Thermo-diffusion of solid cylinders based upon refined dual-phase-lag models

Abstract

Purpose

The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized thermoelasticity theory have been proposed.

Design/methodology/approach

Some models with and without energy dissipation have been presented as well as the simple forms of Green–Naghdi (G–N) theories. These novel multi- and single-/dual-phase-lag models are presented to investigate the thermo-diffusion of the solid cylinder. The closed-form solution of thermo-diffusion governing equations of solid cylinder has been obtained to deduce all field variables.

Findings

A comparison study between the simple G–N II and III models and their improved models has been presented. The validations of outcomes are acceptable and so benchmarks are reported to help other investigators in their future comparisons.

Originality/value

The modified Green and Naghdi theories of types II and III are presented to get novel and accurate models of single- and dual-phase-lag of multiterms. The heat of mass diffusion equation as well as the constitutive equations for the stresses and chemical potential of a solid cylinder is added to the present formulation. The system of three differential coupled equations is solved, and all field variables are obtained for the thermal diffusion of the solid cylinder. Some validation examples and applications are presented to compare the simple and modified Green and Naghdi theories of types II and III. Sample plots are illustrated along the radial direction of the solid cylinder. Some results are tabulated to serve as benchmark results for future comparisons with other investigators. The reported and illustrated results show that the simple G–N II and III models yield the largest values of all field quantities. The single-phase-lag models give the smallest values. However, the dual-phase-lag model yields results that are intermediate between those of the simple and single-phase-lag G–N models.

Citation

Zenkour, A.M. (2020), "Thermo-diffusion of solid cylinders based upon refined dual-phase-lag models", Multidiscipline Modeling in Materials and Structures, Vol. 16 No. 6, pp. 1417-1434. https://doi.org/10.1108/MMMS-12-2019-0213