Configuration of heat sources or sinks in a finite volume

This work documents the design method of allocating channels that serve as heat sources or heat sinks in a conducting body. First, we develop a numerical model to find the optimum channel spacing for specified properties of the surrounding medium, the time scale of the heat transfer process, and the dimensions of the configuration. Second, we show with scale analysis that the optimal spacing (S/D) must equal τ1/2 in an order of magnitude sense, where τ is the dimensionless time scale of the process. This conclusion holds for the two heat transfer histories that were considered, exponential and top hat. We extend the method to a packing of channels of two sizes (diameters and heat source strengths). The optimal spacings and packing density obey the scaling rule determined for packing sources of a single size.