Abstract
In the current article, the dual phase lag theory is used to discussed the waves propagations in poroelastic nanoscale materials by the finite element method. Using the FEM to get the solutions of the complex formulation of the problem numerically. The numerical accuracy is further improved by the implementation of quadratic interpolation functions. The impacts of the thermal delay time and the porosity in a porothermal and elastic mediums are studied. The numerical outcomes for the components of displacement, the temperatures and the components of stress for the solid and liquid are represented graphically. Three theories of thermoelasticity viz. the Classical dynamical coupled (CT), Lord and Shulman (LS), and dual phase-lag (DPL) thermoelasticity theories are considered in this problem. the present analysis may have significant application and contribution in areas utilizing the non-simples porothermoelastic with various phases in details.