Transient Response Analysis Of Generalized Thermoelastic Diffusion Problem With Memory-Dependent Derivative

The heat conduction equation in the classical thermoelastic theory predicts infinite propagation speed for thermal signal,which is contrary to physical observations.To overcome this shortcoming,the non-Fourier's heat conduction law has been developed,which describes the second sound effect of transient heat transfer,i.e.,the thermal wave effect.In the last decade,fractional calculus intensively attracted the focus of scholars due to its successful applications in heat conduction,anomalous diffusion,viscoelasticity,and etc.By introducing fractional calculus into heat conduction equation,the thermoelastic behavior of materials in extreme heat and mass transfer process can be more accurately reflected.Inspired by fractional-order generalized thermoelasticity theory,scholars introduced memory-dependent differential into the heat conduction equation of generalized thermoelasticity theory,and established a generalized thermoelasticity theory,which effectively reflected the memory-dependent behavior and global correlation of materials.Diffusion can be defined as the transport of matter form regions of high concentration to regions of lower concentration.There is now a great deal of interest in the study of this phenomenon due to its diverse applications in the domains of physical chemistry,industry,agriculture,medicine,and so on.Ordinarily,the diffusion process is modeled by the Fick's law,nevertheless,which does not take the mutual interaction between the introduced substance and the substrate as well as coupling effect between electric,magnetic,thermal and elastic into consideration.Based on the generalized thermoelastic diffusion theory considering memorydependent derivative,the transient responses of thermoelastic diffusion in semi-infinite structures and laminated structures are studied in this paper.(1)Based on the generalized thermoelastic diffusion theory with memorydependent derivative in both the generalized heat conduction law and the generalized diffusion law,the transient response of a half-space subjected to a thermal shock and a chemical potential shock on its bounding surface is investigated.The coupled governing equations containing time delay factors and kernel functions,which can be chosen freely according to specific problems,are solved by the Laplace transform together with its numerical inversion.The non-dimensional temperature,chemical potential,displacement,stress as well as concentration at different values of time,time delay factors and kernel functions are obtained and illustrated graphically.(2)The present work is devoted to investigating the transient responses of a sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative.Both the left and the right bounding surfaces are subjected to a thermal shock and a chemical potential shock simultaneously.It is assumed that the values of thermal contact resistance and diffusional contact impedance at the interface are zero with ideal adhesion.The coupled governing equations containing time delay factors and kernel functions,which can be chosen freely according to specific problems,are solved by the Laplace transform together with its numerical inversion.(3)The present work investigates the transient response of a bi-layered structure subjected to a non-Gaussian laser beam on its bounding surface in the context of the time-fractional derivative based on generalized thermoelastic theories.Comparison studies between the fractional order and the memory-dependent derivative models are performed and the thermal contact resistance at the interface is also considered.The coupled governing equations involving with thermal relaxation time,fractional order parameter,time delay and kernel function,which can be chosen freely according to specific problems,are solved by using Laplace transform techniques together with its numerical inversion.