Radiative heat transfer in semitransparent solidifying slab considering space–time dependent refractive index

Radiative heat transfer in semitransparent phase-change media is of great interest in many engineering fields. Its essence is the transient coupled heat transfer of radiation and conduction along with liquid–solid phase change. The difficulty is to solve radiative heat transfer with the consideration of time–space dependent radiative properties. Especially when the refractive index is considered to vary with space and time in phase change, the problem becomes more complicated. This paper investigates the problem of the variable radiative properties with space and time during phase change in semitransparent media. The phase-change medium is assumed to have solid, mushy and liquid zones, and the solid/mushy and liquid/mushy interfaces are considered to be semitransparent and diffuse reflecting. In different zones, there are different physical property parameters. Phase interfaces are always moving in phase change, while the interfaces of control volumes are fixed. Therefore, the interfaces of control volumes and phase interfaces are not always coincided, which will bring errors into the simulation of radiative transfer in phase-change media. However, the errors can be reduced by dividing the medium into enough sub-layers. As long as the number of sub-layers is big enough, the errors can be limited in a very small range. Then using the multilayer radiative transfer model, we can solve the radiative transfer problem in the semitransparent phase-change medium. Considering time–space dependent refractive index, this paper analyzes coupled radiative and conductive heat transfer in semitransparent solidifying media. The results show that the effects of variable refractive index with time and space on transient coupled heat transfer are significant and could not be neglected inside the semitransparent phase-change medium under some conditions.