Keywords: electronics cooling, constructal optimisation, heat generation, Lagrange multiplier method, high conductivity
Constructal optimisation of heat generating volumes
Cooling of electronics by conduction with high thermal conductivity paths located in heat generating, low conductivity volumes are investigated using constructal theory. A new mathematical solution for the fundamental problem of how to collect and channel to one point the heat generated volumetrically in a low conductivity volume of a given size is developed using the Lagrange Multiplier Method. Additionally, at the fundamental step, the optimisation procedure is exact. No approximation has been made about the geometrical characteristics of the fundamental element. In solutions of the fundamental elements, the amount of high conductivity material (high conductivity paths) through the volume is fixed.