Thermoelastic interaction in a two-dimensional infinite space due to memory-dependent heat transfer

Research Article, Pallabi Purkait, Abhik Sur, M Kanoria
2017 Journal homepage: International Journal of Advances in Applied Mathematics and Mechanics   unpublished
The present study deals with a novel mathematical model of thermoelastic interaction in an infinite space introduced in the context of Taylor's series expansion involving memory-dependent derivative of the function for the Green-Naghdi model III (GNIII) heat conduction law, which is defined in an integral form of a common derivative with a kernel function on a slipping interval. The governing equations of this new model are applied to an infinite space which is subjected to finite linear
more » ... mode I crack. The crack is subjected to prescribed temperature and stress distribution in the context of Green-Naghdi theory of generalized thermoelasticity. The analytical expressions of the thermophysical quantities are obtained in the physical domain employing the normal mode analysis. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed due to different choices of the kernel function and delay times. The results to the analogous problem corresponding to the case in absence of memory effect is also shown analytically. Excellent predictive capability is demonstrated due to the presence of memory dependent derivative also. MSC: 74F05 • 74D05