Constructal Optimization of Paths for Heat Transfer

This article is a review of recent work in which heat transfer enhancement, or thermal resistance minimization is achieved by optimizing the internal architecture of a heat-generating volume. When the cooling is provided by a stream that flows through the volume, it is possible to optimize the spacings between the internal features that are being cooled. When the cooling function is served by a point-size heat sink, a fixed amount of high conductivity material can be distributed through the volume to minimize its overall thermal resistance. The discovery is that any volume element can have its shape (or size) optimized such that its flow resistance is minimal. The given volume is covered in successive steps of optimization and construction. The visible portion of the optimized volume-to-point flow path that emerges is a tree network that is completely deterministic. This solution has a definite time direction: from small to large, hence the name “constructal”. Small size and slow and shapeless flow (diffusion) come first, and larger sizes and organized flows (streams) come later.