Fractional Fourier Law with Three-Phase Lag of Thermoelasticity

Thermodynamical consistency of the dual-phase-lag heat conduction equation

“…[26,27,28,29,30,31]. Based on a fractal approach, the idea behind the dual phase lag concept is further extended by Ezzat et al to a three phase lag approach [32] and applied by Akbarzadeh and Pasini along with the DPL model [33]. These generalizations show how easy to apply these ideas.…”

Thermal wave: from nonlocal continuum to molecular dynamics

“…[34][35][36][37] Non-Fourier heat conduction models with timefractional derivatives can be derived by Taylor series expansion of an arbitrary time-fractional order a F on the both sides of eqn (3) or (4). For instance, Ezzat et al 36,38 introduced the threephase-lag heat conduction model with time-fractional derivatives, called fractional three-phase-lag (FTPL), by taking a Taylor series expansion on the both sides of eqn (4) and retaining terms up to 2a F -order for s q and up to the a F -order for s T and s y as follows:…”

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

“…Several linear or nonlinear steady-state bioheat models involving changed thermal conductivity and blood perfusion rate have been numerically solved to analyze the induced temperature distribution in biological tissues [ 3 , 4 , 5 , 6 , 7 , 8 ]. Besides, a non-Fourier heat conduction model in one-dimensional multilayered systems was analyzed by Laplace transform and the fast inversion technique [ 9 , 10 , 11 ]. In this paper, a model for describing transient nonlinear bioheat transfer model in two-dimensional (2D) skin tissue is developed.…”