The need to apply nonlocal heat conduction theory in the physical sciences and engineering dates to the mid-20th century and is associated with attempts to describe experimental data based on the Biot–Fourier hypothesis. In this paper, we investigate the steady-state temperature state of a homogeneous plate, considering spatial nonlocality described by a convolution-type integral term. Analytical solutions are obtained for a one-dimensional problem by considering a simple influence function. The influence of the nonlocality coefficient on the degree of deviation of the temperature distribution across the plate thickness from the classical solution is investigated. The temperature state of the plate, obtained using a macroscale approach, is compared with the results of mathematical modeling of the temperature distribution at the nanoscale using nonequilibrium molecular dynamics.
Savelyeva et al. (Fri,) studied this question.