# Near-field radiative energy transfer between sphere-sphere and sphere-flat surfaces

### From Thermal-FluidsPedia

Near-field thermal radiation between two spheres was first reported by Volokitin and Persson [1] by assuming them as dipoles. When there are two spherical nanoparticles whose dielectric constants are *ε _{1}* and

*ε*, the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as

_{2}

where x_{2} is the position of the particle 2 and α_{2} = 4π*R*^{3}(ε_{2} − 1) / (ε_{2} + 2) is the polarizability of a sphere of radius *R* having the relative permittivity of ε_{2}. The electric field incident on the particle 2, E_{inc}(x_{2},*ω*), is created by the thermal fluctuating dipole of particle 1 at Temperature *T _{1}* :

where is the electric dyadic Green’s function between two dipoles in vacuum and expressed as [2]

where