Thermoelastic diffusion based on a nonlocal three-phase-lag diffusion model with double porosity structure

Abstract

This work aims to develop a new diffusion-elasticity-based model using Eringen’s nonlocal elasticity theory under the purview of the three-phase-lag (TPL) model of hyperbolic thermoelasticity. This problem is treated in the context of a double porosity structure in a homogeneous, isotropic thermoelastic medium. By considering the phase laggings of the diffusion flux vector and using nonlocal continuum mechanics, new constitutive and field equations are derived. The problem is solved by employing the normal mode analysis technique which gives the exact results of all the physical variables. To illustrate the theoretical results, different physical quantities are calculated numerically and presented graphically with respect to distance and time. The influences of different thermoelastic models like TPL (three-phase-lag model), GN-III (Green-naghdi model), DPL (dual-phase-lag model), LS (Lord-Shulman model), and CT (coupled thermoelasticity) on the physical quantities are shown graphically. Additionally, the effects of nonlocal parameters, double voids, and diffusion on the physical quantities are represented graphically. Some limiting and particular cases are also derived from the governing equations and those results have been compared with the existing results available in the literature. Some 3D surface curves are also presented to study the impact of diffusion, nonlocality, and double voids on various physical quantities.

Keywords:

• Diffusion
• double porosity
• Eringen’s nonlocal elasticity theory
• normal mode analysis
• three-phase-lag model

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement

No data is associated with this manuscript.

Additional information

Funding

Chandra Sekhar Mahato’s research is funded financially by a NET-JRF Fellowship from the University Grants Commission of New Delhi, India.