Thermal and Stress Analysis of a Semi-Infinite Hollow Cylinder under Ramp-Type Heating with Memory-Dependent Derivatives

The study of thermal behavior in hollow cylindrical structures under ramp-type heating is critical for applications in aerospace, mechanical, and thermodynamic engineering. However, existing research has largely overlooked the influence of memory-dependent derivatives (MDD) combined with time delay parameters on temperature and stress distributions in such systems. This work addresses this gap by introducing a novel mathematical model for a semi-infinite hollow cylinder subjected to ramp-type heating at its lower surface, incorporating MDD to capture memory effects in heat conduction. The novelty lies in the integration of time delay parameters within the MDD framework, offering a more realistic representation of thermal and stress responses. Using Laplace, Hankel, and Fourier transform methods, analytical solutions are derived in the Laplace domain, with numerical inversion applied to obtained results. The model assumes convective boundary conditions on the cylinder’s curved surfaces and employs copper material properties for numerical analysis. Key contributions include the derivation of closed-form expressions for temperature, displacement, and stress distributions, and the demonstration of significant time delay effects on these variables. Results reveal that increasing time delay parameters reduces temperature and angular stress while altering displacement and radial stress profiles, with maximum stresses observed at specific radial and axial positions. These findings enhance the understanding of memory-dependent thermo-elasticity, providing valuable insights for designing robust cylindrical structures in high-temperature environments, such as spacecraft and industrial machinery.