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

Servicio de Investigación Agraria, P.O. Box 172, 47080 Valladolid, Spain

F. Sobrón and S. Bolado

Dep. of Chemical Engineering, Univ. of Valladolid

*Corresponding author (javier{at}siq.iq.cie.uva.es).

ABSTRACT

We 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.

Received for publication July 26, 1993.