Non-integer order analysis of electro-magneto-thermoelastic with diffusion and voids considering Lord–Shulman and dual-phase-lag models with rotation and gravity
A. A. Kilany, S. M. Abo‐Dahab, A. M. Abd-Alla, Emad A.‐B. Abdel‐Salam
Abstract
This study developed the effect of the diffusion with voids within the generalized thermoplastic half-space having initial stress, rotation, a field of electromagnetism, and gravity for the following two models: Lord–Shulman and dual-phase-lag. The authors expressed the study’s problem in the dimensionless form and resolved it analytically by the normal mode analysis and Lame’s potential method. The analytical solutions for the temperature, stresses, displacements, concentration of diffusion, and volume fraction field were gained in the physical field using the analysis of normal mode. The outcome of all parameters was given and portrayed graphically. Comparisons were made with the findings gained in appearance and nonappearance of the examined variables and presented in graphs. The study reported that the impacts of the initial stress, diffusion, gravity, voids, rotation, and electromagnetic field are obvious on the phenomenon. The impact of fractional calculus and a comparison between the presence and absence of fractal calculus were discussed to clear the physical meaning of the fractional parameter and their related applications in biology, geophysics, etc.