Here we document comparatively the performance of three flow architectures for heat transfer between a buried flow structure and a conducting medium: trees with Y-shaped bifurcations, trees with T-shaped bifurcations, and classical U-shaped and serpentine designs. The competing designs occupy the same volume fraction. The tree architectures have up to four levels of bifurcation (N). We found that the heat transfer performance depends greatly on the flow configuration. The tree shaped designs yield improvements in heat transfer density as N increases from 0 to 4. The Y-shaped design is the best of the three architectures. The scale analysis of tree-in-solid heat transfer anticipates correctly the key features of the thermal performance of the architecture. The paper also shows that the tree architecture, which is derived from minimizing flow resistance, also has the property that it distributes uniformly the flow resistance time throughout the structure. This is true for both laminar and turbulent flow.

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.

Here we document and explain interactions between two thermodynamic trends that determine the optimum performance of refrigeration and heat pump systems. We show analytically why the performance of the system must increase with the size of the installation. The second law efficiency of heat pump systems must increase with their size. We also show that the power requirement for a specific ground-coupled heat pump system must decrease as the size of the ground heat exchanger increases. From these two trends emerges the tradeoff between the size of the heat pump and the size of the ground heat exchanger. The challenge is to find the optimum size of the ground-coupled heat pump. We show numerically the optimum heat pump size and the ground heat exchanger size that correspond to minimum total power requirement subject to a cost constraint.

A heat pump that is coupled thermally with the ground extracts heat from the soil in winter, and discharges heat in the summer. The coupling is made through a buried heat exchanger. In this paper we explore the idea of using a single heat exchanger that serves more than one heat pump. Each heat pump draws its mass flow rate from the heat exchanger and, in addition, a background flow rate circulates permanently through the heat exchanger. The places where the heat pumps are connected to the exchanger vary. The objective of the design is to select the configuration of the multi-component system such that the total enthalpy flow rate delivered to the heat pumps is larger and the total pumping power is smaller. The paper documents the effect of geometry (the connections) and the relative sizes (mass flow rates of heat pumps) on the total enthalpy flow rate. The paper shows the parametric domain in which the design with a single heat exchanger is superior in comparison with the classical design where each heat pump is connected to its own heat exchanger.

In this paper, we review the main advances made by our research group on the heat transfer performance of complex flow architectures embedded in a conducting solid. The immediate applications of this work include the design of ground-coupled heat pumps, seasonal thermal energy storage systems, and district heating and cooling systems. Various configurations are considered: U-shaped ducts with varying spacing between the parallel portions of the U, serpentines with three elbows, and trees with T-shaped and Y-shaped bifurcations. In each case, the volume ratio of fluid to soil is fixed. We found the critical geometric features that allow the heat transfer density of the stream-solid configuration to be the highest. In the case of U-tubes and serpentines, the best spacing between parallel portions is discovered, whereas the vascular designs morph into bifurcations and angles of connection that provide progressively greater heat transfer rate per unit volume. We show that the flow of heat into or out of a solid volume must have an S-shaped history curve that is entirely deterministic. This constructal-design principle unites a wide variety of previously disconnected S-curve phenomena (ground heat storage and retrieval, population growth, cancer, chemical reactions, contaminants, languages, news, information, innovations, technologies, economic activity).

Here we determine the tree-shaped structure that facilitates heat transfer between it and the solid body in which it is embedded. The vascular design evolves toward configurations that provide progressively greater heat transfer per unit volume. Two solid domain sizes are analyzed: a small cube where the tree structure grows to the second-level bifurcation, and a larger cube where the tree design grows to fourth-level branches. We show that when the solid domain and growing tree structure do not interfere with each other, symmetry is a beneficial feature that promotes heat transfer. When the tree structure interferes with the boundaries, asymmetry is the better design feature, and because of it the tree structure fills the available conducting medium.