Validation of a melting fraction-based effective thermal conductivity correlation for prediction of melting phase change inside a sphere

Abstract

Abstract It is complicated and costly to directly simulate the natural convection influenced melting processes involving multiple PCM units in packed bed phase change system. An effective method to simulate such melting process is using an equivalent conduction model, in which the effective thermal conductivity (ETC) of PCM considering the natural convection effects is an important thermal parameter needing to be determined. In this paper, the ETC of PCM is investigated and determined by comparing numerical results based on models considering natural convection and pure conduction, respectively. Parameters of interest include melting fraction (α), Rayleigh number (Ra, 1.5\u202f×\u202f104\u202f≤\u202fRa ≤ 6.3\u202f×\u202f107), Prandtl number (Pr, 17\u202f≤\u202fPr\u202f≤\u202f550) and Stefan number (Ste, 0.011\u202f≤\u202fSte\u202f≤\u202f0.276.). Results show that the ETC of PCM has a strong relation to α and Ra, while it has little relation to Pr and Ste. Hence, an ETC correlation is developed as a function of Ra and α. Validation and application of the ETC correlation are further carried out, and it is found that the melting fraction predicted based on the present ETC correlation can better reflect the effect of liquid zone geometry on the melting heat transfer with natural convection than that predicted based on the previously reported correlations using a liquid gap parameter.