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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. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the propagation of an harmonic plane wave propagating with assigned frequency by implementing the thermoelasticity theory based on a fractional order heat conduction law where the fractional order parameter α satisfies 0 < α < 1 . After formulating the problem, the exact dispersion relation solutions for the plane wave are determined analytically and asymptotic expressions of different characterization of the wave are analyzed in two special cases, namely for a high-frequency field and low-frequency field. We consider the case of longitudinal wave which is coupled with the thermal field and we ignore the transverse wave as it is observed to be independent to the thermal field. Two different modes: predominantly thermal and predominantly elastic mode longitudinal waves are found. Finally we compute wave characterizations for the intermediate values of frequency and verify our analytical results for the limiting cases of wave frequency. A detailed analysis is presented to highlight the effects of the fractional order parameter, α , on the wave fields. Several important points are highlighted and the most important point which we have found is that α plays a very important role in the behavior of the wave. As α ≤ 0 . 5 , the thermal mode wave behaves similarly as in the case of a classical thermoelastic model and the nature of the wave changes significantly as α gets nearer to the value 1, behaving more similarly to the case of a generalized thermoelastic model (Lord–Shulman model). [ABSTRACT FROM AUTHOR]