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

### From Thermal-FluidsPedia

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- | 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<sub>1</sub>'' and ''ε<sub>2</sub>'' , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as | + | 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<sub>1</sub>'' and ''ε<sub>2</sub>'' , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as |

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+ | <div style="text-align: right;"> | ||

+ | <div style="float: left; width: 1115px;">[[File:Sphereee.jpg|center|EQ1]]</div> | ||

+ | (1) | ||

+ | </div> | ||

+ | |||

+ | |||

+ | |||

+ | where x<sub>2</sub> is the position of the particle 2 and <big><math>{\alpha _2} = {4 \pi R^3 (\epsilon_2 -1) / (\epsilon_2 +2)} </math></big> is the polarizability of a sphere of radius ''R'' having the relative permittivity of ε<sub>2</sub>. The electric field incident on the particle 2, E<sub>inc</sub>(x<sub>2</sub>,''ω''), is created by the thermal fluctuating dipole of particle 1 at Temperature ''T<sub>1</sub>'' : | ||

+ | <div style="text-align: right;"> | ||

+ | <div style="float: left; width: 1115px;">[[File:Sphere2.jpg|center|EQ2]]</div> | ||

+ | (2) | ||

+ | </div> | ||

+ | |||

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+ | where <math>\rm \overline {\overline G}_e (x_2,x_1,\omega)</math> is the electric dyadic Green’s function between two dipoles in vacuum and expressed as [2] | ||

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+ | <div style="text-align: right;"> | ||

+ | <div style="float: left; width: 1115px;">[[File:Sphereuc.jpg|center|EQ3]]</div> | ||

+ | (3) | ||

+ | </div> | ||

+ | |||

+ | |||

+ | |||

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+ | where |

## Revision as of 08:09, 3 March 2012

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