Predicting the thermal inactivation of bacteria in a solid matrix: simulation studies on the relative effects of microbial thermal resistance parameters and process conditions

A combined mathematical model for predicting heat penetration and microbial inactivation in a solid body heated by conduction was tested experimentally by inoculating agar cylinders with Salmonella typhimurium or Enterococcus faecium and heating in a water bath. Regions of growth where bacteria had survived after heating were measured by image analysis and compared with model predictions. Visualisation of the regions of growth was improved by incorporating chromogenic metabolic indicators into the agar. Preliminary tests established that the model performed satisfactorily with both test organisms and with cylinders of different diameter. The model was then used in simulation studies in which the parameters D, z, inoculum size, cylinder diameter and heating temperature were systematically varied. These simulations showed that the biological variables D, z and inoculum size had a relatively small effect on the time needed to eliminate bacteria at the cylinder axis in comparison with the physical variables heating temperature and cylinder diameter, which had a much greater relative effect.     

COMPLEX METHOD FOR NONLINEAR CONSTRAINED MULTI-CRITERIA (MULTI-OBJECTIVE FUNCTION) OPTIMIZATION of THERMAL PROCESSING

The goal in a multi‐objective function optimization problem is to optimize the several objective functions simultaneously. the complex method is a powerful algorithm to find the optimum of a general nonlinear function within a constrained region. the objective of this study was to apply the complex method to two different shapes (a sphere and a finite cylinder) subjected to the same thermal processing boundary conditions to find a variable process temperature profile (decision variable) to maximize the volume‐average retention of thiamine. A process temperature range of 5 to 150C was used as an explicit constraint. Implicit constraints were center temperature and accumulated center lethality of the sphere and the finite cylinder. the objective functions for both shapes were combined into a single one using a weighting method. Then, the previously developed complex algorithm was applied using Lexicographic Ordering to order the objective functions with respect to their significance. the results were reported as optimum variable process temperature profiles using the given geometries and objective functions. the thiamine retentions were also compared with a constant process temperature process, and 3.0% increase was obtained in the combined objective function. the results showed that the complex method can be successfully used to predict the optimum variable process temperature profiles in multi‐criteria thermal processing problems.     

OPTIMIZATION OF QUALITY RETENTION IN CONDUCTION‐HEATING FOODS OF CONICAL SHAPE1

A cone frustum is an alternative shape for packaging thermally processed foods that can be useful in modeling the increasing number of microwaveable, ready‐to‐eat conical‐shaped food containers seen on supermarket shelves. Thermal processing in a cone frustum can be optimized by using numerical models for heat transfer to predict temperature distribution profiles, together with thermal destruction kinetics of target organisms and nutrient/quality factors. Iso‐lethality curves, showing combinations of process time and retort temperature that deliver equal lethality, were developed for each of three different cone frustum geometries (different dimensional proportions of major and minor diameters and height). Total volume average quality retention was determined for equivalent process time‐temperature combinations for quality factors with assumed thermal degradation kinetic parameters (D and Z‐values). Response of quality retention to the equivalent process combinations (designated by their retort temperature) revealed optimum process conditions that delivered maximum quality retention. The effect of kinetic parameters, thermal properties, and surface heat transfer coefficient on quality retention response to equivalent process conditions was also studied and compared with findings reported in the literature for the case of more traditional finite cylinder shapes.     

Linear Model for Predicting Transient Temperature during Sterilization of a Food Product

The thermal behavior of a conductive canned food during retorting was represented using an input-output linear system, with a finite order N, and a time-delay. The input of the system was the retort temperature, the output was the temperature at the thermal center of the can. This model was applied for a typical sterilization process composed of two isothermal steps. The can internal temperature was expressed as a sum of N exponential terms in which appeared the constant holding retort temperatures, the come-up and come-down times and N pairs of heat penetration parameters identified in a preliminary experiment. The model was tested on a potato mash packed in metal cans processed in a vertical still retort. Temperatures estimated by the model agreed closely with those measured during thermal processing.     

基于Fluent-EDEM耦合的茶叶红外杀青机

针对目前茶叶杀青机存在杀青不均匀、热能利用率低等缺陷,提出了一种以红外辐射为热源的滚筒式杀青机,将红外热源置于滚筒中心,采用Fluent-EDEM耦合杀青过程中的离散场、流场和温度场,并进行耦合分析,在流体软件Fluent中设置湍流模型和辐射模型,在离散元软件EDEM中建立茶叶与茶叶及茶叶与滚筒的接触模型,耦合求解计算得到杀青机滚筒内流场温度分布和杀青叶升温曲线,实现对茶叶杀青过程中流场的数值模拟,并与同型号的电加热滚筒内流场模拟结果进行比较。模拟结果表明,电加热结构的温度流场在滚筒内均匀分布,热能利用率低;而红外杀青机滚筒内流场温度分布主要集中在滚筒右部及底部,能将大部分热能直接辐射到杀青叶上,热能利用率高,该杀青装置能使杀青叶在短时间内快速升温,从而快速钝化酶的活性,提高茶叶品质。红外杀青机滚筒内的温度实测值与模拟值的相对误差约为0.99％,说明模拟过程中参数设置是合理的。     

A NEURAL NETWORK APPROACH FOR EVALUATION of SURFACE HEAT TRANSFER COEFFICIENT

An artificial neural network (ANN) approach for tackling the inverse heat conduction problems was explored - specifically for the determination of surface heat transfer coefficient at the liquid-solid interface using the temperature profile information within the solid. Although the concept is quite generic, the specific cases considered have a particular relevance to food process engineering applications. the concept was tested with two geometric shapes: a sphere and a finite cylinder, the former representing the simplest geometry and the latter representing a cross product of an infinite cylinder and an infinite plate. In developing the ANN model, two approaches were used. In the first one, the ANN model was trained to predict the surface convective heat transfer function, Biot number (Bi) from the slope coefficient (m) of temperature ratio curve under varying boundary conditions. the associated mean relative prediction errors were as high as 5.5% with a standard deviation of 8%. In the second ANN approach, m was related to tan-¹ (Bi) which significantly improved the model's predictive performance. the second ANN model could be used with Biot numbers up to 100 with a mean error less than 1.5% for either of the two geometries. Heat transfer coefficients evaluated using the developed ANN model were in agreement (<3% error) with those calculated using conventional numerical/analytical techniques under a range of experimental conditions.     

Modelling the cooling phase of heat sterilization processes, using heat transfer coefficients

A mathematical model based on finite differences was presented, which improved the accuracy of current modelling techniques during the cooling period for conduction heating foods undergoing thermal processing. The surface heat transfer coefficient between can and cooling fluid was incorporated into the finite difference equations, with a value of 600 W m⁻² K⁻¹ chosen from literature and confirmed by calculations from surface temperature measurements and a correlation of the form Nu = f(GrxPr)ⁿ.
Experimental results were obtained for a cylinder of Sylgard 184 elastomer (length 62mm, diameter 57mm) and a polypropylene block (26x91x141 mm). At the end of cooling the heat transfer coefficient model predicted a centre temperature just 2.5°C above the measured value for polypropylene, and for Sylgard 184 this difference was 2.7°C.
This model will improve both real-time process control via the 'derived-value' technique, and the use of controlled pressure cooling with less damage to containers. Optimization of quality factors will also be improved with increased knowledge of in-container temperatures.     

SIZE AND SHAPE EFFECT ON NONUNIFORMITY OF TEMPERATURE AND MOISTURE DISTRIBUTIONS IN MICROWAVE HEATED FOOD MATERIALS: PART II EXPERIMENTAL VALIDATION

Experiments were conducted to determine temperature and moisture distributions in brick-shaped, cylinder-shaped and hexagonal prism-shaped products. Center heating for cylindrical shapes, corner heating for brick-shapes and surface drying in all the shapes considered were predicted by the finite element model (FEM) and were observed in the experimental data. The slow rate of heating in the case of hexagonal-prism shaped products predicted by the FEM was validated by the experimental study. The FEM calculated moisture distributions matched the experimentally measured values closely for brick (maximum % error = 9.3% and standard error = 0.9%), cylinder (6.9% and 0.6%) and hexagonal prism (1.5% and 0.15) shaped products. The FEM calculated temperature distributions and experimentally measured values were closer in the case of brick-shaped products (maximum % error = 24.7% and standard error = 4.3C) and cylinder-shaped products (22.0% and 2.8C) when compared to hexagonal prism-shaped products (57.3% and 3.3C).     

NUMERICAL SIMULATION OF CONDUCTION HEATING IN CONICALLY SHAPED BODIES1

A 2‐dimensional energy balance approach was used to model temperature distribution in conduction heated conically shaped bodies. A numerical solution by finite differences to the second order partial differential equation for heat conduction served as basis for the model. The cone was divided into small volume elements. The inner elements were concentric rings of rectangular cross section while those at the side surfaces had triangular cross‐sections. Energy balance equations for the volume elements were solved explicitly. Acrylic of known thermal properties was used to fabricate cones in 3 different geometries and sizes, varying from a frustum to a point cone. Every cone had 3 or 4 thermocouples (36 gauge, T type) inserted at different locations. Heat penetration tests were carried out in a water bath with constant and variable water temperatures. Experimental temperatures at different locations within the cones agreed well with temperatures predicted by the model. Use of the model to predict the location of the slowest‐heating point or “cold point” under different processing conditions was also demonstrated.     

Multiphysics Modeling of Microwave Heating of a Frozen Heterogeneous Meal Rotating on a Turntable

A 3‐dimensional (3‐D) multiphysics model was developed to understand the microwave heating process of a real heterogeneous food, multilayered frozen lasagna. Near‐perfect 3‐D geometries of food package and microwave oven were used. A multiphase porous media model combining the electromagnetic heat source with heat and mass transfer, and incorporating phase change of melting and evaporation was included in finite element model. Discrete rotation of food on the turntable was incorporated. The model simulated for 6 min of microwave cooking of a 450 g frozen lasagna kept at the center of the rotating turntable in a 1200 W domestic oven. Temperature‐dependent dielectric and thermal properties of lasagna ingredients were measured and provided as inputs to the model. Simulated temperature profiles were compared with experimental temperature profiles obtained using a thermal imaging camera and fiber‐optic sensors. The total moisture loss in lasagna was predicted and compared with the experimental moisture loss during cooking. The simulated spatial temperature patterns predicted at the top layer was in good agreement with the corresponding patterns observed in thermal images. Predicted point temperature profiles at 6 different locations within the meal were compared with experimental temperature profiles and root mean square error (RMSE) values ranged from 6.6 to 20.0 °C. The predicted total moisture loss matched well with an RMSE value of 0.54 g. Different layers of food components showed considerably different heating performance. Food product developers can use this model for designing food products by understanding the effect of thickness and order of each layer, and material properties of each layer, and packaging shape on cooking performance.     

Coupled 3D heat and mass transfer model for numerical analysis of drying process in papaya slices

An experimental and numerical study for the drying process of a solid food, Chilean papaya slices, was carried out in a range of air temperatures from 40 to 80 °C. The unsteady temperature and moisture distributions results inside the sample were predicted by using an unsteady tri-dimensional coupled heat conduction and mass diffusion mathematical model. The validation procedure includes a comparison with experimental and numerical temperature and moisture content results obtained from experimental data. The samples thermophysical properties as density, specific heat, and thermal conductivity are assumed to vary non-linearly with temperature. The convective heat and mass transfer coefficients were found by the analytical model. The water effective diffusion coefficient, the drying curves and the center temperature were measured by physical experiments. It was found from the experimental results that slices of papaya present an isotropic behavior with an uncertainty between 6.0% and 9.0%. According to statistical test results (RE%), the finite volume method based calculations gave a very good fit quality.     

火灾环境下应急救援防护服传热数值模拟

 通过建立穿着于模拟人体的应急救援防护织物传热模型,研究模拟火灾环境下的服装传热特征。模拟人体肢体的圆柱体内核保持恒定温度37℃,模型考虑了织物吸收热辐射及热属性随温度变化的特性,运用有限差分完全隐式格式方法模拟计算了织物与人体皮肤的一维径向温度分布,将计算得到的温度值代入Henriques烧伤模型方程以预测皮肤达到二级烧伤所需的时间,其值与实验结果较为一致。研究结果表明,圆柱几何形状对天然阻燃高聚物纤维织物的热防护性能影响效果较为显著,所建立的模型为覆盖于圆柱体的多孔材料传热提供了系统的研究方法。     

HEATING BEHAVIOR AND QUALITY FACTOR RETENTION IN A CANNED MODEL FOOD AS INFLUENCED BY THERMAL PROCESSING IN A ROTARY RETORT

Heat penetration data were obtained for a canned model food (gelatinized starch) during processing in a rotary retort under various conditions (retort temperature, 110–130C; rotation speed, 10–20 rpm, can headspace 6.4–12.8 mm and starch concentration, 3–4%) to establish thermal processes with an equivalent lethality (F₀ value) of 10 min. Apparent viscosity and Hunter L, a and b values were experimentally evaluated both before and after each run. The percentage of selected quality factors (nutrients, color) retained at each processing condition was estimated using the heat penetration data and documented kinetic parameters for each quality factor. The study indicated that the heating behavior was influenced (p < 0.05) by all factors except can headspace. Higher temperatures and higher rotation speeds favored better retention of quality factors and reduction in process times.     

EVALUATION OF THERMAL PROCESSES FOR CONDUCTION HEATING FOODS IN PEAR-SHAPED CONTAINERS

A numerical model was developed to study transient heat conduction in a pear-shaped can. The model was extended to perform bacterial lethality and nutrient retention calculations for foods processed in pear-shaped containers. Transient temperature distributions and lethality predictions obtained from the numerical model when applied to finite cylinders, compared favorably with previously accepted solutions. Calculations of integrated F_s values of processes for pear-shaped containers indicated up to 50% overprocessing by the single point lethality concept. An "equivalent cylinder" was defined as one having a geometry index and characteristic heat transfer length corresponding to those of a pear-shaped container. Process evaluations for "equivalent cylinders" were in agreement with solutions obtained for the pear-shaped model.     

PARTICLE HEAT TRANSFER COEFFICIENTS UNDER VARIOUS RETORT OPERATING CONDITIONS WITH END-OVER-END ROTATION

Forced convection heat transfer in cans was studied experimentally during end-over-end sterilization in a full-immersion, hot-water rotary sterilizer. A polypropylene spherical particle (diameter = 19 mm) was suspended in a high temperature bath oil (Newtonian liquid) using a flexible fine-wire thermocouple attached to the can wall providing uninhibited heat transfer conditions. the overall heat transfer coefficient, U, was determined using a lumped capacity heat balance approach and the fluid-to-particle heat transfer coefficient, h_fp, was determined from transient temperature data at the center of the particle using a finite difference computer simulation. the effects of retort temperature (110 to 130C), rotational speed (0 to 20 rpm), radius of rotation (0 to 27 cm) and can headspace (6.4 and 10 mm) were examined on the associated heat transfer coefficients. Higher heat transfer coefficients were obtained with increasing values of all four variables, and the effects of rotational speed and headspace were more significant than those of retort temperature and radius of rotation. U values ranged from 120 to 187 W/m². K and h_fp values ranged from 23 to 145 W/m². K depending on the operating conditions.     

Combined heat transfer and kinetic models to predict cooking loss during heat treatment of beef meat

A heat transfer model was used to simulate the temperature in 3 dimensions inside the meat. This model was combined with a first-order kinetic models to predict cooking losses. Identification of the parameters of the kinetic models and first validations were performed in a water bath. Afterwards, the performance of the combined model was determined in a fan-assisted oven under different air/steam conditions. Accurate knowledge of the heat transfer coefficient values and consideration of the retraction of the meat pieces are needed for the prediction of meat temperature. This is important since the temperature at the center of the product is often used to determine the cooking time. The combined model was also able to predict cooking losses from meat pieces of different sizes and subjected to different air/steam conditions. It was found that under the studied conditions, most of the water loss comes from the juice expelled by protein denaturation and contraction and not from evaporation.     

OPTIMIZATION OF PASTEURIZATION PROCESSES FOR A SOUS VIDE PRODUCT IN RECTANGULAR THIN PROFILE FORMS

A Hawaiian mackerel and rice product was prepared for sous vide processing. Heat penetration data were gathered and used to verify the values predicted by a computer model. Heat penetration data were collected during pasteurization regimes at five degree intervals between 65C and 85C. The measured time-temperature data were used to evaluate heat penetration parameters for the sous vide product. These data were then used to calculate the process time required for a specific pasteurization value (P_v), that is equivalent to 13 times the decimal reduction (13D) of Streptococcus faecium at 85C. The optimum time-temperature (33 min at 75C) combination was obtained using the maximum value of a multi-factor objective function (OF). The optimal pasteurization temperature was chosen to minimize the volume average cook value (C_av) and to maximize the OF. Results show that optimization of certain quality factors can be achieved using a mathematical model for heat conduction in rectangular plastic containers.     

HEAT TRANSFER TO WATER AND SOME HIGHLY VISCOUS FOOD SYSTEMS IN A WATER-COOLED SCRAPED SURFACE HEAT EXCHANGER

Heat transfer in a water-cooled scraped surface heat exchanger has been investigated. The overall heat transfer coefficient in the heat exchanger is composed of three elements: heat transfer coefficient in the coolant jacket, resistance to heat flow in the separation wall and heat transfer coefficient inside the scraped cylinder. A method for assessing the heat transfer coefficient at the coolant side was developed. In contrast with studies published elsewhere, heat transfer was investigated with food systems which are non-newtonian and possess a complicated and unknown flowing behavior at higher shear rates. For water and three starch-based food products (starch content 12–18%) the heat transfer coefficients inside the scraped cylinder were measured for shaft speeds ranging from 1.67 to 10 revolutions/s. The experimental results were compared with heat transfer coefficients calculated with a model based on the penetration theory. For the starch-based products, in general, no consistent interactions between mass flow rates and internal heat transfer coefficients were observed. In the shaft speed range studied heat transfer coefficients at scraped surface varied from 3200 to 7800 W/m² K for water, from 500 to 3150 W/m² K for velouté sauce, from 670 to 1330 W/m² K for roux and from 780 to 1900 W/m² K for ragout.     

纸页干燥过程计算模型

基于多孔介质传热传质理论，建立了计算纸页抄造过程干燥参数变化规律的模型，以此模型计算了纸板在烘缸表面和自由行走阶段的温度、水分的变化。计算结果表明，自由行走阶段水分的蒸发率大于纸在烘缸表面的蒸发率；在干燥部的中前段，相对水分蒸发率随烘缸数增加呈线性增加。与实测值的比较证明了模型计算结果的准确性，该模型还可用于烘缸数的选择与设计。