scholarly journals A New Mathematical Model for Food Thermal Process Prediction

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Dario Friso
Keyword(s):  
Mathematical Model ◽  
Thermal Process ◽  
Absolute Error ◽  
Process Time ◽  
Heating Process ◽  
Canned Food ◽  
Heat Penetration ◽  
The Difference ◽  
Input Variables ◽  
The Mathematical Model

A mathematical model was developed to correlate the four heat penetration parameters of 57 Stumbo’s tables (18,513 datasets) in canned food:g(the difference between the retort and the coldest point temperatures in the canned food at the end of the heating process),fh/U(the ratio of the heating rate index to the sterilizing value),z(the temperature change required for the thermal destruction curve to traverse one log cycle), andJcc, (the cooling lag factor). The quantitiesg,z, andJcc, are input variables for predictingfh/U, whilez,Jccandfh/Uare input variables for predicting the value ofg, which is necessary to calculate the heating process timeB, at constant retort temperature, using Ball’s formula. The process time calculated using thegvalue obtained from the mathematical model closely followed the time calculated from the tabulatedgvalues (root mean square of absolute errors RMS = 0.567 min, average absolute error = 0.421 min with a standard deviation SD = 0.380 min). Because the mathematical model can be used to predict the intermediate values of any combination of inputs, avoiding the storage requirements and the interpolation of 57 Stumbo’s tables, it allows a quick and easy automation of thermal process calculations and to perform these calculations using a spreadsheet.

Thermal Process Evaluation of Analogue Shrimp Product (ASP) from Lizard Fish (Saurida tumbil) in Retort Pouches

2021 ◽  
Author(s):  
K. Hema ◽  
P. Velayutham ◽  
C.O. Mohan ◽  
D. Sukumar ◽  
B. Sundaramoorthy ◽  
...  
Keyword(s):  
Thermal Processing ◽  
Thermal Process ◽  
Water Immersion ◽  
Value Added ◽  
Steam Injection ◽  
Process Time ◽  
Thermally Processed ◽  
Total Process ◽  
Heat Penetration ◽  
The Difference

Background: Seafood analogue is a ready to make value added product prepared out of surimi. Thermal processing of restructured products in retort pouches such as fish ball in curry medium, surimi stew in white tripod, boneless rohu balls in curry. Also no work had done on thermal processing of shrimp analogue products in retort pouches. The main objective of this work was to develop the analogue shrimp product from lizardfish and to compare the heat penetration attributes of analogue shrimp curry and masala using retort pouches and different sterilization methods such as steam / air over pressure retort and water immersion retort.Methods: Analogue shrimp products were prepared and thermally processed in retortable pouches. About 125g of shrimp analogue product and 100g of curry (masala) were filled in retort pouches of size, 150x200mm. Air inside the pouch was exhausted by steam injection followed by heat sealing and processing at 121.1°C in a retort by steam/air over pressure retort and water immersion retort. The difference in the heat penetration characteristics of analogue shrimp products processed in retort by steam/air over pressure retort and water immersion retort were studied. Result: The results showed that minimum heating lag factor and minimum come up time led to faster heating rate which decreased total process time in imitated shrimp curry by steam/ air retort. At the same time the cook value was low in curry medium processed by steam air retort. So finally conclude that imitated shrimp curry processed by steam air retort was good.

Condition Monitoring Technology for Connecting Part and Sliding Part of Reciprocating Compressor

2017 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Error Function ◽  
Connecting Rod ◽  
Value Analysis ◽  
Before And After ◽  
The Difference ◽  
Bending Modes ◽  
Parameter Values ◽  
The Mathematical Model

We focused on vibration characteristics of reciprocating compressors and constructed the mathematical model to calculate the natural frequencies and modes for crank angles and proposed a method to estimate the degree and the suspicious portion of failure by difference of temporal parameter values obtained using measuring data in operation and the mathematical model. In this paper, according to the proposed method, a case study is carried out using the field data, where the data were acquired before and after the failures occurred in the connecting parts of connecting rod, to prospect the difference between each parameter value for two operating states. Inspecting resonant characteristics each in the frequency response data relating to the natural frequencies for bending modes of the piston rod, we determined two resonant frequencies, which could correspond to the 1st and 2nd mode about bending of the piston rod. To equate the calculated each natural frequency from eigen value analysis based on the proposed model with each resonant frequency, we define the error function for the identified problem, namely optimum problem. In the identified results, it is found that some parameter values have much difference and the corresponding failure could occur around the connecting rod. We could show the possibility to detect both the change of the parameter values and the deterioration parts for two different kinds of the operating states by our proposed method.

Updating the Mathematical Model of a Structure Using Vibration Data

2005 ◽  
Vol 11 (12) ◽  
pp. 1469-1486 ◽  
Author(s):  
Ashutosh Bagchi
Keyword(s):  
Mathematical Model ◽  
Model Updating ◽  
Three Dimensional ◽  
Field Tests ◽  
Mode Shapes ◽  
Actual Structure ◽  
Shell Elements ◽  
Vibration Data ◽  
The Difference ◽  
The Mathematical Model

Model updating is an important step for correlating the mathematical model of a structure to the real one. There are a variety of techniques available for model updating using dynamic and static measurements of the structure’s behavior. This paper concentrates on the model updating techniques using the natural frequencies or frequencies and mode shapes of a structure. An iterative technique is developed based on the matrix update method. The method hasbeenappliedtothefiniteelement models of a three span continuous steel free deck bridge located in western Canada. The finite element models of the bridge have been constructed using three-dimensional beam and facet shell elements and the models have been updated using the measured frequencies. From the study it is clear that the initial model needs to be built such that it represents the actual structure as closely as possible. The results demonstrate that the difference between the modal parameters from the model and field tests affect the quality of the model updating process.

scholarly journals A Study on the Application of Sensitivity Analysis for Ship Hydrodynamic Coefficients

2018 ◽  
Vol 7 (4.36) ◽  
pp. 953
Author(s):  
Khanh Toan Tran ◽  
. .
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Mathematics Model ◽  
Hydrodynamic Coefficients ◽  
Ship Manoeuvring ◽  
Multiple Input ◽  
Sensitivity Analysis Method ◽  
Ship Hydrodynamic ◽  
Input Variables ◽  
The Mathematical Model

In the mathematical model with multiple input variables, the sensitivity analysis of the input variables is an important step to ensure the reliability of the mathematical model. In order to optimize the ship manoeuvring simulation, in particular the optimization of the trajectory ship, the sensitivity analysis should be performed in the mathematical model to select the group of the most sensitive hydrodynamic coefficients. In this paper, the author applied the sensitivity analysis method in mathematics model of ship manoeuvring programming in order to optimize the ship trajectory of Esso Bernicia 193000DWT tanker model.  

An optimized mathematical model for cancer patient care planning in the COVID-19 era.

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. e18663-e18663
Author(s):  
Isabel Blancas ◽  
David Martínez-Rodríguez ◽  
Fernando Rodríguez-Serrano ◽  
Rafael Jacinto Villanueva ◽  
Jose Manuel Garrido
Keyword(s):  
Mathematical Model ◽  
Demographic Data ◽  
Real Data ◽  
Oncologic Surgery ◽  
Number Of Patients ◽  
Oncologic Patients ◽  
Hospital Resources ◽  
The Difference ◽  
Using Data ◽  
The Mathematical Model

e18663 Background: The COVID-19 pandemic has threatened to collapse hospital and Intensive Care Unit (ICU) services, and it seems to limit the care of oncologic patients. The objective was to develop a mathematical model designed to predict the hospitalization and ICU admission demands due to COVID-19 to forecast the availability of hospital resources for the scheduling of oncological surgery and medical treatment that require hospitalitation or possible use of ICU services. Methods: We have implemented a SEIR model designed to predict the number of patients requiring hospitalization and ICU admissions for COVID-19. We evaluated the model using the number of cases registered in the hospitals of the province of Granada (Spain), that altogether cover 914,678 inhabitants. Calibration was performed using data recorded between March 15 and September 22, 2020. After that, the model was validated by comparing the predictions with data registered between September 23 and November 7, 2020. Besides, we performed a predictive analysis of scenarios regarding different possible sanitary measures. Results: Using patient registered data we developed a mathematical model that reflects the flow among the different sub-groups related to COVID-19 pandemics (Table). The best algorithm that fitted the disease dynamics was Particle Swarm Optimization, that minimized the difference between model output and real data used to calibrate the model. The validation phase showed the accuracy of the predictions, especially concerning trends in hospitalizations and ICU admissions. The different scenarios modelled on November 10, 2020 allowed us to predict the evolution of the pandemic until July 1, 2021, and to detect the peaks and valleys of disease prevalence. Conclusions: The mathematical model presented provides predictions on the evolution of COVID-19, the prevalence and hospital or ICU care demands. The predictions can be used to detect periods of greater availability of hospital resources that make it possible to schedule the oncologic surgery and intensify the care for oncologic patients. Furthermore, our model can be adapted to other population by recalibrating the model according to demographic data, the local evolution of the pandemic and the health policies. [Table: see text]

scholarly journals Mathematical Modelling of Acetaminophen Release in HPC/PAAm Hydrogel: Synthesis and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Abigail M. Díaz-Guerrero ◽  
Claudia A. Castillo-Miranda ◽  
Carlos F. Castro-Guerrero ◽  
Hernán Peraza-Vázquez ◽  
Ana B. Morales-Cepeda ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Phosphate Buffer Solution ◽  
Absolute Error ◽  
Programming Algorithm ◽  
Test Results ◽  
Buffer Solution ◽  
Drug Molecules ◽  
Hydrogel Synthesis ◽  
The Mathematical Model

Hydrogels are commonly used as Drug Delivery Systems (DDS) as patches due to its ability to store drug molecules within their structures. The release can be activated under certain stimuli, such as temperature and pH. In this paper, the mathematical modelling of acetaminophen release in hydroxypropyl cellulose with polyacrylamide (HPC/PAAm) is reported. The HPC/PAAm gel was synthesized in proportions of 25/75 wt% and was characterized by FTIR, DSC, optical microscopy, SEM, and TGA, with and without acetaminophen. The release tests were performed for hypothermic, normal, and febrile human body conditions, at 35, 37, and 39°C, respectively, on two release media: water and phosphate buffer solution. In order to describe the release of acetaminophen in HPC/PAAm gel, a genetic programming algorithm was used to accomplish Multigene Symbolic Regression (MSR). Characterization results showed that the drug was crystallized on the surface of the HPC/PAAm gel. Release test results showed that several simultaneous processes occurred in the acetaminophen diffusion phenomenon. A unique mathematical model was obtained by MSR. This model was able to describe the release of acetaminophen in HPC/PAAm gel with high values of R2 and adjusted R2 and to simulate the drug release at times beyond the end of the experiment. High values of R2 and low values of Coefficient of Variation (CV), Root-Mean-Square Error (RMSE), and Mean Absolute Error (MAE) were obtained from the comparison between the simulated and the experimental data. This allows to conclude that the mathematical model is reliable to represent and simulate the acetaminophen release in HPC/PAAm gel at 35, 37, and 39°C.

Investigation on feed direction cutting force in ultrasonic vibration-assisted grinding of dental ceramics

2016 ◽  
Vol 231 (19) ◽  
pp. 3493-3503 ◽  
Author(s):  
Heng Meng ◽  
Kan Zheng ◽  
Xingzhi Xiao ◽  
Wenhe Liao
Keyword(s):  
Mathematical Model ◽  
Cutting Force ◽  
Ultrasonic Vibration ◽  
Abrasive Particle ◽  
Force Model ◽  
Zirconia Ceramics ◽  
Feed Direction ◽  
Input Variables ◽  
The Mathematical Model ◽  
Ultrasonic Vibration Assisted Grinding

The feasibility of ultrasonic vibration-assisted grinding in dental restoration has been preliminarily proved. Improving the machining quality of zirconia ceramics by controlling cutting force is the focus of the researchers. However, the existing feed direction cutting force model for ultrasonic vibration-assisted grinding does not take the ultrasonic vibration amplitude and frequency into account. This paper presents a mathematical model for feed direction cutting force in ultrasonic vibration-assisted grinding of zirconia under the consideration of amplitude and frequency, and assuming that brittle fracture is the primary mechanism of material removal in ultrasonic vibration-assisted grinding of zirconia. The effects of amplitude and frequency on the motion, effective cutting distance, and theoretical removal of an abrasive particle have been analyzed. Besides, the number of active abrasive particles is calculated with analyzing the influences of lateral cracks and ultrasonic vibration. The variation laws of cutting force and penetration depth of an abrasive particle during ultrasonic vibration-assisted grinding have also been analyzed. Therefore, the relationship between feed direction cutting force and input variables is predicted through the developed model. Finally, pilot experiments are conducted for the mathematical model verification. Experimental results show that the trends of input variables for feed direction cutting force agree well with the trends of the developed cutting force model. Hence, the mathematical model can be applied to evaluate the feed direction cutting force in ultrasonic vibration-assisted grinding of zirconia ceramics.

Effect of Continuous Heating on Grain Growth in Fe-40Ni-Ti Alloy

2014 ◽  
Vol 988 ◽  
pp. 151-155
Author(s):  
Shao Qiang Yuan ◽  
Yue Hui Yang ◽  
Zhen Liang Wang
Keyword(s):  
Mathematical Model ◽  
Grain Size ◽  
Grain Growth ◽  
Experimental Results ◽  
Continuous Heating ◽  
Heating Process ◽  
Ti Alloy ◽  
Size Growth ◽  
Metallographic Observation ◽  
The Mathematical Model

The grain growth of Fe-40Ni-Ti alloy was investigated by means of metallographic observation during continuous heating. The experimental results indicate that: the microstructures consist of multi-polygon austenite. No transformation happens of tested alloy during heating only the grain size increases gradually. The size of grain grows steadily below 1160°C until 1200°C, the grain size growth unusually. The process of grain growth has relations with the dissolving of TiN particles. Finally, the mathematical model of grain growth in continuous heating process was obtained for the tested alloy.

scholarly journals The Effect of Functionally Graded Materials on Temperature during Frictional Heating: Under Uniform Sliding

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4285
Author(s):  
Aleksander Yevtushenko ◽  
Katarzyna Topczewska ◽  
Przemysław Zamojski
Keyword(s):  
Mathematical Model ◽  
Functionally Graded Materials ◽  
Frictional Heating ◽  
Ceramic Materials ◽  
Functionally Graded ◽  
Heating Process ◽  
Spatial Distributions ◽  
Graded Materials ◽  
Exponential Change ◽  
The Mathematical Model

The mathematical model of heating process for a friction system made of functionally graded materials (FGMs) was proposed. For this purpose, the boundary-value problem of heat conduction was formulated for two semi-spaces under uniform sliding taking into consideration heating due to friction. Assuming an exponential change in thermal conductivities of the materials, the exact, as well as asymptotic (for small values of time), solutions to this problem were obtained. A numerical analysis was performed for two elements made of ZrO2–Ti-6Al-4V and Al3O2–TiC composites. The influence of the gradient parameters of both materials on the evolution and spatial distributions of the temperature were investigated. The temperatures of the elements made of FGMs were compared with the temperatures found for the homogeneous ceramic materials.

scholarly journals Mathematical modeling of chilling process of polymer tube billets

2020 ◽  
Vol 8 (2) ◽  
pp. 24-33
Author(s):  
I. Kuzyayev ◽  
◽  
O. Mitrokhin ◽  
I. Kazimirov ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Integral Transform ◽  
Extrusion Process ◽  
Polymer Processing ◽  
Heating Process ◽  
Transform Method ◽  
Polymer Tube ◽  
Main Components ◽  
The Mathematical Model

There are many works about producing of polymer tubes. But less attention is paid to the process of chilling of polymer products. The chilling of polymer tube billets, as most polymer processing processes, is a non-isothermal process. This means that it is necessary to solve the heat problem. Accurate calculation of the heat balance is one of the main components for the final result of the extrusion process. The mathematical model had been created for process of chilling of polymer tube billets after extrusion in this work. Several mathematical models of heating process for heat and power equipment have been created. Different calculation schemes, methods and equations for its solution are suggested. The mathematical model for process of chilling of polymer tube billets after it extrusion can be considered an expansion of research. The mathematical model is based on cylindrical coordinate system with assumption of axisymmetric along angular coordinate. The initial problem statement considered non-stationary process. A transition was made to the differential equation in partial derivatives along two linear coordinates. Solution of this equation was found using the operation method (Laplace integral transform method). The final solution of the problem (after direct and reverse Laplace transform) was obtained from the Bessel function. It was calculated in MathCAD with the help of built-in functions and computing modules. The mathematical model was created for modeling and optimization of process of chilling of polymer tube billets. The results of calculation were presented as graphs that make it possible to characterize the adequacy of the materials. Keywords: mathematical model, balance equation, Laplace transform, program block.

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