The vascularization of smart materials with the property of localized self-cooling is investigated here on the basis of a simple configuration. A solid body (slab) is subjected to intense heat flux from one side; temperatures are controlled by pumping a coolant from the other side. The coolant flows through parallel channels that traverse the slab. The objective is to find the channel configuration that maintains the least nonuniform temperature distribution in the solid (i.e., the coolest hot spots). The optimal spacing between channels and the minimum hot-spot excess temperature are deduced analytically for two configurations, equidistant parallel-plates channels, and arrays of equidistant parallel cylindrical channels. These analytical results are confirmed based on numerical simulations of the conjugate heat transfer in channels and surrounding solid material. The results for the optimal geometry and performance are robust: they are essentially the same for parallel-plates and cylindrical channels.
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