Modelling of coupled heat and mass transfer during a contact baking process

A mathematical model of coupled heat and mass transfer of a contact baking process is developed. In the current model formulation, a local evaporation of water is described with a reaction-diffusion approach, where a simultaneous diffusion and evaporation of water takes place. The resulting coupled model equations (unsteady state heat transfer, liquid water and water vapour) were solved using the Finite Element Method (COMSOL Multi-physics® version 3.5). During the baking process, local temperatures and overall moisture loss were measured continuously. The model - predicting temperature, liquid water content in the product and water in the vapour phase - was calibrated and partially validated using data obtained during baking of a representative food model (a pancake batter) under controlled conditions on a specially designed experimental rig. The unknown parameters in the model equations were estimated using the standard least squares method by comparing the measured with the predicted temperature profile. Good agreement was achieved between model predictions and the experimental values.     

Development and validation of a probabilistic second-order exposure assessment model for Escherichia coli O157:H7 contamination of beef trimmings from Irish meat plants

A second-order quantitative Monte Carlo simulation model was developed for Escherichia coli O157:H7 contamination of beef trimmings in Irish abattoirs. The assessment considers initial contamination levels, cross-contamination and decontamination events during the cattle slaughter process. The mean simulated prevalence of E. coli O157:H7 on trimmings was 2.36% and the mean simulated counts of E. coli O157:H7 on contaminated trimmings was -2.69log(10)CFU/g. A parallel validation survey provided some confidence in the model predictions. An uncertainty analysis indicated that microbial test sensitivity is a significant factor contributing to model uncertainty and requires further investigation while also indicating that risk reduction measures should be directed towards reducing the hide to carcass transfer (correlation coefficient 0.25) during dehiding and reducing the initial prevalence and counts on bovine hides (correlation coefficients 0.19 and 0.16, respectively). A characterisation of uncertainty and variability indicating that further research is required to reduce parameter uncertainty and to achieve better understanding of microbial transfer in meat plants. The model developed in this study highlights the need for further development of quantitative risk assessments in the food industry.     

基于不确定性理论的乳品降膜蒸发器设计

基于蒙特卡洛不确定性方法,研究了乳品三效降膜蒸发器中参数和模型两类不确定性对设计结果的影响。结果表明,与参数不确定性相比,模型不确定性导致的蒸发器传热性能变化更为显著。通过综合考虑参数不确定性与模型不确定性的影响,提出模型集成法以降低模型不确定性,提高模型预测可靠性。基于不同的设计概率选取蒸发器传热面积,可为不同设计条件和不同操作条件下的蒸发器设计和运行提供理论依据。     

Recent developments in numerical modelling of heating and cooling processes in the food industry—a review

Numerical modelling technology offers an efficient and powerful tool for simulating the heating/cooling processes in the food industry. The use of numerical methods such as finite difference, finite element and finite volume analysis to describe the heating/cooling processes in the food industry has produced a large number of models. However, the accuracy of numerical models can further be improved by more information about the surface heat and mass transfer coefficients, food properties, volume change during processes and sensitivity analysis for justifying the acceptability of assumptions in modelling. More research should also be stressed on incorporation of numerical heat and mass transfer models with other models for directly evaluating the safety and quality of a food product during heating/cooling processes. It is expected that more research will be carried out on the heat and mass transfer through porous foods, microwave heating and turbulence flow in heating/cooling processes.     

Modeling of simultaneous heat and mass transfer during convective oven ring cake baking

The convective oven ring cake baking process was investigated experimentally and numerically as a simultaneous heat and mass transfer process. The mathematical model described previously by the authors for cup cake baking was modified to simulate ring cake baking. The heat and mass transfer mechanisms were defined by Fourier’s and Fick’s second laws, respectively. The implicit alternating direction finite difference technique was used for the numerical solution of the representative model. Prior to the utilization of the developed model in predicting the temperature and moisture profiles for ring cake baking, the results of the numerical model were compared with analytical results involving only heat or mass transfer with constant thermo-physical properties. Excellent agreement was observed. The numerical temperature and moisture contents predicted by the model were compared with the experimental profiles. They agreed generally reasonably well with the experimental temperature and moisture profiles.     

Multiphase porous media modelling: A novel approach to predicting food processing performance

The development of a physics-based model of food processing is essential to improve the quality of processed food and optimize energy consumption. Food materials, particularly plant-based food materials, are complex in nature as they are porous and have hygroscopic properties. A multiphase porous media model for simultaneous heat and mass transfer can provide a realistic understanding of transport processes and thus can help to optimize energy consumption and improve food quality. Although the development of a multiphase porous media model for food processing is a challenging task because of its complexity, many researchers have attempted it. The primary aim of this paper is to present a comprehensive review of the multiphase models available in the literature for different methods of food processing, such as drying, frying, cooking, baking, heating, and roasting. A critical review of the parameters that should be considered for multiphase modelling is presented which includes input parameters, material properties, simulation techniques and the hypotheses. A discussion on the general trends in outcomes, such as moisture saturation, temperature profile, pressure variation, and evaporation patterns, is also presented. The paper concludes by considering key issues in the existing multiphase models and future directions for development of multiphase models.     

A NUMERICAL APPROACH WITH VARIABLE TEMPERATURE BOUNDARY CONDITIONS TO DETERMINE THE EFFECTIVE HEAT TRANSFER COEFFICIENT VALUES DURING BAKING OF COOKIES

The increasing trade of ready‐to‐eat foods such as cookies highlights an interest in quality defects during baking. Heat (h and thermal diffusivity) and mass (mass transfer and diffusion coefficients) transfer parameters are significant parameters affecting the quality changes. Therefore, it is important to determine these parameters for modeling and process optimization studies. Among these, the h is important, revealing the relationship between the heating medium and product surface. As baking involves a simultaneous heat and mass transfer involving moisture diffusion and heat conduction inside and convective heat and mass transfer outside, a lumped system method may not be an accurate choice to determine the h value. Changes in the product volume and contact heating from bottom of the product also bring extra challenges to the determination of h. Therefore, the objective of this study was to use realistic approaches including simultaneous heat and mass transfer to determine the changes in h. The h_effvalues for the bottom and top surface of the cookies were then determined, applying a numerical procedure where the surface temperature changes were the boundary conditions with evaporation on the surface. The h_band h_t values increased with baking temperature and varied with baking time. The results of this study showed that evaporative mass flux for the top surface, heat flux for the bottom surface and the product's volume changes were significant in the variation of h values.     

Determination of Local Heat-Transfer Coefficients Around a Circular Cylinder Under an Impinging Air Jet

Heat transfer coefficients around a model food shaped as a circular cylinder placed on a flat surface and impinged by a slot air jet has been determined using an inverse heat transfer method. The determination was based on time-temperature data measured with a thermocouple in the cylinder and in the air jet. The cylinder was rotated around its horizontal axis to determine the heat-transfer coefficients at different locations around the cylinder. A sensitivity analysis using Monte Carlo simulations was also performed. The local heat-transfer coefficients determined, were compared to computational fluid dynamics (CFD) simulations using the k-ω SST and RSM models. The heat-transfer coefficients determined from temperature measurements was larger than predicted by the CFD simulations. The heat-transfer rates were in better agreement on the upper part of the cylinder, including the decrease along the cylinder due to flow separation, than on the lower part close to the wake recirculation area. The SST model predicted in general a slightly higher heat-transfer rate on the upper part of the cylinder and slightly lower on the lower part of the cylinder, as compared to the RSM model.     

Multimedia fate model for hexachlorocyclohexane in Tianjin, China

A level III fugacity model was applied to characterize the fate of gamma-HCH in Tianjin, China, before the 1990s when the contamination reached its maximum at steady state. Geometric means were used as model inputs. The concentrations of gamma-HCH in air, surface water, soil, sediment, crops, and fish as well as transfer fluxes across the interface between the compartments were derived under the assumption of steady state. The calculated concentrations were validated by independent data collected from the literature. There was generally good agreement between the estimated and the observed concentrations, and the differences were all less than 0.6 log units for air, water, soil, sediment, and fish and approximately 1 order of magnitude for crops. Around 97% of gamma-HCH accumulated in soil and sediment. Wastewater irrigation was not an important pathway for delivering gamma-HCH to soil as compared to the dominant source of agricultural application. Degradation and advective airflow carried much gamma-HCH out of the system. Sensitivities of the model estimates to input parameters were tested, and a coefficient of variation normalized sensitivity coefficient was defined for the test. The most influential parameters were degradation rates in sediment and soil, application rates, concentrations in wastewater, and adsorption coefficients. Monte Carlo simulation was conducted for model uncertainty analysis. The model was run 20 000 times using randomly generated data from predefined log-normal distribution density functions. All calculated concentrations and fluxes were log-normally distributed. The dispersions of the calculated and observed concentrations were compared in terms of coefficients of variation to distinguish between true variability and model uncertainty.     

Heat Transfer Coefficients on Cakes Baked in a Tunnel Type Industrial Oven

Using an h-monitor, surface heat flux and effective surface heat transfer coefficients were evaluated during baking of two cakes in a tunnel-type multi-zone industrial oven. An average 75–80% of total heat flux was counted as radiation heat. Air-mass temperature outside the boundary layer was determined from the experimental temperature profiles over the h-monitor top plate. In the range of baking temperatures (186–22 5°C), relative air velocities (0.02-0.437 m/s) and absolute humidities (0.0267–0.0428 kg H₂O/kg dry air) heat transfer coefficients were 20 to 48.0 W/m²K. A simple regression model was developed based on experimental data.     

Quality prediction of bakery products in the initial phase of process design

The development of food production processes is facilitated by tools which explore the interaction between process design, operation conditions and product characteristics. In this work an approach how to set-up a simulation model is presented for the phenomena and transformations which occur during baking and which fix the product quality. The simulation model has three consecutive parts: mass and heat transport in the product, transformations concerning starch state transition and color, and the formation of quality attributes (color, softness, crispness and staling). The model for mass and heat transfer is based on laws of conservation and expressed in partial differential equations for spatial products. The starch state transition and color formation are a mixture of qualitative and quantitative information, while the product quality model is mainly based on qualitative information. The model is applied to three bakery products: bread, biscuit and a cake-type. The results show that the model estimates the product quality and its transformations as a function of dough composition, baking and storage condition. The results fit well to observed changes of properties and product quality during baking.Industrial relevanceFood industries require tools to evaluate processing options in the feasibility phase of process design. Therefore, simulation of process models is important for this purpose. However, knowledge of different aspects is subject to area of expertise (for example heat and mass transfer versus product quality formation) and often these areas are hardly connected. This work presents a systematic modeling approach for the dominant processes during baking and their interconnection. The main functions of the model are to explore the consequences of choices in design, to rank design options and to find in what direction properties will change when operational conditions change. Moreover, the model can be used for sensitivity analysis to explore on what items further information must be gathered.     

A methodology for evaluating the formation and human exposure to acrylamide through fried potato crisps

Potato crisps are a popular snack food which have been implicated as a potential source of acrylamide. This study develops a farm-to-fork human exposure assessment model for acrylamide in fried potato crisps for Irish consumers. The model used Monte Carlo simulation techniques to model the various stages from on farm production of potatoes, storage, processing, crisp production and final human consumption of potato crisps. A baseline model is created and a number of scenarios are subsequently created to look at the impact of different model assumptions and input parameters. The baseline model found that the mean level of acrylamide in potato crisps in Ireland was 720 μg/kg. Irish consumer exposure to acrylamide in potato crisps was estimated to be 0.052 and 0.064 μg/kg bw/day for males and females, respectively. A sensitivity analysis revealed the important parameters influencing the model predictions. The initial level of reducing sugars was found to be the most important parameter (correlation coefficient 0.58 and 0.57 for glucose and fructose, respectively), highlighting the importance of selecting cultivars with low reducing sugar levels for crisp production. The cooking regime had a significant impact on model predictions, highlighting the need for further research into the impact of different time and temperature combinations. Blanching and soaking of potatoes were also identified as important risk reduction processes.     

Heat transfer analysis of cheese cooling incorporating uncertainty in temperature measurement locations: Application to the industrial process

A cylindrical cheese product with an irregular cross sectional geometry is cooled by partial immersion in brine. It is essential to calculate the temperature–time history of the product during this cooling phase to ensure its microbiological safety. The heat transfer analysis is complicated by both the non-standard product geometry and the non-uniform surface heat transfer coefficients that prevail. The flotation behaviour of the cheese at the air/brine interface is analysed to determine the heat transfer areas exposed to each cooling fluid. A finite element model is developed to predict temperature histories at various points in the product and to determine the slowest cooling region in the product. The cooling performance of the cheese is also studied experimentally. Comparison of the theoretical and experimental temperature histories is complicated by uncertainty in the location of the thermocouples in the product. By statistically quantifying the imprecision in thermocouple position, the expected temperatures in each region of interest can be found from the thermal model by Monte Carlo sampling. With the model, the top region of the cheese stick has been shown to determine cooling time because the existence of the non-uniform boundary condition is significant in determining the evolution of temperature.     

Estimating exposure to chemical contaminants in drinking water

A model is developed that predicts exposure and absorbed dose for chemical contaminants in household drinking water via three pathways: inhalation, direct and indirect ingestion, and dermal penetration. Extensive probability distributions for building characteristics, activity and water use patterns, operating conditions of water devices, and physiological characteristics of the general population are developed. The impacts of different operating conditions on mass transfer coefficients for the shower, bath, washing machine, dishwasher, and faucet are established. Dichlorobromomethane, inorganic lead, and endosulfan, three compounds associated with adverse birth outcomes that have significantly different chemical properties, are selected for analysis. The primary exposure pathways for dichlorobromomethane are inhalation (62%) and ingestion (27%). Seventy percent of total exposure to endosulfan comes from ingestion, and 18% from dermal sorption with the remaining 12% due to inhalation. Virtually all (99.9%) of the exposure to lead occurs via ingestion. A nested Monte Carlo analysis shows that natural variability contributes significantly more (a factor of 10) toward total uncertainty than knowledge uncertainty (a factor of 1.5). Better identification of certain critical input variables (ventilation rate in the shower and bathroom, ingestion rate, the boiling water mass transfer coefficient, and skin permeability) is required.     

Monte Carlo Simulation to establish the effect of pH, temperature and heating time on the final load of Bacillus stearothermophilus spores

Bacillus stearothermophilus heat treatment studies at different pH levels were carried out in order to predict the final microbiological load as affected by the temperature and pH treatment. For that, distribution functions were obtained for the initial number of microorganisms, the decimal reduction coefficient, the z _T and the z _pH parameters, and Monte Carlo Simulation was used as a tool to determine this microbial load after a heat treatment introducing in this way the variability and uncertainty. The mean value of the predictions made by Monte Carlo Simulation, when compared with independent data, rendered Accuracy Factors close to 1, values close to 1 indicated good predictions. Bias values were close to 1, but some values were below 1 and others above 1. The tornado graphs indicated that the main factor contributing to the final load after the heat treatment was the initial number of microorganisms followed by the temperature and pH.     

Sensitivity Analysis in Predictive Models for assessing the Level of β-Glucan in Oats and Barley Cultivars Using Meta-Models

Oats and barley β-glucans are well-known for their many health benefits; this has encouraged the food industry to develop new functional foods containing oats and barley. This study aims to develop an advanced sensitivity analysis to analyse and evaluate the most significant model inputs contributing to uncertainty in assessing the level of β-glucan content in harvested oat and barley grains. Two methodologies, nominal value and regression method sensitivity analysis, were adopted. The nominal sensitivity analysis highlighted that cultivar selection is the predominant factor with a correlation coefficient 0.66 for hulled oats and barley cultivars, whereas the correlation was 0.80 and 0.77 for naked oats and hull-less barley, respectively. Advanced sensitivity analysis using regression modelling highlighted that cultivar selection, storage days and germination time (days) were the most important parameters in both the oats and barley model. Regression analysis using the response surface methodology shows that prediction models were found to be significant (P < 0.0001) with low standard errors and high coefficients of determination (R ²  > 0.94). This study shows that regression modelling is an effective tool to highlight the effect of key input variables and their interactive effects on the predictive response of β-glucan in harvested oats and barley cultivars.     

Probabilistic modelling: theory and practice

Probabilistic modelling techniques allow much more realistic estimates of exposure and risk by computing the use of the full range of potential exposures rather than single 'worst case' exposures. However, these techniques require additional considerations regarding the appropriate data and models. This article reviews the theoretical aspects of probabilistic modelling and also considers some of the practical applications. The most common method, called Monte Carlo analysis, is discussed in some detail. The practical application of Monte Carlo to risk assessments is presented along with an evaluation of the input parameters. Topics also discussed include considerations of the requirements for precision and procedures for validation of assessments.     

基于蒙特卡洛法的溶解性总固体测量不确定度评定

目的研究出一种基于蒙特卡洛法的溶解性总固体测量不确定度评定的方法。方法按照溶解性总固体实验过程,建立对应的数学模型。根据蒙特卡洛法分布传播和总结过程,得出蒙特卡洛法的评定结果。同时使用Guide 98-3:2008《测量不确定度表示指南》进行评定,得出对比结果。结果使用蒙特卡洛法所得结果为208.0 mg/L,扩展不确定度为5.2 mg/L。区间为197.82~218.18 mg/L。指南法评定结果为208.6 mg/L,扩展不确定度为5.6 mg/L,计算结果为(208.6±5.6)mg/L。结论蒙特卡洛法评定结果与测量不确定度表示指南法评定的数据相近,可以用于计算溶解性总固体的测量不确定度,为实验室工作人员提供了一种实用的测量不确定度评定方法。     

Use of sensitivity analysis to aid interpretation of a probabilistic Bacillus cereus spore lag time model applied to heat-treated chilled foods (REPFEDs)

The microbiological safety and quality of REfrigerated Processed Foods of Extended Durability (REPFEDs) relies on a combination of mild heat treatment and refrigeration, sometimes in combination with other inhibitory agents that are not effective when used alone. In this context, the output of a probabilistic model predicting the lag time of heat-treated Bacillus cereus spores under realistic heat-treatment profile and chilled supply-chain conditions, has been investigated using a sensitivity analysis technique. Indeed, knowing that there was uncertainty in the model (e.g. due to lack of data to build the model input probability density function), the objective of the analysis was to evaluate if the variability associated with some inputs (e.g. the consumers' refrigerator temperature values reported in Europe and US markets were different) had a significant impact on the model output, i.e. on the expected lag time of heat-treated B. cereus spores in REPFEDs. To do so, the uncertainty and variability associated with the various model inputs have been identified and then separated using a second order Monte Carlo decomposition. Concerning the variability, there was a significant difference between the chilled supply-chains (Europe, US) and between the raw material groups (low, medium or high contamination levels). For example, in the European market, after a heat treatment of 90 degrees C for 10 min, with a high raw material contamination level, the predicted 5th percentile of the lag time was 17 days, while it was 35 days with a low raw material contamination level. This was confirmed with an ANOVA. The impact of the uncertainty on the lag time has been illustrated graphically by building confidence intervals around its 5th percentile. A sensitivity analysis based upon uncertainty and variability decomposition is clearly a complex and time consuming exercise; however, it provides a greater confidence (greater transparency and better understanding) in the model output when making food safety decisions (e.g. determining the safe shelf-life of REPFEDs).     

Two-dimensional CFD modeling and simulation of crustless bread baking process

A special type of baking oven was developed where crustless bread was made by gently baking the dough at controlled temperature by spraying water at prefixed intervals on the surface of the dough. In this study, a two-dimensional (2D) CFD model for crustless bread during baking has been developed to facilitate a better understanding of the baking process. Simultaneous heat and mass transfer from the bread during baking was successfully simulated. It was found that core temperature of the bread reached at 95 °C at the end of baking where as moisture of the bread satisfies the normal bread quality. The model can be successively applied to study the unsteady heat and mass transfer from the crustless bread during baking.