The Dynamic Response Of Generalized Magneto-thermoelastic Diffusion Problem For Infinitely Long Cylinder

In classical thermoelasticity, the heat conduction equation is of diffusion type, the propagating speed of heat was predicted to be infinite, which is contrary to physical experiments. To eliminate the intrinsic paradox in classical thermoelasticity, different generalized thermoelastic theories were developed. The generalized thermoelastic theories, including Lord and Shulman theory (L-S) and Green and Lindsay theory (G-L), are widely adopted in applications now. Both theories can characterize heat wave propagating with finite speed and the coupling effect between the deformation field and the temperature field.In the view of molecular dynamics, temperature is the macro reflection of the intensity of micro molecular motion. Due to the unbalanced thermal motion of molecules, energy exchange occurs between molecules through the molecular collisions, which leads to the heat transfer from one region to another in macro. Similarly, if the concentration of particles inside medium is uneven, it would lead to the migration of particles from regions of high concentration to regions of lower concentration. This phenomenon is called as diffusion. Diffusion widely exists in physical science as well as material science. Normally, diffusion is described by Fick’s law. Recently, Sherief et al. proposed the generalized thermoelastic diffusion theory based on L-S theory and Fick’s law. This theory can be used to describe not only the coupling effects among diffusion field, deformation field and temperature field, but also the nature of these three fields propagating as wave with finite speed.In present thesis, the dynamic response for infinitely long cylinders subjected to a thermal shock and a chemical potential shock is investigated in the context of generalized thermoelastic diffusion theory by means of Laplace transform together with its numerical inversion. The concrete contents include the following two problems:(1) the dynamic response of generalized magneto-thermoelastic interaction with diffusion for an infinitely long solid cylinder is investigated. The non-dimensional temperature, displacement, stress, chemical potential, concentration and induced magnetic field are obtained and illustrated graphically;(2) the generalized magneto-thermoelastic interaction with diffusion for an infinitely long hollow cylinder is investigated. The non-dimensional temperature, displacement, stress, chemical potential, concentration and induced magnetic field are obtained and illustrated graphically. The results obtained from the above two problems show that both thermoelastic wave and diffusive wave propagate with finite speeds and the speed of diffusive wave is larger than that of thermoelastic wave.