Mathematical Modeling of the Drying Process of Chrome Shavings

2015 ◽  
Vol 1101 ◽  
pp. 463-466
Author(s):  
Juan Carlos Beltrán-Prieto ◽  
Nguyen Huynh Bach Son Long ◽  
Karel Kolomazník
Keyword(s):  
Mathematical Modeling ◽  
Laplace Transformation ◽  
Deterministic Model ◽  
Separation Of Variables ◽  
Effective Diffusion ◽  
Water Molecules ◽  
Drying Process ◽  
Tunnel Dryer ◽  
Free Moisture ◽  
Modeling Data

This paper described the mathematical modeling of chrome shavings drying by performing a microscopic balance for water content to describe the unidimensional transfer of water within the solid at a certain temperature. The deterministic model was solved using Laplace transformation and separation of variables methods in order to determine the average free moisture content at different intervals of time during the drying period. Agreement was observed between both, experimental and modeling data. The effective diffusion coefficient of water molecules during the drying of chrome shavings in a tunnel dryer was determined to be 5.8x10-6m2/h.

Mathematical Modeling of Betanin Extraction from Red Beet (Beta vulgaris L.) by Solid–Liquid Method

2015 ◽  
Vol 11 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Honggao Xu ◽  
Qiang Peng ◽  
Fang Yuan ◽  
Yanxiang Gao
Keyword(s):  
Mathematical Modeling ◽  
Effective Diffusion ◽  
Spherical Model ◽  
Extraction Process ◽  
Extraction Temperature ◽  
Optimal Parameters ◽  
Practical Application ◽  
Sulfurous Acid ◽  
Red Beet ◽  
Solid Liquid

Abstract Effective diffusion coefficient (D-value) is an important parameter for the extraction process. In this study, a cylindrical model to estimate the D-value of betanin extraction from red beet roots was developed. The influence of extraction temperature, pH, cylindrical thickness and type of acids on the D-value was also investigated. The optimal parameters of betanin extraction were 30°C, pH 4.0 adjusted with sulfurous acid or acetic acid. D-values under the above conditions were 18.95×10−11 m2/s and 17.87×10−11 m2/s, respectively. The result showed that D-value elevated with the increase of cylindrical thickness, which was consistent with earlier conclusion from spherical model. The modeling may be useful for the investigation into extraction process and practical application.

Technological Features of the Liquid-Solid State of the Boundary Layer in the Processes of Bimetallic Products

2022 ◽  
Vol 1049 ◽  
pp. 53-61
Author(s):  
Valeriy Lykhoshva ◽  
Dmitry Glushkov ◽  
Elena Reintal ◽  
Valeriy V. Savin ◽  
Ludmila Alexeyevna Savina ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Boundary Layer ◽  
Solid State ◽  
Liquid Phase ◽  
Contact Zone ◽  
Thermal Field ◽  
Thermal State ◽  
Existence Time ◽  
Modeling Data

The hydrodynamic and thermal state in the contact zone of the layers of a bimetallic product obtained by pouring liquid iron onto a solid steel billet, which changes in time and is responsible for the strength of the diffusion joint and the geometric parameters of the transition layer, has been investigated. Simplified analytical dependences, mathematical modeling data and experimental results of the liquid phase existence time in the contact zone based on research of the melt velocities during pouring and changes in the thermal field are presented. It is shown that simplified calculations data coincide in order and are close in values ​​to the calculations of mathematical modeling and experimental data, which makes it possible to use them for preliminary rough estimates by technologists and metallurgists.

scholarly journals Freeze-drying microscopy in mathematical modeling of a biomaterial freeze-drying

2012 ◽  
Vol 48 (2) ◽  
pp. 203-209 ◽  
Author(s):  
Camila Figueiredo Borgognoni ◽  
Joyce da Silva Bevilacqua ◽  
Ronaldo Nogueira de Moraes Pitombo
Keyword(s):  
Mathematical Modeling ◽  
Freeze Drying ◽  
Drying Process ◽  
Critical Temperatures ◽  
Fundamental Properties ◽  
Moving Interface ◽  
Energy Consuming ◽  
Sublimation Rates ◽  
Time And Energy

Transplantation brings hope for many patients. A multidisciplinary approach on this field aims at creating biologically functional tissues to be used as implants and prostheses. The freeze-drying process allows the fundamental properties of these materials to be preserved, making future manipulation and storage easier. Optimizing a freeze-drying cycle is of great importance since it aims at reducing process costs while increasing product quality of this time-and-energy-consuming process. Mathematical modeling comes as a tool to help a better understanding of the process variables behavior and consequently it helps optimization studies. Freeze-drying microscopy is a technique usually applied to determine critical temperatures of liquid formulations. It has been used in this work to determine the sublimation rates of a biological tissue freeze-drying. The sublimation rates were measured from the speed of the moving interface between the dried and the frozen layer under 21.33, 42.66 and 63.99 Pa. The studied variables were used in a theoretical model to simulate various temperature profiles of the freeze-drying process. Good agreement between the experimental and the simulated results was found.

scholarly journals Mathematical modeling of the SARS-CoV-2 epidemic in Qatar and its impact on the national response to COVID-19

2020 ◽  
Author(s):  
Houssein H. Ayoub ◽  
Hiam Chemaitelly ◽  
Shaheen Seedat ◽  
Monia Makhoul ◽  
Zaina Al Kanaani ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Acute Care ◽  
Hospital Admissions ◽  
Deterministic Model ◽  
Infection Prevalence ◽  
Care Hospital ◽  
Healthcare Needs ◽  
National Response ◽  
The Impact ◽  
Second Wave

AbstractBackgroundMathematical modeling constitutes an important tool for planning robust responses to epidemics. This study was conducted to guide the Qatari national response to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic. The study investigated the time course of the epidemic, forecasted healthcare needs, predicted the impact of social and physical distancing restrictions, and rationalized and justified easing of restrictions.MethodsAn age-structured deterministic model was constructed to describe SARS-CoV-2 transmission dynamics and disease progression throughout the population.ResultsThe enforced social and physical distancing interventions flattened the epidemic curve, reducing the peaks for incidence, prevalence, acute-care hospitalization, and intensive care unit (ICU) hospitalizations by 87%, 86%, 76%, and 78%, respectively. The daily number of new infections was predicted to peak at 12,750 on May 23, and active-infection prevalence was predicted to peak at 3.2% on May 25. Daily acute-care and ICU-care hospital admissions and occupancy were forecast accurately and precisely. By October 15, 2020, the basic reproduction number R0 had varied between 1.07-2.78, and 50.8% of the population were estimated to have been infected (1.43 million infections). The proportion of actual infections diagnosed was estimated at 11.6%. Applying the concept of Rt tuning, gradual easing of restrictions was rationalized and justified to start on June 15, 2020, when Rt declined to 0.7, to buffer the increased interpersonal contact with easing of restrictions and to minimize the risk of a second wave. No second wave has materialized as of October 15, 2020, five months after the epidemic peak.ConclusionsUse of modeling and forecasting to guide the national response proved to be a successful strategy, reducing the toll of the epidemic to a manageable level for the healthcare system.

scholarly journals Mathematical modeling of the drying process of corn ears

2011 ◽  
Vol 33 (4) ◽  
Author(s):  
Paulo Cesar Corrêa ◽  
Fernando Mendes Botelho ◽  
Gabriel Henrique Horta Oliveira ◽  
André Luis Duarte Goneli ◽  
Osvaldo Resende ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Drying Process

Data Mining and Optimize TCM Prescription Compatibility Based on WDS-PLS

2014 ◽  
Vol 687-691 ◽  
pp. 1385-1388
Author(s):  
Zhuo Wang ◽  
Bin Nie ◽  
Ri Yue Yu
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Data Mining ◽  
Regression Coefficient ◽  
Uniform Design ◽  
Herbal Medicines ◽  
Data Standardization ◽  
Modeling Data ◽  
Pls Method ◽  
Original Formula

Data mining and optimize traditional Chinese medicine (TCM) prescription compatibility based on wavelet denoise spectral and partial least squares (WDS-PLS). Method: First of all, experimental design: with reference to the original formula, the herbal medicines in a prescription designed nine formula based on mixing uniform design; Secondly, obtain experimental data and data standardization; Finally, mathematical modeling, data mining and optimize TCM prescription compatibility base on WDS-PLS.Results: gain the regression coefficient and equation, VIP sorting, loadings Bi plot, and seek out the optimized direction of the prescription. Conclusion: the method data mining and optimize the compatibility of the dachengqi decoction is feasible and effective.

Investigation of glass transition behavior in a rice kernel drying process by mathematical modeling

2019 ◽  
Vol 38 (8) ◽  
pp. 1092-1105 ◽  
Author(s):  
Lijuan Zhao ◽  
Junhong Yang ◽  
Shanshan Wang ◽  
Zhonghua Wu
Keyword(s):  
Mathematical Modeling ◽  
Glass Transition ◽  
Drying Process ◽  
Transition Behavior
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