This review addresses the modeling approaches for heat transfer processes in oil-immersed transformer. Electromagnetic, thermal, and hydrodynamic thermal fields are identified as the most critical aspects in describing the state of the transformer. The paper compares the implementation complexity, calculation time, and details of the results for different approaches to creating a mathematical model, such as circuit-based models and finite element and finite volume methods. Examples of successful model implementation are provided, along with the features of oil-immersed transformer modeling. In addition, the review considers the strengths and limitations of the considered models in relation to creating a digital twin of a transformer. The review concludes that it is not feasible to create a universal model that accounts for all the features of physical processes in an oil-immersed transformer, operates in real time for a digital twin, and provides the required accuracy at the same time. The conducted research shows that joint modeling of electromagnetic and thermal processes, reducing the dimensionality of models, provides the most comprehensive solution to the problem.

Transient plasma events, such as plasma disruptions, are anticipated in the future magnetic-confinement nuclear fusion reactors. The events are accompanied by a rapid change in the magnetic field generated by the plasma current and, accordingly, induction of strong eddy currents and Lorentz forces within the reactor structure. This work targets processes within liquid-metal components of the reactor's breeding blankets. Order-of-magnitude analysis and exploratory numerical simulations are performed to understand the response of liquid metal to a rapidly changing magnetic field and to evaluate the accuracy of commonly used simplifying model assumptions. The response is found to consist of two stages: an initial brief stage (∼1 ms) characterized by a rapid increase in the induced currents, forces, and fluid velocity; and a subsequent stage, which is triggered by the growing velocity of the metal and marked by reversals of Lorentz force, and oscillations and decreases in the amplitude of the induced fields. The transition to the second stage sets the upper limit of the velocity (∼0.5 m/s in our tests), to which an initially quiescent metal can be accelerated during the event. The simulations indicate that many widely used model assumptions, such as the negligible role of Joule dissipation in the heat balance and the constancy of physical property coefficients, remain valid during the response. However, the assumption of liquid metal incompressibility is found to be questionable due to the potential significant effects of pressure waves.

Purpose: This paper aims to create mathematical models and control algorithms allowing the authors to study and form effective modes of operation of multi-inductor system of electrical heating of moving hollow cylindrical blanks. Design/methodology/approach: The developed mathematical models were based on the finite-difference method, the control volume method and their combination. The reliability of the results obtained was verified by comparing the calculated results with the experimental ones. The temperature control system was synthesized using methods of the object management theory with distributed parameters. Findings: A set of mathematical instruments has been created that allow modelling the operation modes of installation for induction heating of moving hollow cylindrical blanks. Recommendations were given on the formation of an automatic control system that provides heating of a moving hollow cylindrical billet to the required temperature with simultaneous equalization of temperature along the length of the billet in case of highly uneven initial temperature along the length of the billet. Practical implications: Part of the paper will be used by the industrial plant for the purpose of heat treatment of iron alloys workpiece. Particularly, a control system will be basically formed based on the models. Originality/value: The scientific novelty of the paper is to create control algorithms and mathematical models for the induction heating system of tubular workpieces allowing to explore interrelated electromagnetic and thermal processes taking into account nonlinearities and design features of the system, as well as to form effective modes of its operation based on transfer functions and methods of the object management theory with distributed parameters.

The development of digital twins for power transformers has become increasingly important to predict possible operating modes and reduce the likelihood of faults. The accuracy of these predictions relies heavily on the numerical models used, which must be both simple and computationally efficient. This work focuses on creating a simplified numerical model for a template oil-immersed power transformer (100 MVA, 230/69 KV). The study investigates how the number of elements and the strategies used to set up the mesh in the domain of interest influence the results, aiming to identify the key parameters that affect the outcomes. Furthermore, a significant effect of resolving thermal boundary layers on the accurate identification of hot spots is demonstrated. Two approaches to resolving thermal boundary layers are explored in this work. This study presents a comprehensive analysis of three numerical models for conjugate heat transfer simulations, each with distinct features and computational domain compositions. The results show that the addition of extra calculation domains leads to the emergence of new vortex structures, affecting the velocity profile at the channel inlet and altering the location of hot spots. This study provides valuable insights into the configuration and composition of calculated domains in numerical models of oil-immersed power transformers, essential for the accurate prediction of hot spot temperatures and ensuring reliable operation.