between 50 and 60 C for shrinkage parallel to the myofibrils and collagen denaturation and with Bendall and Restall
Fig. 3. Pork loin percentage errors for final SHP temperature and cooking time. FC Forced Convection; S Static.
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Fig. 4. Roast beef percentage errors for final SHP temperature and cooking time. FC Forced Convection; S Static.
(1983) which reported that shrinkage begins when the outer part of the meat reached 64e65 C. Roast beef SHP locations showed the same trend of the pork loin samples: a significant dimensional change began after the 40% of the total cooking time (Fig. 5B). Obtained dimensional changes (Table 1) were similar to those reported by Goñi and Salvadori (2010) for beef semitendinosus cooked at similar oven temperatures. Thus, this last part of cooking could represent the most critical phase for the microbiological inactivation. In those cooking stages, single thermocouples may also probably change their position leading to great errors for final SHP temperature with serious
Fig. 5. SHP location real-time estimation (expressed as cm from the oven tray). A pork loin; B roast beef.
Fig. 6. Measured and estimated final characteristic dimensions for pork and beef samples.
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microbiological hazards for consumers. The proposed approach which combined multipoint probe and mathematical modelling may probably allow managing cooking procedure by assuring microbial safety. Finally, estimated characteristic dimensions were very close to those measured at the end of the cooking process both for pork loin and roast beef although meat samples presented irregular geometries (Fig. 6), quite different to respect the cylindrical shape assumed for the mathematic simulation. 4. Conclusions A real-time procedure for heat transfer modelling was developed and validated for pork and beef cooking by coupling a multipoint probe for the temperature measurement and a finitedifference algorithm previously applied to meat cooking. This approach appeared to be useful for the real-time estimation of characteristic dimension and slowest heating point (SHP) location without measuring the initial product dimensions, as well as for the prediction of final cooking time and SHP temperature. In conclusion, this procedure could be used for a real-time management of cooking time by varying the treatment temperature and modelling the SHP temperature profile in order to reach the safe cooking temperature for meat in a desired time. Further studies will consider cooking procedures in which treatment temperature continuously varies and/or residual heat within the oven chamber will be recovered and used to cook: the developed real-time model could help to define the exact time at which the heating can be stopped in order to save energy reaching safe temperatures at SHP. Acknowledgements The authors gratefully acknowledge Angelica Di Gianvito for her technical assistance in performing part of the experiments. References AOAC. (2002). Official methods of analysis (16th ed.). Arlington, VA: Associaton of Official Analytical Chemists. Barbera, S., & Tassone, S. (2006). Meat cooking shrinkage: measurement of a new meat quality parameter. Meat Science, 73(3), 467e474. Bendall, J. R., & Restall, D. J. (1983). The cooking of single myofibres, small myofibre bundles and muscle strips from beef M. psoas and M. Sternomandibularis muscles at varying heating rates and temperatures. Meat Science, 8(2), 93e117.
Bottani, E., & Volpi, A. (2009). An analytical model for cooking automation in industrial steam ovens. Journal of Food Engineering, 90(2), 153e160. Chen, H., Marks, B. P., & Murphy, R. Y. (1999). Modeling coupled heat and mass transfer for convection cooking of chicken patties. Journal of Food Engineering, 42, 139e146. European Community, European Commission, Directorate General for Health and Consumers (2000). [Internet document] URL: http://ec.europa.eu/dgs/health_ consumer/events/event35_en.pdf [Accessed 26.07.11]. FDA. Food Code. (2009). Recommendations of the United States Public Health Service, Food and Drug Administration. National Technical Information Service Publication. PB2009e112613. Goñi, S. M., & Salvadori, V. O. (2010). Prediction of cooking times and weight losses during meat roasting. Journal of Food Engineering, 100(1), 1e11. Medeiros, L. C., Hillers, V. N., Kendall, P. A., & Mason, A. (2001). Food safety education: what should we be teaching to consumers? Journal of Nutrition Education, 33(2), 108e113. Micklandery, E., Peshlovy, B., Purslow, P. P., & Engelseny, S. B. (2002). NMR-cooking: monitoring the changes in meat during cooking by low-field 1H-NMR. Trends in Food Science & Technology, 13(9e10), 341e346. Obuz, E., Powell, T. E., & Dikeman, M. E. (2002). Simulation of cooking cylindrical beef roasts. LWT - Food Science and Technology, 35, 637e644. Obuz, E., Dikeman, M. E., Erickson, L. E., Hunt, M. C., & Herald, T. J. (2004). Predicting temperature profiles to determine degree of doneness for beef biceps femoris and longissimus lumborum steaks. Meat Science, 67(1), 101e107. Palka, K., & Daun, H. (1999). Changes in texture, cooking losses, and myofibrillar structure of bovine M-semitendinosus during heating. Meat Science, 51(3), 237e243. Pittia, P., Furlanetto, R., Maifreni, M., Tassan Mangina, F., & Dalla Rosa, M. (2008). Safe cooking optimisation by F-value computation in a semi-automatic oven. Food Control, 19(7), 688e697. Rinaldi, M., Chiavaro, E., & Massini, R. (2010). Apparent thermal diffusivity estimation for the heat transfer modelling of pork loin under air/steam cooking treatments. International Journal of Food Science & Technology, 45(9), 1909e1917. Santos, M. V., Zaritzky, N., & Califano, A. (2008). Modeling heat transfer and inactivation of Escherichia coli O157:H7 in precooked meat products in Argentina using the finite element method. Meat Science, 79(3), 595e602. Santos, M. V., Zaritzky, N., & Califano, A. (2010). A control strategy to assure safety conditions in the thermal treatment of meat products using a numerical algorithms. Food Control, 21(2), 191e197. Tornberg, E. (2005). Effects of heat on meat proteins e Implications on structure and quality of meat products. Meat Science, 70(3), 493e508. Trout, G. R. (1988). Techniques for measuring water binding capacity in muscle foods-a review of methodology. Meat Science, 23(4), 232e252. United States Department of Agriculture Food Safety and Inspection Service. (2007). Cooking for groups: A volunteer’s guide to food safety. [Internet document] URL: http://www.fsis.usda.gov/Fact_Sheets/Cooking_for_Groups_index/ [Accessed 26.07.11]. United States Department of Agriculture Food Safety and Inspection Service. (2003a). Color of cooked ground beef as it relates to doneness. [Internet document] URL: http://www.fsis.usda.gov/Factsheets/Color_of_Cooked_Ground_ Beef/index.asp [Accessed 26.07.11]. United States Department of Agriculture Food Safety and Inspection Service. (2003b). Is it done yet. [Internet document] URL: http://www.IsItDoneYet.gov [Accessed 26.07.11]. United States Department of Agriculture Food Safety and Inspection Service. (2006). Thermy. [Internet document] URL: http://www.fsis.usda.gov/Thermy [Accessed 26.07.11].