An optimum spacing problem for five chips on a horizontal substrate in a vertically insulated enclosure

The optimum spacing problem for five heated chips rested on a conductive substrate in a vertically insulated enclosure filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. It is found that the conventional equi-spaced 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. The maximum relative temperature drop in the optimum configuration can be as much as 20% of the equi-spaced arrangement.