An optimum spacing problem for three chips mounted on a vertical substrate in an enclosure

The optimum spacing problem for three heated chips mounted on a conductive substrate in a two-dimensional enclosure filled with air is solved by an operator-splitting pseudo-timestepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. The conventional equispaced arrangement is not an optimum option. An optimum thermal performance can be obtained when the center-to-center distances between the chips follow a geometric series, especially when the geometric ratio is the golden mean (1.618). Usually the relative temperature drop is about 10%.