The Solution to the Heat Conduction Problem of a Cylinder During Its Heating and Cooling from the Lateral Surface

In this paper, the problem of heat conduction in a cylinder during its heating and cooling from the lateral surface is addressed. Qualitative functions for the distribution of temperature across the cylinder's radius, along its surface, and along a coaxial axis of the cylinder have been found. The work also presents graphical interpretations of these dependencies with given parameters of the cylinder's volumetric characteristics, heat transfer coefficients, thermal conductivity of the material, as well as the material's density and specific heat capacity. The study employs a combination of analytical and numerical methods to solve the heat conduction equations, allowing for a comprehensive analysis of temperature distribution within the cylinder. The findings highlight the critical role of material properties and geometric dimensions in influencing the heat distribution pattern, demonstrating the effectiveness of the proposed model in predicting temperature changes. Furthermore, the study suggests potential applications in designing thermal management systems for cylindrical structures, emphasizing the importance of optimizing material selection and structural parameters.