Determining the thermal diffusivity of sediments using the fractional nonlocal heat conduction equation

Abstract

Based on the heat conduction equation with fractional-order derivatives and the experimental measurements of temperature distribution in the upper layers of the Earth, the depth dependence of thermal diffusivity is studied at different values of the parameters of nonlocality in time and along the coordinates. It is shown that thermal diffusivity increases with depth, and the values of thermal diffusivity observed in the experiments coincide with the theoretical predictions provided by the solution of the nonlocal heat-conduction equation that allows for the memory effects in fractional-order time derivatives.