This paper presents a stochastic analysis of the behaviour of heat transfer by soil moisture in a partially saturated heterogeneous aquifer. A spectral approach based on Fourier-Stieltjes representations for the perturbed quantities is used to develop closed-form expressions that describe the field-scale heat advection and the variability of temperature profile. It is shown that the field-scale heat advection is related to the variability of the specific discharge, which, in turn, is related to the variation of hydraulic conductivity. Our analysis is, therefore, focused on the impact of the correlation scale of the log saturated hydraulic conductivity field on these analytical results. It is found that the correlation scale of log saturated hydraulic conductivity has an influence on enhancing the heat advection and the variability of the mean temperature field.
- Fourier analysis
- Heat flow