Analysis of wave propagation in the presence of a continuous line heat source under heat transfer with memory dependent derivatives

Abstract

In the present work, the recently proposed new concept of “memory dependent derivative” in heat transfer process in a solid body has been employed to investigate the problem of wave propagation in a homogeneous, isotropic and unbounded solid due to a continuous line heat source. Both Laplace and Hankel transform techniques are employed for the solution of the problem. Analytical results for the distributions of different fields like temperature, displacement and stresses inside the medium have been derived. The problem is illustrated by computing the numerical values of the field variables for a particular material. We have attempted to exhibit the significance of a kernel function and a time-delay parameter that are characteristic of memory dependent derivative heat transfer in the behavior of field variables such as temperature, displacement and stresses with the help of numerical results. Detailed comparative analysis is represented through the numerical results to estimate the effects of the kernels and time-delay parameter on the behavior of all of the field variables such as temperature, displacement and stresses in the presence of a heat source in the medium.