Thermal Radiation in Rayleigh-Be´nard Instability

Thermal radiation from finite-conductivity boundaries can strongly affect the stability of horizontally unbounded, plane fluid layers heated from below. The role of thermal radiation in plane layer instabilities is studied under the assumption that the fluid medium is transparent, as a model of infrared transfer through gas layers. The solution procedure modifies a previous formulation of the conductive boundary problem to account for the gray radiant interchange between boundaries. The nonisothermal character of the boundaries is shown to bias instability toward higher wavenumbers and to substantially increase the stability of fluid layers between radiative, nonconductive boundaries relative to layers having nonradiative boundaries. A single layer is studied first, and then a case of parallel, interacting fluid layers is considered. Critical Rayleigh numbers are presented as both tabulations and correlations. The implications for solar collector design are discussed.