Heat transfer analysis of cheese cooling incorporating uncertainty in temperature measurement locations: Model development and validation

Successful modelling of the thermal behaviour of food products requires accurate knowledge of both the thermal properties of the product and the cooling media to which it is exposed to and a correct approach to validation of the model output against experimental temperature histories. This procedure is complicated where there is uncertainty in the location at which temperature is measured in the product. The cooling of a soft cylindrical cheese product that is partially immersed in brine and air is examined. As the cheese is very deformable, it is not possible to exactly identify the measurement location of the temperature-recording thermocouples. The Uniform and Exponential probability distributions were found to best represent the variability in thermocouple location at the centre and surface of the product, respectively. Expressions for the mean measured temperature at the centre and surface that result from the distributed nature of thermocouple location were obtained. These expressions were used to derive equivalent locations in the cheese which should be used when comparing model and experimental temperature predictions. The theoretical approach was also checked against Monte Carlo simulations and there was excellent agreement between them. It was shown that when validating model temperature histories against experimental readings that this phenomenon must be taken into account.     

Temperature evolution in a partially submerged approximate cheese cylinder

An approximate cheese cylinder is cooled while partially submerged in a flowing brine solution. Microbiological considerations require the cheese to be cooled to 4 °C or less prior to packaging. Knowledge of the temperature evolution of the product is desirable from a manufacturing perspective, and we propose a model to describe the temperature time-history of a single cheese cylinder during cooling. The combination of unusual product geometry and the discontinuity in surface temperatures motivate the use of the finite element method (FEM). The FEM solution is used to describe the cooling process, and to ascertain the minimum time necessary for the cheese to attain the required packaging temperature. The FEM solution exhibits excellent agreement with the corresponding experimental findings. The discontinuity in surface temperatures has a significant influence on the cooling regime. Future process optimisation should focus on developing methods to increase the cheese surface area in contact with the brine.     

Processes that contribute to radiocesium decontamination of feta cheese

In a series of experiments, the transfer of radiocesium from ovine milk to feta cheese was investigated through modifications of the standard cheese making procedure. All variations explored showed no significant change in the percentage of radiocesium transfer and the milk-to-cheese transfer coefficient was determined as f=.79 plus/minus .04 L.kg-1. It is concluded that cesium, like the rest of the alkali metals, remains in the water phase and thus follows very closely the distribution of moisture into the products of cheese making. The possibility of radiocesium decontamination of mature feta during the customary storage of the product in brine was also explored in a second series of experiments. The theoretical model employed in the analysis of cesium transport from feta to brine is presented in the Appendix to this paper. Predictions of the model were validated by experiments. A procedure is thus proposed for decontaminating mature feta during storage through successive replacements of the storage medium. Nomograms are presented for the determination of the optimum time interval between changes of the brine and the radiocesium concentration remaining in the feta. Changes in the properties of the product induced by the proposed treatment were also investigated with respect to composition, taste, and overall quality.     

Modeling NaCl and KCl Movement in Fynbo Cheese during Salting

A model considering a ternary diffusion in axial and radial directions of a finite cylindrical solid was developed for predicting NaCl and KCl concentrations in cheese during brining. The generalized Fick's law form, negligible external mass transfer resistance, and an equilibrium between cheese and brine solution were assumed. Cheese samples (12 × 6 cm) were salted in a KCl-NaCl) brine solution. NaCl and KCl concentrations were determined experimentally and theoretically at 5, 10 and 15 hr. The average relative error of the model was higher for KCl than for NaCl and increased with brining time. The model can be applied to systems of similar geometry and conditions provided diffusion constants are known.     

Measurement of Convective Heat Transfer Coefficients During Food Freezing Processes

Any prediction of freezing time for a food product depends on accurate heat transfer coefficients. The purpose of this investigation was to examine experimental procedures for accurate determination of convective transfer coefficients during freezing of food products. Measurements of heat transfer coefficients during cooling of any acrylic transducer and ground beef with similar size and shape were conducted at air temperatures below initial freezing point of the product. The results indicate that accurate measurements of the coefficients can be achieved through nonlinear regression analysis of temperature histories within an acrylic transducer.     

An accurate account of mass loss during cheese ripening described using the reaction engineering approach (REA)‐based model

Cheese ripening is an important step in cheese making for modifying surface and curd properties. Due to physical, chemical and biological changes, mass loss usually occurs during the process. Although these changes are essential for developing the texture and flavour of cheese, mass loss decreases product yields. A reliable mathematical model is used to quantify mass loss during cheese ripening so that the processing conditions can be fine‐tuned to achieve the desirable throughput. In this study, for the first time, the reaction engineering approach (REA)‐based model is applied to model the cheese ripening. The study shows that the REA‐based model is accurate to model cheese ripening of Camembert and French smear cheese. In addition, the REA is able to model the cheese ripening under time‐varying environmental conditions. For this purpose, the equilibrium activation energy is evaluated according to the corresponding humidity and temperature in each period, while the same relative activation energy for ripening under constant environmental conditions is implemented. The REA is a simple yet effective approach to model the simultaneous heat and mass transfer process accompanied by chemical and biological reactions. Considering its effectiveness, the REA can be applied in industrial settings for predicting mass loss during cheese ripening.     

OVERALL HEAT TRANSFER COEFFICIENTS AND AXIAL TEMPERATURE DISTRIBUTION IN A TRIPLE TUBE HEAT EXCHANGER

Computation of overall heat transfer coefficients in a triple tube heat exchanger (TTHE) is more complicated than in the case of a double tube heat exchanger (DTHE) as the two overall heat transfer coefficients are not independent of one other. A new procedure was developed to calculate these overall heat transfer coefficients and an effective overall heat transfer coefficient value for known inlet and outlet temperatures, and heat capacities of the fluids (product and heating/cooling medium). In this study, this newly developed procedure was utilized and the overall heat transfer coefficients and axial temperature distribution of fluids were computed for a cooling process for different flow rates and inlet temperatures of the fluid streams. The effectiveness of the TTHE was compared to that of a DTHE of identical length. It was observed that when the fluids were flowing in a cocurrent manner, the temperature of the cooling medium with lower heat capacity exceeded the temperature of the product before the fluids exit the TTHE, which caused a decrease in the effectiveness of the TTHE.     

HEAT AND MASS TRANSFER PROPERTIES OF PIZZA DURING BAKING

ABSTRACT

Mathematical models of pizza baking by forced and natural convection heating methods were developed describing heat and mass transfer phenomena. The models were solved using finite difference technique and a simulation language. Moisture and temperature histories were collected at different baking conditions. The models and experimental data were used to determine mass transfer properties—moisture diffusivities of crust, tomato paste and cheese, and moisture transfer coefficient. Heat transfer coefficient was measured by minimizing the internal heat resistance.     

食品真空贮藏过程中温度变化的数值模拟与有限元分析

食品真空贮藏过程是复杂的传热传质过程，该过程涉及到扩散、传热、传质等机理。在能量守衡基础上建立数学模型，通过数值求解得到不同真空压力下食品温度随时间的变化曲线，并通过有限元分析，与数值模拟的结果进行对比分析，为下一步的实验验证及食品冷冻冷藏工程的实践提供理论依据。     

Influence of the temperature of salt brine on salt uptake by Ragusano cheese

The influence of temperature (12, 15, 18, 21, and 24 degrees C) of saturated brine on salt uptake by 3.8-kg experimental blocks of Ragusano cheese during 24 d of brining was determined. Twenty-six 3.8-kg blocks were made on each of three different days. All blocks were labeled and weighed prior to brining. One block was sampled and analyzed prior to brine salting. Five blocks were placed into each of five different brine tanks at different temperatures. One block was removed from each brine tank after 1, 4, 8, 16, and 24 d of brining, weighed, sampled, and analyzed for salt and moisture content. The weight loss by blocks of cheese after 24 d of brining was higher, with increasing brine temperature, and represented the net effect of moisture loss and salt uptake. The total salt uptake and moisture loss increased with increasing brine temperature. Salt penetrates into cheese through the moisture phase within the pore structure of the cheese. Porosity of the cheese structure and viscosity of the water phase within the pores influenced the rate and extent of salt penetration during 24 d of brining. In a previous study, it was determined that salt uptake at 18 degrees C was faster in 18% brine than in saturated brine due to higher moisture and porosity of the exterior portion of the cheese. In the present study, moisture loss occurred from all cheeses at all temperatures and most of the loss was from the exterior portion of the block during the first 4 d of brining. This loss in moisture would be expected to decrease porosity of the exterior portion and act as a barrier to salt penetration. The moisture loss increased with increasing brine temperature. If this decrease in porosity was the only factor influencing salt uptake, then it would be expected that the cheeses at higher brine temperature would have had lower salt content. However, the opposite was true. Brine temperature must have also impacted the viscosity of the aqueous phase of the cheese. Cheese in lower temperature brine would be expected to have higher viscosity of the aqueous phase and slower salt uptake, even though the cheese at lower brine temperature should have had a more porous structure (favoring faster uptake) than cheese at higher brine temperature. Therefore, changing brine concentration has a greater impact on cheese porosity, while changing brine temperature has a larger impact on viscosity of the aqueous phase of the cheese within the pores in the cheese.     

An inverse lumped capacitance method for determination of heat transfer coefficients for industrial air blast chillers

An inverse model using lump body was developed to calculate heat transfer coefficients as a dynamic function of time. The model used sequential function specification algorithm to calculate surface heat flux from transient temperature measurements inside a lump body system. Transient temperature measurements were collected during cooling inside an industrial chiller at two different positions with different air velocities using four replicates for each position. The calculated surface heat flux was found to be very accurate as the maximum value of the root mean squares error (RMSE) for temperature is 0.045 °C, lower than the expected error form thermocouple measurements. The calculated heat flux was then used to calculate heat transfer coefficients as a dynamic function of cooling time followed by calculation of time average heat transfer coefficient using numerical integration. The approach developed here could be a pragmatic powerful dynamic method to model spatial variation of heat transfer coefficients for industrial chillers and freezers.     

Evaluation of a commercial process for collection and cooling of beef offals by a temperature function integration technique.

The hygienic adequacy of a commercial process for the collection and cooling of beef offals was assessed by a temperature function integration technique. The diverse operations for collection of offals were inspected. The rates of product movement through those operations, and the temperatures of products at the time of their being packed, were determined. From that information, four of the nine product types were selected for examination of their temperature histories during the assembly and cooling of the cartoned products. The products selected encompassed product at near-body and near-air-ambient temperatures at the time of packaging, product in the largest and smallest cartons used in the process, and product with relatively short and long residence times in an unchilled carton stack assembly area. Twenty-one temperature histories were collected for each of the products, and the possible proliferation of an indicator organism, Escherichia coli, calculated for each temperature history. The results were assessed against a temperature function integration criterion derived from studies of beef carcass and cartoned meat cooling processes. Products packaged at near-ambient temperature readily met with the criterion, but products packed at near-body temperatures did not comply. The latter non-compliance was extreme for product packaged in large cartons. However, the principal cause of non-compliance was identified as highly variable cooling conditions in the carton freezing facility. A brief survey of air speeds and temperatures within that facility indicated means by which product cooling could be better controlled.     

Cooling of Shell Eggs with Cryogenic Carbon Dioxide: a Finite Element Analysis of Heat Transfer

Cryogenic carbon dioxide cooling of shell eggs was simulated using an axisymmetric unsteady state finite element heat transfer model. The egg was assumed to be a composite system of elliptical shape, consisting of yolk, albumen, air cell, and shell, each isotropic. An enthalpy formulation of the heat transfer problem was used to account for ice formation and growth in the region between the albumen and the shell during cooling. Simulated temperature profiles were compared with analytical and observed data and showed good agreement. The numerical simulation was used to gain an understanding of the two processes encompassed by cryogenic cooling, rapid cooling and equilibration.     

Influence of brine concentration, brine temperature, and presalting on early gas defects in raw milk pasta filata cheese

Thirty-one 3.8-kg blocks of Ragusano cheese were made on each of 6 d starting with a different batch of raw milk on each day. On d 1, 3, and 5, cheeses were not presalted and on d 2, 4, and 6, all cheeses were presalted. Before brine salting, one of the 31 blocks of cheese was selected at random for analysis (i.e., at d 0). The remaining 30 blocks were randomly divided into 2 batches of 15 blocks each, one group was placed in 18% brine, and the other group was placed in saturated brine. For the 15 blocks within each of the 2 brine concentrations, 5 blocks each were placed in brine tanks at 12, 15, and 18 degrees C. Cheese blocks were sampled immediately before brine salting (d 0) and after 1, 4, 8, 16, and 24 d of brine salting. Presalting the curd with 2% added salt before stretching reduced the coliform count in the cheese by 1.41 log and resulted in a major reduction in early gas formation. Across all treatments in the present study, the average reduction in gas formation due to presalting was 75%. Reducing brine temperature had the second largest impact on reducing gas production, but did not reduce the coliform count in the cheese. Reducing brine temperature from 18 to 12 degrees C made a larger reduction in early gas formation in cheeses that were not presalted (from 6.8 to 1.8% gas holes, respectively) than in cheeses that were presalted (from 1.9 to 0.5% gas holes, respectively). To achieve the same absolute level of gas production in the nonpre-salted cheese as was achieved in presalted cheese in combination with 18 degrees C brine, the brine temperature for the nonpresalted cheese had to be lowered from 18 to 12 degrees C. Reducing brine concentration, although effective at increasing the rate of salt penetration into the block, did not have any impact on coliform count and had minimal impact on reducing gas production. The condition where reducing brine concentration was able to make a reduction in gas production was for cheeses that were not presalted and brined at 18 degrees C. Presalting is a very simple and practical approach to reducing the problem of early gas formation in combination with strategies to improve milk quality and cheese making conditions. Further work is needed to understand the impact of different levels of presalting on death of coliforms and gas production in the cheese.     

Influence of brine concentration and temperature on composition, microstructure, and yield of feta cheese

The protein matrix of cheese undergoes changes immediately following cheesemaking in response to salting and cooling. Normally, such changes are limited by the amount of water entrapped in the cheese at the time of block formation but for brined cheeses such as feta cheese brine acts as a reservoir of additional water. Our objective was to determine the extent to which the protein matrix of cheese expands or contracts as a function of salt concentration and temperature, and whether such changes are reversible. Blocks of feta cheese made with overnight fermentation at 20 and 31°C yielded cheese of pH 4.92 and pH 4.83 with 50.8 and 48.9 g/100 g of moisture, respectively. These cheeses were then cut into 100-g pieces and placed in plastic bags containing 100 g of whey brine solutions of 6.5, 8.0, and 9.5% salt, and stored at 3, 6, 10, and 22°C for 10 d. After brining, cheese and whey were reweighed, whey volume measured, and cheese salt, moisture, and pH determined. A second set of cheeses were similarly placed in brine (n = 9) and stored for 10 d at 3°C, followed by 10 d at 22°C, followed by 10 d at 3°C, or the complementary treatments starting at 22°C. Cheese weight and whey volume (n = 3) were measured at 10, 20, and 30 d of brining. Cheese structure was examined using laser scanning confocal microscopy. Brining temperature had the greatest influence on cheese composition (except for salt content), cheese weight, and cheese volume. Salt-in-moisture content of the cheeses approached expected levels based on brine concentration and ratio of brine to cheese (i.e., 4.6, 5.7 and 6.7%). Brining at 3°C increased cheese moisture, especially for cheese with an initial pH of 4.92, producing cheese with moisture up to 58 g/100 g. Cheese weight increased after brining at 3, 6, or 10°C. Cold storage also prevented further fermentation and the pH remained constant, whereas at 22°C the pH dropped as low as pH 4.1. At 3°C, the cheese matrix expanded (20 to 30%), whereas at 22°C there was a contraction and a 13 to 18 g/100 g loss in weight. Expansion of the protein matrix at 3°C was reversed by changing to 22°C. However, contraction of the protein matrix was not reversed by changing to 3°C, and the cheese volume remained less than what it was initially.     

SIMULATION OF THE EVAPORATIVE COOLING PROCESS FOR TORTILLAS

A simulation model was developed to predict temperature, moisture content and water activity of evaporatively cooled tortillas. The overall model was based on three parts: (1) the predicted equilibrium moisture isotherm for the product, (2) a correlation model for predicting the saturated water vapor pressure for a given temperature, and (3) the energy and mass balances for simultaneous convective heat and moisture transfer between product and cooling air. The simulation model was verified with experimental data and was found to accurately describe the behavior of the tortilla cooling system. The model predicted the simultaneous decrease in temperature, moisture content, and water activity of the product exposed to varying simulated processing conditions. It was found that cooling air velocity and temperature had the primary effect on product cooling and moisture loss rates.     

Lipolysis and proteolysis in Ragusano cheese during brine salting at different temperatures

The influence of temperature (12, 15, 18, 21, and 24 degrees C) of saturated brine on lipolysis and proteolysis in 3.8-kg blocks of Ragusano cheese during 24 d of brining was determined. Twenty-six 3.8-kg blocks were made on each day. The cheese making was replicated on 3 different days. All blocks were labeled and weighed prior to brining. One block was sampled and analyzed prior to brine salting. Five blocks were placed into each of 5 different brine tanks at different temperatures. One block was removed from each brine tank after 1, 4, 8, 16, and 24 d of brining, weighed, sampled, and analyzed. Both proteolysis and lipolysis in Ragusano cheese increased with increasing brine temperature (from 12 to 24 degrees C), with the impact of brine temperature on proteolysis and lipolysis becoming progressively larger. Proteolysis was highest in the interior of the blocks where salt in moisture content was lowest and temperature had more impact on proteolysis in the interior position of the block than the exterior position. However, the opposite was true for lipolysis. The total free fatty acid content was higher and temperature had more impact on lipolysis at the exterior position of the block where salt in moisture was the highest. This effect of increased salt concentration on lipolysis was confirmed with direct salted cheeses in a small follow-up experiment. Lipolysis increased with increasing salt in the moisture content of the direct salted cheeses. It is likely that migration of water-soluble FFA from the brine into the cheese and from the interior portion of the cheese to the exterior portion of the cheese also contributed to a higher level of FFA at the exterior portion of the blocks. As brine temperature increased the profile of individual free fatty acids released from triglycerides changed, with the proportion of short-chain free fatty acids increasing with increasing brine temperature. This effect was largest at high salt in moisture content.     

Minimization of aflatoxin M1 content in Iranian white brine cheese

A chemometric approach was used to minimize the aflatoxin M1 (AFM1) content of Iranian white brine cheese. The effects of processing factors such as renneting temperature (30–40°C), cutting size (0.5–1 cm), stirring time (10–20 min), press time (1–2 h), curd size (64–256 cm³) and saturated brine pH (4.6–6) on the AFM1 content of the cheese curds were explored. Renneting temperature, press time and saturated brine pH were, respectively, the most significant factors. The aflatoxin content of the cheese samples decreased with increasing renneting temperature and press time. Lowering of the saturated brine pH reduced AFM1 in the cheese curds. Taking account of all of the factors studied, optimum processing conditions for minimization of AFM1 in the cheese curds were: renneting temperature = 39.91°C, cut size = 0.51 cm, stirring time = 17.71 min, press time = 19.48 min, curd size = 73.27 cm³ and saturated brine pH = 4.79.     

Natural convective cooling of cheese: Predictive model and validation of heat exchange simulation

The proposed FEM model describes natural convective air cooling of cheese curd and cheeses with different sizes, chemical composition and initial temperature, including temperature-dependent functions accounting for the variation of specific heat capacity and thermal conductivity of cheeses. Both the calculated convective heat transfer coefficients (from 3.58 to 15.15 W/m² K) and the ratio between Grashof and square Reynolds numbers confirmed that heat exchange was natural convective. The model permitted to accurately predict the transient temperature change into the cheese, as shown by the mean RMSEs values (from 0.34 to 2.29 °C). Higher RMSEs values (up to 3.29 °C) were obtained for cheese curds, because some deviations from the assumptions of the model occurred. These higher RMSEs values for cheese curds quantify the importance of compliance with the model’s assumptions to ensure a best fit between the simulated and experimental data.     

Heat Transfer During Brining of Cuartirolo Argentino Cheese

The heat transfer which occurs during the brining of Cuartirolo Argentino cheese is mathematically modelled as a conduction process. The thermal diffusivity of the cheese was determined experimentally and shown to agree with the value calculated from thermal conductivity, density and heat capacity measurements. The theoretical and experimental temperature profiles in the time and spatial domains showed good agreement, thus demonstrating the applicability of the proposed model.