Effect of nonlocality and Goufo-Caputo kernel in heat transfer nonsimple model within an infinite-length hollow cylinder subjected to diverse sectional heat supply
Nikita Karde, Dilip Kamdi, Vinod Varghese
Abstract
This paper aims to derive the mathematical model of modified heat conduction by utilizing the Goufo-Caputo fractional operator in an infinite-length cylinder subjected to various time-dependent sectional heat supplies. As a limiting case, the two-parameter Goufo-Caputo fractional derivative can be converted into a fractional Atangana-Baleanu derivative. For the application of the derived model, the study material considered for investigation is presumed to be homogenous and isotropic, with surface pressure assumed to be uniform over the boundaries. An exact solution of the modified nonsimple heat conduction subjected to different sectional heat loads is considered, and a solution is obtained utilizing the integral transformation technique. The inverse transformation from the Laplace domain to the time domain is achieved by employing the Gaver-Stehfest algorithm. In this paper, the effects of temperature distribution play an essential role in predicting the behavior of nonlocal thermoelastic displacement and stress functions using the two-parameter Goufo-Caputo fractional operator. The stress theory model is derived from Eringen’s nonlocal continuum theory. The results have been computed numerically and illustrated graphically. The solution considers a special case where various sectional heat supplies affect the inner curved surface, examining their non-Fourier thermal behavior and the influence of nonlocal parameters. The parameters significantly impact transient thermoelastic responses, the result crucial for accurately predicting them in micro- and nanostructure design and processing.