International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

A mathematical model is proposed, describing the movement of a gas bubble in a viscous liquid medium under the action of the Archimedean force. In addition to Archimedean forces and fluid viscosity it takes into account the influence of temperature and pressure of the fluid and of the gas in the bubble. Solutions have been obtained for the movements of a gas bubble in the conditions of a solidifying casting, considering the influence of the bubble size, the pressure in the liquid and the viscosity of the medium on the speed of movement. Software based on the FORTRAN language has been created, which implements the solutions of the model for specific values of the input parameters. The capabilities of the model are illustrated by numerical experiments under different conditions.

A mathematical approach is presented for estimation of inertia of thermocouples in unsteady heat transfer processes. The approach allows to estimate the systematic error in measured data and to make a first-order correction, bringing the measurement data significantly closer to the real ones. The efficiency of the method is illustrated by computer simulation of two examples from foundry practice. The symmetry of heat transfer processes is used to identify an important and determining parameter of the inertia of the thermocouple.

Modern intensification of materials processing technology leads to an increase in the role of non-stationary interconnected exchange processes compared to stationary unconnected interconnected exchange processes compared to stationary unconnected. This fact is still insufficiently reflected in the field of solving energy and mass transfer problems (EMT) at small Fourier numbers (Fourier numbers ≤0.1) at short-term phase contact (SPC). In this article, a generalized mathematical model of interconnected non-stationary irregular energy and mass transfer mode at short-term contact across a boundary with selective permeability of phases is formalized. In vector-matrix form, a conjugate mixed boundary value problem is solved with excitation in each of the phases of flows of substances absent in the other phase. By analogy with heat exchange and mass exchange, matrices of potential assimilation of phases and a contact matrix are introduced, which allows obtaining a uniform solution for a number of special cases and especially simplified the entry for the vector of interphase flow densities. The mathematical notation of the solutions of the considered parabolic system of partial differential equations of the second order for intensive irreversible processes (Fourier numbers ≤0.1) are written in vector-matrix form and are close to the scalar Higbee theory for mass transfer.

Aluminum alloys are critical in industries such as aerospace and automotive due to their lightweight, strength, and corrosion resistance. Optimizing their properties is challenging and benefits from advanced predictive tools. This paper explores the use of mathematical modeling in understanding and designing aluminum alloys. Techniques like thermodynamic modeling (e.g., CALPHAD), phase transformation kinetics, and mechanical property simulations are reviewed. Computational methods, including finite element analysis and machine learning, are highlighted for their roles in alloy design and manufacturing, such as casting and additive manufacturing. Comparisons between model predictions and experimental results demonstrate accuracy and limitations. Applications in optimizing material properties and improving manufacturing processes are discussed. By accelerating alloy development and enabling tailored properties, mathematical modeling emerges as a transformative tool, advancing aluminum alloy research and driving innovation across industries.

The present work concerns the development of a model which have the capability to represent accurately the skin/sensor contact in an electromagnetic problem study. The later consist of elctro-encyphalography (EEG ) signals encountered in neuroscience health diagnosis. The electromagnetic problem studied is governed by Poisson’s equation and solved using finite element method. The skin/sensor contact is modeled by an analytical solution, which is coupled to finite element resolution. The signals induced by neuronal equivalent charges are presented and investigated. A comparison with existing results is then performed. Neuron loss effect is also investigated.

The use of artificial intelligence systems in public administration is of great importance and has great prospects. Artificial intelligence facilitates the interaction of various structures of the state system and the implementation of the direct activities of these structures. For public administration, it is important to analyze the mechanisms of behavior of a mass gathering of people. Since experimental analysis of crowd behavior is impossible, the creation of mathematical models with their subsequent software implementation is of particular importance.

Commercial kitchen products have a larger capacity than household products and are required to withstand harsh conditions because they are used more intensively. In addition, commercial refrigerators, among these products, are critical for the long-term preservation of food and beverages for many commercial businesses. Commercial refrigerators are generally expected to provide operating conditions between -2ºC and +8ºC. Variations in cooling conditions are observed due to the intensive use of commercial refrigerators in businesses (refrigerator doors being opened too much, irregular placement of different food products, etc.). Therefore, this situation does not allow the commercial refrigerator to be used efficiently. It can also cause food waste. It was first evaluated on a vertical commercial refrigerator using mathematical modeling to eliminate these drawbacks. This study aimed to obtain data to provide the most suitable cooling conditions by evaluating the temperature and air circulation at different points of the vertical commercial refrigerator through simulation studies.

The development and use of mathematical models is of great importance not only in the research field, but also in the practical field. Mathematical research in psychology is based on the construction of an image of the studied object or group of objects, fixing the basic properties and relationships. The complexity lies in the heterogeneous nature of individuals, in the diversity of their behavioral characteristics, interests, and features of social behavior. Statistical models can be divided into separate groups; models that consider processes that affect individual behavior at the micro level, that is, at the level of low-level human thinking processes; meso-level models; macro-level models that consider and predict general trends in the behavior of people in a group, for example, in a crowd.

On the basis of separate fractions of granular foam glass and inorganic binders, various modifications of heat-insulating composite material have been developed. A promising opportunity for potential application of the material is the preparation of composite elements and profiles suitable for installation around doors and windows during the construction or reconstruction of buildings. In connection with the study of the possibilities for optimal distribution of the granules, various options for their arrangement have been analyzed and evaluated. The mathematical tools of stereometry and 3D computer modeling were used. Visualizations of the obtained structures are presented and their compactness is evaluated. Recommendations are made for the ratio between the sizes and quantities of the granules used in order to achieve maximum density.

The possibilities for simulation and optimization of foundry technologies using the latest MAGMA6.0 version of the world-famous software package MAGMASOFT are presented. The capabilities of the software are illustrated both for the quick and efficient construction of the 3D geometric models and for the diagnosis of almost all possible defects in a wide range of casting methods. Special attention is paid to the possibilities for autonomous and automatic optimization of casting technologies in order to reduce defects and increase the profitability of castings.

In recent years, the problem of food safety and traceability has been one of the difficulties faced by restaurant and hotel businesses. Food spoilage can occur at any stage of the food chain; most of all food spoilage is due to improper storage conditions in refrigerators. Increasing attention to food quality and safety requires the development of sensitive and reliable analysis methods as well as innovative technologies for maintaining freshness and food quality. Freshness is a factor that has both health qualities and features that affect customer satisfaction and business profitability. Within the scope of this study, simulation studies were carried out to improve the cooling performance with mathematical modeling on a horizontal commercial refrigerator (operating temperature: -2/+8°C) prototype. Along with the original design, evaluations were made with mathematical modeling according to many different variables (temperature, airflow distribution, etc.) that affect the cooling performance, and R&D gains were achieved in developing the prototype according to the most suitable working conditions.

An important task of analyzing the behavior of individuals in society, in a large crowd of people is the development of mathematical models of behavior. The complexity lies in the heterogeneous nature of individuals, in the diversity of their behavioral characteristics, interests, and features of social behavior. Here the possibility of mathematical modeling of crowd behavior is considered and a mathematical model is proposed.