Analysis of EAHE through a coupled mathematical model solved by Laplace transform and Gaver-Stehfest algorithm

Abstract

The earth-air heat exchangers (EAHEs) are devices that are shown to be a great alternative to assist in the thermal comfort of buildings, mainly due to their low energy cost. The proposed model considers the heat exchange between the soil, the duct and the air, generating coupled equations. This work seeks to employ and verify EAHE applications in two scenarios, first in a literature experiment and then in a EAHE application in Pelotas. In both scenarios, it is considered that the soil and air temperature functions are time dependent. The solution is obtained by applying the Laplace transform and for the inversion of the integral transform the numerical method known as the Gaver-Stehfest Algorithm was used. The obtained results show that the proposed model follows the behavior of the experimental data. In addition to the experimental data, the proposed model was compared with the analytical model by Nóbrega, where the results had a small variation (of 0.20 ºC between them) by considering the heat transfer process in the duct material, modeling a more close to the real situation.