| Summary: | Recently, Yu et al. (2014) proposed a new model in generalized thermoelasticity based on heat conduction with the memory-dependent derivative. The magneto–thermoelastic responses in a perfectly conducting thermoelastic solid half-space is investigated in the context of the above new theory. Normal mode analysis together with an eigenvalue expansion technique is used to solve the resulting non-dimensional coupled governing equations. The obtained solutions are then applied to a specific problem for thermoelastic half-space whose boundary is subjected to a time-dependent thermal shock and zero stress. The effects of the kernel function, time-delay parameter, magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically. The results show that these parameters has significant influence on the variations of the considered variables. Keywords: Magneto–thermoelasticity, Memory-dependent derivative, Time-delay, Normal mode analysis
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