Mathematical Innovations in Thermal Dynamics and Optimization

Dear Colleagues,

The development of mathematical tools, broader exact knowledge, and the design of more accurate and innovative models in the field of thermal dynamics enable a deeper understanding and more effective control of thermal processes in various applications, from mechanical engineering to district heating systems to environmental sciences. Ordinary and partial differential equations, integral transformations, and numerical methods are used in thermal dynamics. These tools allow for the analysis of phase transitions, modeling of heat and mass transfer, and prediction of systems' behavior under various temperature conditions. Innovations include, e.g., the development of more efficient algorithms for solving complex nonlinear equations, which leads to more accurate simulations. In the analysis and synthesis of thermal process dynamics, subproblems naturally arise that require the search for the most accurate and precise model parameters, the optimal design of heat exchangers, the streamlining of cooling and freezing processes, or the setting of the control law that leads, e.g., to maximizing efficiency and minimizing costs or losses in thermal systems. Various optimization algorithms are applied here, whether classical and well-established or using machine learning and artificial intelligence.

This Special Issue aims to present new mathematical findings, especially their innovative applications from the realm of modeling and controlling thermal processes using optimization procedures and algorithms, including artificial intelligence tools in the process of human creative work.

Dr. Libor Pekař
Dr. Radek Matušů
Dr. Xuan Zhang
Dr. Long Zhang
Guest Editors

Manuscript Submission Information

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• ordinary and partial differential equations in modeling thermal processes
• finite element method
• finite volume method
• delay-differential equations for heating–cooling loops
• diffusive representation
• thermal sigma-delta modulation
• transformation thermotics
• thermal boundary condition
• adaptive and predictive control of thermal processes
• cooling and freezing models
• linear and nonlinear programming
• genetic algorithm
• swarm algorithms
• simulated annealing
• deep and reinforcement learning