Resonances and near field heat transfer of finite structures

We describe a formulation for near field heat transfer for a finite size system so that the heat conductance can be expressed as sums of contributions from the resonances of the combined structure of the "receiver" and the "source". Our work opens the door to investigating near field heat transfer between finite systems and in particular metamaterials whose resonances have been well studied. We illustrated our results with an analytically tractable example of energy transfer between two split ring resonantors separated by a distance d on top of each other. When the cuts of the two rings are opposite each other, the heat conductance is smaller than when the cuts of the two rings are on top of each other. This result can only come from a finite system calculation.Copyright (c) 2022 EPLA