Multilayer finite line source model for vertical heat exchangers

This paper introduces a finite line source model for vertical heat exchangers considering a layered soil profile. The existing analytical models assume a homogeneous soil profile, where the thermal properties of the ground along the entire length of the heat exchanger are uniform. This assumption can be unreliable since the typical length of heat exchangers is 60–100 m (200–300 ft.) and stratified ground is expected over this length. In the approach presented herein, the heat exchanger is divided into a number of segments to represent various soil layers along its length. Heat exchange induced temperature change at a certain location within the soil formation is evaluated by summing up the individual contributions of all these segments. The effect of the heat exchanger segment within the soil layer around itself is estimated using the finite line source model. Furthermore, the finite line source model is utilized on transformed sections for estimating the contributions of heat exchanger segments at locations outside their layer domains. The proposed model also incorporates two adjustments; the first accounts for the different heat rates within different soil layers while the second adjustment considers the heat exchange along the vertical direction between soil layers. Estimated results using the proposed model agree well with the results obtained from a calibrated finite element analysis. The proposed procedure is promising and can also be adapted within the framework of cylindrical models.