Analytical modeling of thermoelastic–diffusion in a microstructured rod subjected to gradually increasing internal heating
Year: 2026
Type: article
Abstract: This study investigates the transient interaction of heat, deformation, and mass transport in a homogeneous isotropic rod with microconcentrations subjected to gradually increasing internal heat generation. Understanding this interaction is important for thermally active components in which temperature-driven species migration and microscale transport can alter stress and structural reliability. A one-dimensional generalized thermoelastic-diffusion model is nondimensionalized and solved analytically using the Laplace transform. The coupled transformed equations are reduced to an eighth-order differential equation, and the time-domain fields are recovered through numerical inversion. The novelty lies in combining a progressively increasing volumetric heat source with microconcentration-dependent higher-order mass transport in a finite rod. As dimensionless time increases from 0.1 to 5.0, peak displacement rises from approximately 0.21 to 1.14, peak temperature from 0.16 to 0.87, and peak concentration from 0.18 to 1.02. Maximum microconcentration simultaneously increases from about 0.015 to 0.078, while the positive peak of the mass-diffusion flux moment grows from approximately 0.22 to 1.22. Temperature and concentration exhibit related interior profiles because of thermodiffusion coupling, whereas the microconcentration variables show distinct spatial behavior. Stress develops tensile and compressive regions owing to constrained thermal and diffusion expansion. These results demonstrate that microconcentration effects are essential for predicting higher-order mass transport in internally heated rods.
Source: Results in Engineering
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,940
Funder: Islamic University of Madinah
OpenAlex ID: W7204534965