Mathematical Model Of Temperature Research Articles

Fuzzy‐PID controller based on improved LFPSO for temperature and humidity control in a CA ripening system

AbstractTemperature and humidity as the key factors affecting the storage and ripening of fruits and vegetables directly determine the quality of fruits and vegetables. In this paper, a temperature and humidity model was constructed based on an integrated device of controlled atmosphere storage and ripening. Aiming at the shortcomings of the temperature and humidity model such as large inertia, nonlinearity, and model uncertainty, a fuzzy‐PID controller based on the improved Lévy flight particle swarm algorithm (LFPSO) is proposed. Initially, a mathematical model of temperature and humidity is developed through mechanism research and parameter estimation. Subsequently, a temperature and humidity fuzzy‐PID control strategy is proposed for regulating temperature and humidity. An improved LFPSO is then introduced to optimize the key parameters of the fuzzy‐PID controller, such as the quantization factor and the scale factor. The superiority of the improved LFPSO algorithm is verified by comparing the test functions. Finally, the improved LFPSO‐fuzzy‐PID controller, fuzzy‐PID controller, and Smith‐PID controller are applied to the simulation model for comparison using the MATLAB Simulink simulation platform. The results show that the improved LFPSO‐fuzzy‐PID control algorithm has a good control effect in the temperature and humidity simulation system of controlled atmosphere (CA) ripening container, which provides a reference for solving the optimization problem of actual engineering design.Practical applicationsIn order to reduce the postharvest cold chain losses of fruits and vegetables, this paper proposes a containerized style device that combines fruits and vegetables storage and ripening for simplifying the losses caused by transshipment at cold chain nodes. Since temperature and humidity play a key role in fruits and vegetables storage and ripening, which directly affect the product quality, this paper establishes a complete mathematical model of CA ripening temperature and humidity system by combining mechanism modeling and parameter identification. In order to keep the temperature and humidity within the ideal range, Smith‐PID controller, fuzzy‐PID controller, and fuzzy‐PID control method based on improved Lévy flight particle swarm optimization are proposed to regulate the air conditioner and humidifier. The performance of three different types of controllers was tested on the MATLAB. The simulation results demonstrate that the improved LFPSO‐fuzzy‐PID controller is superior and more effective than Smith‐PID and fuzzy‐PID controllers.

Mathematical modeling of temperature and natural antimicrobial effects on germination and outgrowth of Clostridium perfringens in chilled chicken

Effects of ginger essential oil (GEO) and grape seed extract (GSE) treatments on germination and growth of Clostridium perfringens spores in chicken after linear cooling and isothermal storage were evaluated. GEO or GSE (1%) can properly inhibit the germination and growth of C. perfringens spores during cooling from 50 °C to 4 °C. The kinetic models of Gompertz and Rat-kowskyt were carried out to describe the spore germination and growth of C. perfringens in GEO- and GSE-treated chickens at 15 °C–45 °C. Results showed a high degree of fit. The addition of GEO and GSE increased the lag phase at all storage temperatures (λ), decreased the growth rate (Rmax), and extended the time it took to rise by 1 lg of bacteria in chicken compared with the control group. GSE demonstrated stronger inhibitory activity than GEO at the corresponding storage temperature. The models provided a cost-effective and fast technology for replacing traditional culture methods and evaluating the effect of temperature and plant extracts on the shelf life of meat.

Mathematical modeling of temperature and pressure effects on permeability, diffusivity and solubility in polymeric and mixed matrix membranes

Due to the temperature and pressure dependency of gas transport through polymeric and mixed matrix membranes, probing of their separation performance at different operational conditions seems crucial to determine an optimal operational condition. To minimize the number of costly and time consuming experiments, a modified form of van’t Hoff-Arrhenius model was developed to consider the simultaneous effects of temperature and pressure on the separation performance of polymeric and mixed matrix membranes. Moreover, the proposed model is capable to consider pressure dependency of energetic parameters of Arrhenius model including activation energies of permeability and diffusivity, heat of sorption and the corresponding pre-exponential factors. The validity of the proposed model was investigated by using permeation coefficients of CO2 and N2 in a binary mixture through 6FDA-DAM at different temperatures in the range of 35–55 °C and in the feed pressure range from 2 to 5 atm. Besides, from data taken from the literature, the proposed model was validated by the prediction of temperature and pressure dependency of transport properties of glassy and rubbery polymers as well as mixed matrix membranes (MMMs) for different gas molecules including He, H2, CO2, O2, N2, CH4 and C4H10. Predictions corresponding to 300 data points revealed that the maximum average absolute relative error was 5.1%.

Gear and Runge–Kutta Numerical Discretization Methods in Differential Equations of Adsorption in Adsorption Heat Pump

The main aim of this paper was to find the correct method of calculating equations of heat and mass transfer for the adsorption process and to calculate it numerically in reasonable time and with proper accuracy. An adsorption heat pump with a silica gel adsorbent and water adsorbate is discussed. We developed a mathematical model of temperature and uptake changes in the adsorber/desorber comprising the set of heat and mass balance partial differential equations (PDEs), together with the initial and boundary conditions and solved it by the numerical method of lines (NMOL). Spatial discretization was performed with equally spaced axial nodes and the PDEs were reduced to a set of ordinary differential equations (ODEs). We focused on the comparison of results obtained when the set of heat and mass balance ODEs for an adsorber was solved using: (1) the Runge–Kutta fixed step size fourth-order method (RKfixed), (2) the Runge–Kutta–Fehlberg 4.5th-order method with a variable step size (RK45), and (3) the Gear Backward Differentiation Formulae numerical (Gear BDF) methods. In our experience, all three types of ODE numerical methods (RKfixed, RK45, and Gear BDF) can be applied in simple models to model an adsorber with attention on their limitations. The Gear BDF method usually requires much fewer steps than the RK45 method for almost the same calculating time. RK methods require many more steps to obtain results, and the calculating time depends on accuracy or defined time step. Moreover, one should pay attention to the number of nodes or possible oscillations.

Influence of thermo-gravitational convection to temperature fields in small surroundings of the heat source

The mathematical modeling of temperature and velocity fields in the system “the heat source - environment - the object of heating” was conducted. The impact assessment of thermo-gravitational convection to the temperature field in comparison with the model of conductive heat transfer was done.

Mathematical modeling of temperature during laser forming using bimodal beam

Article history: Received 6 January, 2015 Accepted 15 April 2015 Available online 17 April 2015 An analytical and numerical solution is developed for a transient heat conduction equation in which a plane slab is heated by a bimodal distribution beam over the upper surface. In laser heat treatment of steel few methods are used to produce a wider and nearly uniform average irradiance profile. This may be achieved by a bimodal (TEM11) shaped laser beam. In this paper, Green function method is employed to derive an analytical solution for thermal field distribution induced by laser forming process. Then 3-D finite element modeling of a slab in the ANSYS code is used to model the thermal field of laser forming with bimodal beam distribution. The results show that bimodal beam is useful for obtaining a uniform heat intensity distribution. © 2015 Growing Science Ltd. All rights reserved.

Mathematical Modeling of Temperature in Bread Baking

This paper aims to obtain a mathematical model to describe the evolution of temperature during the baking of bread and pastry bakers, and how these developments affect the main qualitative characteristics of the finished product such as skin color, temperature heating of the product and weight loss in cooking.

Numerical Simulation of the Casting Process with Coupled Thermal and Stress Field

To understand the thermal distribution in a complex structure and high quality linkage casting, a mathematical model of temperature and stress field was established. Numerical simulation techniques was applied by using Procast software in the temperature and stress fields of solidification process, and the foundry defect such as old lap, misrun, shrinkage and dispersed shrinkage was predicted. The stress distribution and deformation in cooling process of casting were analyzed. The simulation results can supply a scientific foundation for foundry technology.

Heat transfer analysis of blast furnace stave

The three-dimensional mathematical model of temperature and thermal stress field of the blast furnace stave is built. The radiation heat transmitted from solid materials (coke and ore) to inner surface of the stave, which has been neglected by other studies, is taken into account. The cast steel stave is studied and the finite element method is used to perform the computational analysis with soft ANSYS. Numerical calculations show very good agreement with the results of experiment. Heat transfer analysis is made of the effect of the cooling water velocity and temperature, the cooling channel inter-distance and diameter, the lining material, the cooling water scale, the coating layer on the external surface of the cooling water pipe as well as the gas clearance on the maximum temperature and thermal stress of the stave hot surface. It is found that reducing the water temperature and increasing the water velocity would be uneconomical. The heat transfer and hence the maximum temperature and thermal stress in the stave can be controlled by properly adjusting operating conditions of the blast furnace, such as the gas flow, cooling channel inter-distance and diameter, lining material, coating layer and gas clearance.

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.

The study of structure optimization of blast furnace cast steel cooling stave based on heat transfer analysis

The three-dimensional mathematical model of temperature and thermal stress field of cast steel cooling stave in a blast furnace has been modeled. Kinds of the parameters optimization of cast steel cooling stave in a blast furnace are proposed based on the heat transfer analysis. The results indicate that the values of the parameters optimization for a cast steel cooling stave are 200 mm for cooling channels interdistance, 25 mm for inner radius of the water channel, 180 mm for thickness of the cooling stave body, 70 mm for thickness of inlaid brick and 1.5 m/s for speed of cooling water. Reducing the water temperature would be uneconomical. The water temperature can be chosen according to the local conditions. The best choice for lining material is silicon nitrogen bond silicon carbide brick or silicon carbide brick.

DEVELOPMENT OF A MATHEMATICAL MODEL FOR HIGH–INTENSITY INFRARED PROCESSING (MICRONIZATION) OF PEAS

A mathematical model of temperature and moisture changes for granular material exposed to infrared (IR) heatprocessing (micronization) was developed. The model was based on a radiation exchange principle in an enclosure composedof diffusegray surfaces. The validation of the model was performed for experiments conducted with peas tempered to threeinitial moisture contents of 20%, 25%, and 30% w.b. (wet basis). The simulation results were in good agreement with theexperimental values. Further simulation experiments quantified the effect of such micronization variables as the temperatureof the IR emitter, emissivity, configuration factor, temperature of the conveying trough, temperature of the surroundings, andemissivity of the processed material.

Mathematical Modeling of Temperature and Gas Composition Effects on Visual Quality Changes of Cut Endive

ABSTRACTQuantitative descriptive analysis was used to evaluate the influence of different temperature (1‐16°C) and gas conditions (air, 11% and 19% CO2) on visual quality changes in cut endive. Based on the coefficient of determination (R2), the residuals, the estimated intercept and the variance‐stabilizing characteristics of a logarithmic transformation, a first order model was selected to represent quality deterioration kinetics. The influence of temperature and gas composition on quality deterioration rate was modeled using a combined temperature (Arrhenius)‐gas composition (exponential relation)‐quality deterioration (first order) model. The model was validated under dynamic temperature conditions showing limitations of the Time‐Temperature‐Tolerance‐concept.

A comparative study and mathematical modeling of temperature, light and growth of three microalgae potentially useful for wastewater treatment

Using growth rate data obtained for light intensities from 3 to 650 μE m −2s −1, and for temperatures from 5 to 35°C, the effects of these two variables on the growth of Ankistrodesmus falcatus, Phormidium bohneri and Oscillatoria agardhii have been compared and mathematically formulated. At temperatures of 20°C or less, A. falcatus showed the best growth; no significant difference existed between P. bohneri and A. falcatus at 25°C. At 30 and 35°C, P. bohneri better withstood high light intensities. The effect of light intensity on growth at the various temperatures tested was modeled simultaneously to express growth as a first step towards a model for the management and optimization of intensive algal cultures for the biotreatment of wastewaters.