Near-field radiation across a spherical pore in mesoporous silica

A mesoporous silica substrate consists of uniformly distributed and unconnected spherical pores. Since the pore diameter is less than the characteristic wavelength of thermal radiation,near-field radiative heat transfer cannot be ignored. In this paper,near-field radiation across a spherical pore in mesoporous silica was simulated by employing the fluctuation dissipation theorem and the Green function. The calculated equivalent thermal conductivity of radiation was further developed to modify the thermal conductivity of mesoporous silica. The combined thermal conductivity of mesoporous silica was obtained by using the porosity weighted dilute medium(PWDM) model to combine the equivalent thermal conductivity of radiation across the pore,the thermal conductivity of confined air in the pore and the thermal conductivity of the silica substrate. Such factors as the pore diameter and the material temperature were further analyzed. Research results show that the radiative heat transfer at the mesoscale is 2-7 orders higher than that at the macroscale.The heat flux and equivalent thermal conductivity of radiation across a spherical pore decrease exponentially with increasing pore diameter,but increase with increasing temperature. The combined thermal conductivity of mesoporous silica decreases gradually with increasing pore diameter,while increases smoothly with increasing temperature. The smaller the pore diameter,the more significant the near-field effect,which cannot be ignored. When the pore diameter is greater than 50 nm,the size effect gradually disappeared.