A spherical cavity problem with nonlocal elastic effect considering memory-dependent thermoelastic diffusion and laser pulse heat source

Abstract

With expanding demand of electronic gadgets at miniature/nano-scales, mathematical modelling of the related problems calls for the study of various properties of nanostructures. Also, memory dependence phenomenon plays significant role to make models more rational. Considering this frame, thermoelasticity with diffusion based on memory-dependent derivatives and nonlocal elastic effect is studied under unified model of four theories of thermoelasticity. Infinite body containing a spherical cavity whose inner surface is acted upon by chemical and thermal shock in stress-free state is considered. Initially the medium is assumed to be quiescent. In heat conduction equation, laser pulse heat source which is decaying exponentially with time is present. Laplace transformation technique is adopted to obtain the solution by direct approach. The consideration of spherical cavity in infinite medium and combined model of thermoelastic theories with coupling of elastic, thermal, diffusion processes augments the novelty of present work. The study analyzes the effect of memory-dependent and nonlocal parameters on the various field quantities involved in the model which are calculated numerically using MATLAB software & presented graphically. Memory dependence of heat conduction and diffusion with nonlocal elasticity is observed to have significant impact on the variations of considered field quantities.