Simulation of radiation physics

Radiation heat transfer was simulated using Surface-to-Surface Radiation module based on Hemicube method at a surface-to-surface radiation resolution of 256. Radiation module and Heat Transfer in Solids and Fluids were coupled using Heat Transfer with Surface-to-Surface Radiation. Radiative heat flux was modeled using Stefan–Boltzmann equation^24,25,37,38, described below:

In which qr is the radiative heat flux from surface 1 to surface 2, F1→2 is the visualization factor between surface 1 and surface 2, sigma is the Stefan-Boltzmann constant. T₁ and T₂ are the absolute temperatures of surface 1 and surface 2, respectively. Surface-to-surface radiation model in COMSOL V 6.0 is a powerful technique which incorporates shadowing effect and automatically calculates the shape factor between each pair of surfaces. In this model, following assumptions were made based on previous studies^26,27,40,41:

Equations (10–13) were used to calculate view factor for vial M, therefore calculating K_r and ultimately K_CC from experiments to be used for simulations. The calculation of view factors in simulations was carried out using COMSOL Multiphysics built-in Hemicube method which takes into account any changes in the geometry. This method automatically updates changes in the geometry arrangements within the model and updates the view factors accordingly using the updated mesh. The method Hemicube has been previously used and compared with experimental data in the literature, showing very good agreement and prediction power^44,45. This method analyzes the view factor of the face of each element in the mesh by rendering digital images of the geometry in five directions⁴⁶. A full description of the method used to calculate view factors using Hemicube method can be found in Refs.^46,47. Emissivity was estimated based on available data in the literature, namely⁴⁸ for COP and¹² for glass.