This paper presents a seminumerical method for solving inverse heat conduction problems (IHCP) encountered in the monitoring of thermal stresses in pressurized thick-walled elements of steam boilers. The objective is to give a simple and quick method of determining transient temperature histories in thick-walled components based on temperature measurements on the outer thermally insulated surface. The method is suitable for solving one-dimensional problems. However, it can be extended to multidimensional temperature fields. The IHCP will be solved using the control volume approach. The accuracy of the method is demonstrated by comparing computational and experimental results. Gram orthogonal polynomials are used to smooth the measured time-dependent temperature and for evaluating time derivatives of noisy data with high accuracy. Due to the simplicity of the final formulations, the developed method is very useful for estimating the thermal stresses and controlling the fatigue damage of boiler components.

The growing global energy demand, coupled with environmental concerns, necessitates the development of efficient energy storage technologies. Phase Change Materials (PCMs) have emerged as a promising solution for thermal energy storage (TES) due to their ability to store and release latent heat during phase transitions. This review provides a comprehensive analysis of PCMs, exploring their classifications based on phase transition types, chemical compositions, and thermophysical properties. Additionally, the review highlights advancements in developing organic, inorganic, and metallic PCMs and evaluates their potential applications in sectors such as solar energy, construction, and automotive industries. Methodologies include a detailed examination of the strengths, limitations, and solutions to challenges such as low thermal conductivity, phase separation, and supercooling. The results summarize the diverse applications of PCMs, emphasizing their critical role in enhancing energy efficiency and sustainability. The review concludes with recommendations for overcoming current limitations and future directions for PCM research and technology integration across various industries.