An Analytical Solution for the Heat Conduction–Convection Equation in Non-homogeneous Soil

Abstract

Heat transfer through the soil is important in shallow geothermal applications, in plant growth as well as in the surface energy balance. In this work, an analytical solution for a conduction–convection equation that models heat transfer is presented for non-homogeneous soil. The main assumption underlying the solution is that the thermal diffusivity of soil is piecewise-constant. A method to determine the depth-dependent thermal diffusivity and the water flux density through the porous medium based on temperature measurements is also developed and applied to field data from a site in Ioannina, Greece. The thermal diffusivity was found to increase in the layer below the surface and decrease for larger depths, while convection through the porous medium was found to be present in wet conditions and to account for about 10% of the heat flux in terms of the annual variability of temperature. Finally, the capability of the novel method in capturing the spatio-temporal variability of soil temperature is compared to three commonly used algorithms: the amplitude, the phase, and the conduction–convection algorithm. The novel method is able to reduce the root-mean-square error for the predicted variability of temperature at all depths by an order of magnitude compared to the other three algorithms.