The Optimal Shape of the Interface Between Two Conductive Bodies With Minimal Thermal Resistance

This paper considers the fundamental problem of optimizing the geometry of the interface between two conductive bodies, with the objective of minimizing the thermal resistance. The interface geometry is free to change. For simplicity, the geometry is assumed to be two-dimensional with equidistant tooth-shaped features. The tooth shape varies from triangles, to trapezoids and rectangles. The aspect ratio (height/width) of the tooth also varies. The third degree of freedom of the interface architecture is the volume fraction of the higher-conductivity tooth material that is present in the interface region. It is shown that the interface geometry can be optimized with respect to tooth shape. The global thermal resistance minimized with respect to tooth shape varies monotonically with the tooth aspect ratio and volume fraction. The optimized geometry and performance are reported graphically as functions of the physical properties and geometric parameters of the interface region.