Analysis of a magneto-thermoelastic problem in a piezoelastic medium using the non-local memory-dependent heat conduction theory involving three phase lags

One of the most important features of the non-local heat conduction theory is that it is able to analyze and investigate the effect of all points of the body on a material point. Studying this non-local phenomenon helps researchers to capture microscopic effects at the macroscopic level with greater accuracy. This paper is devoted to understanding the non-local behavior of a piezoelastic half-space permeated with a magnetic field in the context of three-phase lag heat conduction with a memory-dependent derivative. The current study, which includes the presence of the propagation of thermal waves at limited speeds and non-locality in space and delay in time, has great significance in its application in many different physical fields. A thermal shock has been applied to the non-traction boundary. The problem has been solved by employing the Laplace transform technique. Physical variables such as temperature, displacement as well as stress have been determined in the time-domain by an accurate numerical method. Computational results have been provided to show the influence of effective parameters such as non-local correlation length parameter, kernel functions as well as time delay on the physical variables. By discussing the numerical results that have been graphically represented, significant differences have been seen to be attributable to the studied fields due to the non-locality effect, memory effect and time delay.