Underground heat flow patterns for dense neighborhoods with heat pumps

In this paper we consider the placement of buildings with ground coupled heat pumps on a densely populated area. The assemblies of pipes that constitute the ground heat exchangers occupy volumes that are shaped as parallelepipeds, the short dimension of which is vertical. Viewed from above, the assemblies occupy rectangular areas with variable shapes. Two area sizes are considered: few large areas surrounded by many smaller areas. The area shapes are viewed systematically such that the total heat transfer rate between ground and buried assemblies is maximum. For each shape of the large assembly, the best shape of each smaller assembly is the most slender that can be installed on its available territory. This feature of the neighborhood design does not change when the volume fraction occupied by all the assemblies increases.