Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model

Abstract

In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically.