NONLINEAR CONSTRAINED OPTIMIZATION OF THERMAL PROCESSING: I. DEVELOPMENT OF A MODIFIED ALGORITHM OF COMPLEX METHOD

The complex method, a general and flexible optimization algorithm, was used to determine the optimum process temperature profiles during thermal processing to maximize (optimize) the objective function of volume average retention of thiamine in conduction heated foods with restrictive explicit and implicit constraints. Implicit constraints were the target lethality at the coldest point, and a threshold below which the center temperature must reach at the end of the process. A process temperature range of 5–150C was used as an explicit constraint. Another explicit constraint was that the process temperature had to reach 5C at the end of the process. Control variable for the optimization was process temperature profile discretized at equidistant time steps throughout the process. All calculations were performed using a computer program written in Microsoft Visual Basic V. 6.0. This Windows‐based software calculated the optimum temperature profiles with resulting objective functions and implicit constraints. The developed algorithm for the Complex Method was found to be satisfactorily usable for the optimization of thermal processing of conduction heated foods.     

NONLINEAR CONSTRAINED OPTIMIZATION of THERMAL PROCESSING II. VARIABLE PROCESS TEMPERATURE PROFILES to REDUCE PROCESS TIME and to IMPROVE NUTRIENT RETENTION IN SPHERICAL and FINITE CYLINDRICAL GEOMETRIES

Conventional methods for thermal processing of foods use constant processing temperature profiles (CPTPs) for a prescribed processing time, which is based on achieving a required microbial lethality to comply with public health standards. This also results in degradation of nutrients and quality factors. the variable process temperature profiles (VPTPs) obtained by using optimization methods can reduce quality losses and/or processing time compared to CPTPs. the objective of this research was to evaluate VPTPs using the Complex Method to reduce the processing time and/or improve quality retention for a specified level of lethality in thermal processing of conduction heated foods. the VPTPs were obtained for volume average retention of thiamine considering different sizes of spheres (small and large) and finite cylinders (small and large), and the thiamine retention and processing time results were compared with a conventional method (processing at 121.1C) for a specified lethality level. the use of VPTPs resulted in a 37 and 10% decrease in processing times in spherical and 40 % and 6 % for finite cylindrical shapes, for the same objective function value and specified lethality compared to the CPTP process. For the same processing time, the improvements in thiamine destruction were 3.7 and 2 % for spheres, and 3.9 and 2.2% for finite cylinders.     

PREDICTING INTERNAL TEMPERATURE RESPONSE TO CONDUCTION-HEATING OF ODD-SHAPED SOLIDS

Heat penetration experiments were carried out in a hot water bath with small blocks of a solid polycarbonate material cut into various shapes (cylinder, cube and oval) to obtain heat penetration factors for each shape. These factors, along with characteristic dimensions from the odd shapes were then used in the finite cylinder heat transfer model to predict accurately the temperature at the center of each block in response to measured dynamic bath temperatures. Results showed sufficiently good agreement between predicted and measured center temperature profiles to justify use of the finite cylinder model for rapid evaluation of process deviations in thermal processing of foods in odd-shaped containers.     

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.     

Effects of different objective functions on optimal decision variables: a study using modified complex method to optimize hamburger cooking

Hamburger patties are prepared from ground beef and cooked to obtain a safe product before consumption. Cooking process eliminates microbial hazards and results in certain quality changes (e.g., cooking loss, textural changes). All these changes can be used as an objective function to achieve an optimum cooking process, but their effects on decision variable (e.g. process temperature profiles) of the optimization should be known. The use of different objective functions (minimization of cooking losses, hardness, chewiness, and shear to work) was compared to see their effects on plate temperature profiles for double-sided contact cooking. Modified Complex Method was applied as the optimization procedure. Lower and higher limits of grill temperatures (177–220°C) were explicit constraints while lethality and temperature at the patties center (F₀⩾15 s; T_c⩾71°C) were implicit constraints. The objective functions and implicit constraints were determined using a previously developed numerical heat transfer simulation model. Constant temperature profiles (decision variables) for different objective functions at different processing times (121 and 130 s) were determined. Same decision variables were found regarding the different objective functions (198.3°C and 184.1°C) for the given processing times.     

SELECTION OF VARIABLE RETORT TEMPERATURE PROCESSES FOR CANNED SALMON

Variable retort temperature processes (VRT), in which retort temperature is a function of time, were developed for sterilization of Pacific salmon in 307 × 115 steel cans, with objectives of minimizing loss of quality criteria such as surface quality or thiamine, or minimizing process time, all while maintaining constant center-point lethality (F). A finite difference computer model of conduction within a finite cylinder was used to test different temperature-time profiles. Processes were constrained to include steam vent schedules and to exclude temperature decrease during the heating process as well as temperature modulation during cooling, thereby improving compatibility with typical salmon canning facilities. Rho, the fraction of total lethality accumulated at steam-off time, was found to be a function of final unaccomplished temperature, retort temperature, salmon thermal diffusivity and container geometry. The search for favorable processes was aided by Random Centroid Optimization (RCO). Minimum surface cook in constant retort temperature (CRT) processes varied with retort temperature and z of surface quality, but the best VRT process was consistently better than the best CRT process. VRT reduced operator's process time from 64 min to 54 min and maintained equal F₀ and surface quality. Thiamine losses were reduced from 19.6% loss by CRT to 16.8% loss by VRT.     

Simultaneous optimisation of surface quality during the sterilisation of packed foods using constant and variable retort temperature profiles

The differences in temperature dependence between spore inactivation and degradation of quality factors allow the optimisation of thermal processes in terms of maximisation of quality retention by choosing an optimum heating profile. While the maximisation of the retention for a single quality factor has received considerable attention in research, the possibilities of simultaneously maximising the retention of different quality factors have up to now not been addressed.

In this article the possibilities of the simultaneous optimisation for more than one quality factor were theoretically assessed. The use of both constant and variable retort temperature profiles was considered. A special emphasis was given to the formulation of appropriate objective functions for the simultaneous optimisation of the surface retention of quality factors.

For the simultaneous optimisation of quality factors the objective functions should be formulated in terms of maximising final retention and not, as in the case of single component optimisation, in terms of minimisation of cook values. The use of variable retort temperature profiles was shown to be particularly interesting for the simultaneous optimisation of more than one quality factor, as the final retention calculated compared well with the maximum retention achieved using individual calculated optimum constant retort temperature control for each of the components.     

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.     

VARIABLE CONTROL of A BATCH RETORT and PROCESS SIMULATION FOR OPTIMIZATION STUDIES

A microcomputer was interfaced with a batch retort for digital PI control of the retort temperature. Six retort temperature profiles (three isothermal, sinusoidal, step, and ramp) were examined for processing pea puree to nearly the same lethality values in 211 × 400 cans. Thiamine content and steam consumption were measured. Thiamine retentions in non-isothermal processes were greater than in the isothermal processes, but there was no significant difference in the steam consumption.
Lethality and thiamine retention were also simulated using a finite difference model for the same heating profiles, with good agreement with experimental results. the simulation suggests that differences in thiamine retention due to differing heating regimes are significant only for large lethality values and smaller cans. For F₀ values smaller than 10 min, the simulation suggests that the sinusoidal heating regime will provide better thiamine retention. Limitations of the model and suggestions for future improvement are also discussed.     

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.     

Mathematical Models for Nonsymmetric Freezing of Beef

A microscopic balance with simultaneous change of phase together with equations for predicting the thermal properties as a function of the ice content and a cryoscopic descent model are used to simulate the nonsymmetric freezing of a beef slab. The equations are solved numerically to obtain temperature profiles as well as freezing times. Comparison with experimental results shows good agreement. A variation of the thermal center position throughout the freezing process is detected and assumptions to predict its position in the different periods of freezing are supplied. On the basis of these assumptions a simplified model for calculating processing times in plate freezers is proposed, showing good agreement with experimental freezing times and with predictions obtained from the numerical model.     

Heat Transfer during Blanching and Hydrocooling of Broccoli Florets

The objective of this work was to simulate heat transfer during blanching (90 °C) and hydrocooling (5 °C) of broccoli florets (Brassica oleracea L. Italica) and to evaluate the impact of these processes on the physicochemical and nutrimental quality properties. Thermophysical properties (thermal conductivity [line heat source], specific heat capacity [differential scanning calorimetry], and bulk density [volume displacement]) of stem and inflorescence were measured as a function of temperature (5, 10, 20, 40, 60, and 80 °C). The activation energy and the frequency factor (Arrhenius model) of these thermophysical properties were calculated. A 3‐dimensional finite element model was developed to predict the temperature history at different points inside the product. Comparison of the theoretical and experimental temperature histories was carried out. Quality parameters (firmness, total color difference, and vitamin C content) and peroxidase activity were measured. The satisfactory validation of the finite element model allows the prediction of temperature histories and profiles under different process conditions, which could lead to an eventual optimization aimed to minimize the nutritional and sensorial losses in broccoli florets.     

Original article: Apparent thermal diffusivity estimation for the heat transfer modelling of pork loin under air/steam cooking treatments

Apparent thermal diffusivity linear functions vs. product temperature were estimated for pork cooked under two different treatments (forced convection, FC and forced convection/steam combined, FC/S) at 100, 110, 120 and 140 °C by means of experimental time–temperature data and a developed finite‐difference algorithm. Slope and intercept of each function were employed to calculate apparent thermal diffusivity at 40, 55 and 70 °C. Generally, FC/S treatments gave significantly higher apparent thermal diffusivities in comparison with FC conditions. Apparent thermal diffusivities were used to develop a model for cooking time and final core temperature prediction on the basis of oven setting. The model was validated by means of additional cooking tests performed at different temperatures of those employed for model development. Root mean square error values lower than 3.8 °C were obtained comparing predicted and experimental temperature profiles. Percentage errors lower than 3.1% and 3.5% were, respectively, obtained for cooking times and final core temperatures.     

Analysis of temperature variability during the thermal processing of hazelnuts

The variability in temperature that occurs between hazelnuts during roasting is investigated. Two deterministic models of unsteady state heat transfer in a hazelnut are developed; one is based on the analytical solution for a spherical solid body and the other is a numerical model of heat flow in a hollow sphere. The mean and standard deviation in the thermal and physical properties of hazelnuts have been measured. Also the mean and standard deviation in hazelnut temperature vs. time during a roasting process has been quantified. Theoretical solutions based on functions of random variables are employed to characterise the output of such a thermal process where the rate constants are randomly distributed. In addition, the Monte Carlo method is applied to both the analytical solid sphere and numerical hollow sphere heat transfer models to estimate temperature variability. All three approaches gave satisfactory predictions of mean hazelnut temperature vs. time. However, only the Monte Carlo solution of the numerical hollow sphere model provided a good estimate of the standard deviation in hazelnut temperature vs. time. The prediction of variability in hazelnut temperature during roasting is important in the context of optimising the roasting process with respect to uniformity in product quality and safety.     

OPTIMIZATION CRITERIA FOR BATCH RETORT BATTERY DESIGN AND OPERATION IN FOOD CANNING-PLANTS

Optimization of thermal processing in the commercial sterilization of canned foods is of great interest because the canning industry plays an important role within the economy of the food processing sector. Many food canning plants operate in a batch mode with a battery of individual batch retorts. The aim of this study was to propose and analyze several criteria and methodologies for optimum design and operation of such retort systems. Two criteria were proposed in the case of choosing the optimum number of retorts to be installed when designing a new batch‐operated canning line. The third criterion dealt with seeking optimum process conditions for maximizing output from a fixed number of retorts when processing small batches of different products and container sizes. In the case of new plant design optimization, one objective was to determine the optimum number of retorts that would minimize on‐going processing costs related to labor and energy. Retort scheduling (programming) was studied from which a simple mathematical expression was derived for this purpose. A second objective was to determine the optimum number of retorts that would maximize the net present value of initial investment. Approaches based upon engineering economics were studied from which to develop a mathematical procedure for this purpose. In the case of maximizing output from a fixed number of retorts for different products and container sizes, isolethal processes were identified for various product/containers from which a common set of process conditions could be chosen for simultaneous processing of different product lots in the same retort.     

Shape Characterization for a Simple Diffusion Analysis of Air Drying of Grains

This work proposes a simple method to characterize which of the elemental geometries (slab, cylinder or sphere) would be a better approximation for the diffusion analysis of air drying of grains having “nonconventional shapes.” The method is tested with experimental drying data obtained for soybeans, rough rice, wheat and peanuts.     

汾酒地缸发酵系统热过程模式及数值模拟研究

了解白酒发酵系统的热过程特征与机理对发酵过程温度控制及发酵系统的机械化具有重要意义。通过比较不同季节汾酒发酵过程中酒醅及地缸周边土壤的温度分布,确认了汾酒地缸系统发酵过程生物热产生及扩散传递的方式,确定了地缸中酒醅温度的变化特征及发酵传热的主要机理(热传导),并且探讨了气温对发酵热过程的重要影响。根据研究结果认为发酵过程酒醅温度的变化模式符合白酒发酵的基本特征和要求,白酒的生产和研究应满足之。     

A SEMI-EMPIRICAL APPROACH TO HANDLE BROKEN-LINE HEATING: DETERMINATION OF EMPIRICAL PARAMETERS AND EVALUATION OF PROCESS DEVIATIONS

An existing semi-empirical model for simulating product temperature profiles during thermal processing of conduction or convection heating foods under time varying boundary conditions (variable retort temperatures) was extended for the case of broken-line heating products. The use of the method for determination of the empirical heat penetration parameters for broken-line heating curves as defined by Ball (j_h, f_hl, f_h2, x_bh) was evaluated. Starch solutions, showing broken-line heating behavior, were used as a food simulant.
To investigate the consistency of the determined broken-line heating parameters, and to test the applicability of the method when boundary conditions are time dependent, process deviations consisting of drops on the heating medium temperature during the holding phase of a process were evaluated. The model is a promising approach, if the correct empirical parameters are used.     

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.