The error of neglecting natural convection in high temperature vertical shell-and-tube latent heat thermal energy storage systems

The results showed that the error is a function of the process under analysis (melting or solidification) and the ratio of stored/delivered energy divided by the maximum capacity of PCM (i.e. its effectiveness). Geometry also plays a critical role in the relative importance of natural convection. The study demonstrates that a specific system geometry (i.e. a dimensionless number defined based on the inner and outer radius as well as the length of shell-and-tube geometry: S=R2-ro22roL) can be used to determine the relevance of natural convection. It was found that regardless of PCM type, the error is of neglecting natural congestion is small if S<0.005. For S>0.005, the error depends on the following non-dimensional groups: roL,Ra,Ste,andBi. As might be expected, the Rayleigh number was found to be the most influential group. Notably, a critical Rayleigh number value (8 × 105) was found, below which the error of neglecting natural convection is <1%. Finally, two correlations were developed in order to quantify the error achieved - one for melting and another for solidification.