Eringen’s Non-Locality and Unified Exponential Operators Induce Thermoelasticity in a Cylindrical Cavity under Thermal Loads

Abstract

This paper develops a mathematical model for modified heat conduction by applying exponential operators and Eringen’s non-locality stress theory within an infinite-length cylindrical cavity subjected to various time-dependent sectional heat supplies. The study employs both the Caputo-Fabrizio and Rabotnov fractional differential operators, which, despite both utilizing exponential functions, differ significantly in their definitions. The Caputo-Fabrizio operator is widely used in fractional calculus due to its nonsingular kernel and broad applicability. In contrast, the Rabotnov operator is particularly effective for modeling complex physical processes and real-life phenomena. The study material is homogeneous and isotropic with uniform surface pressure across boundaries; the model derives exact solutions to the modified heat conduction equations using the integral transformation technique. Solutions in the Laplace transform domain are inverted back to the time domain via the Gaver-Stehfest algorithm. This research highlights the importance of temperature distribution in predicting the behavior of non-local thermoelastic displacement and stress functions with fractional exponential operators. The model, grounded in Eringen’s non-local continuum theory, provides numerical solutions illustrated graphically. The special case analyzed involves various sectional heat supplies affecting the inner curved surface, emphasizing the non-Fourier thermal behavior and the influence of non-local parameters on transient thermoelastic responses. These findings are crucial for accurate predictions in the design and processing of micro- and nanostructures.