Generalized thermoelastic interaction in a two-dimensional porous medium under dual phase lag model Aatef Hobiny Department of Mathematics, Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia, and Ibrahim Abbas Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt and Department of Mathematics, Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia Abstract Purpose – The purpose of this study is to use the generalized model for thermoelastic wave under the dual phase lag (DPL) model to compute the increment of temperature, the components of displacement, the changes in volume fraction field and the stress components in a two-dimensional (2D) porous medium. Design/methodology/approach – Using Fourier and Laplace transformations with the eigenvalue technique, the exact solutions of all physical quantities are obtained. Findings – The derived method is evaluated with numerical results, which are applied to the porous medium in a simplified geometry. Originality/value – Finally, the outcomes are graphically represented to show the difference among the models of classical dynamical coupled, the Lord and Shulman and DPL. Keywords Porous medium, Laplace-Fourier transforms, Eigenvalues approach, Dual-phase lag model Paper type Research paper Introduction Porous materials are appearing in vast forms of environments, natural and artificial and in various applications of technology. As a result, the series of problems have developed under the statics and resistance, fluid currents and thermal conduction, and the dynamics of these materials. The problems of porous fluid-saturated material have been investigated for many years. A restricted list of articles relevant to this investigation includes Biot (1941) and Biot (1956). Lord and Shulman (1967) introduced the theory of a generalized thermo-elasticity with one relaxation time for the special case of an isotropic body. This theory was extended by Dhaliwal and Sherief (1980) in 1980 to include the anisotropic case. In this theory, a modified This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under the Grant No (D-250-130-1439). The authors acknowledge the technical and financial support provided by DSR. Generalized thermoelastic interaction Received 24 December 2019 Revised 27 January 2020 Accepted 29 January 2020 International Journal of Numerical Methods for Heat & Fluid Flow © Emerald Publishing Limited 0961-5539 DOI 10.1108/HFF-12-2019-0917 The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/0961-5539.htm