Thermoelastic diffusion interaction of fractal medium with non-integer dimensional space via nonlocality and memory effect
Nitin Chandel, Lalsingh Khalsa, Vinod Varghese
Abstract
In this study, we utilize a generalization of vector calculus for spaces with non-integer dimensions to investigate the thermoelastic properties of fractal materials. Fractal materials are modeled as continua in non-integer-dimensional spaces. We propose generalized thermoelasticity equations for these spaces and present solutions that describe their equilibrium state. The work examines a one-dimensional interaction between thermoelastic diffusion, chemical potential, and thermal loading on the boundary plane, grounded in diffusion concepts. Moreover, we outline the thermoelastic diffusion model, incorporating a well-defined integral form of a common derivative over a slipping interval, integrating memory-dependent heat transport laws and the nonlocal continuum theory proposed by Eringen. By solving equations in the Laplace domain and applying inverse transforms, we can obtain time-based findings for temperature, stress, chemical potential, and diffusion in fractal media, as well as physical interpretations through numerical inversion. The proposed study is validated by graphic results, which show that important characteristics related to memory and nonlocality have a significant impact on thermoelastic diffusion. These findings highlight the crucial role of memory and nonlocality in thermoelastic diffusion behavior, underscoring their significance for accurate modeling strategies in the structural design of advanced nanomaterials.