Optimal conductive constructal configurations with “parallel design”

• A new parallel design is proposed for conductive cooling of heat generating rectangles.
• The geometric features are optimized analytically.
• The internal structure morph as a function of available conductive material.
• Thermal performance is superior to the previously numerically optimized designs.

Today, conductive volume to point cooling of heat generating bodies is under investigation as an alternative method for thermal management of electronic chipsets with high power density. In this paper, a new simple geometry called “parallel design” is proposed for effective conductive cooling of rectangular heat generating bodies. This configuration tries to minimize the thermal resistance associated with the temperature drop inside the heat generating volume. The geometric features of the design are all optimized analytically and expressed with simple explicit equations. It is proved that optimal number of parallel links is equal to the thermal conductivity ratio multiplied by the porosity (or the volume ratio). With the universal aspect ratio of H/L = 2, total thermal resistance of the present parallel design is lower than the recently proposed networks of various shapes that are optimized with help of numerical simulations; especially when more conducting material is available.