Solution For Heat Flow in Soil with a Heat Source at a Fixed Depth

Abstract

AbstractWe developed a computationally efficient model for estimating the transient soil temperature distributions resulting from a heat source at a fixed depth beneath a greenhouse. The model was developed for use as a submodel of the air‐soil systems in greenhouses where the soil is used as a heat storage medium, with a network of buried pipes acting as a heat exchanger. The model assumes soil thermal properties are spatially and temporally constant and that energy transfer between the greenhouse and soil is primarily a result of net radiation and sensible heat transfer. First‐order energy transfer terms are also used to account for lateral energy exchanges with the surrounding soil and the heat source is included as a plane at a fixed depth. This was achieved by obtaining a Green's function solution in the Laplace domain and performing a numerical inversion with a fast Fourier‐transform algorithm, which requires very little computational time. Model parameters are optimized using a Simplex algorithm during a 3‐d simulation to show the ability of the method to describe the greenhouse soil temperature. This method provides a reasonable description of the heat flux under these conditions.