A half-analytical correlation of total melting time for shell-and-tube latent-heat thermal energy storage unit

This study proposes a new concept of dimensionless total melting time in view of the nonlinear dynamic characteristic of latent-heat thermal energy storage unit (LHTESU). This dimensionless total melting time has a mild nonlinear relationship with its influence parameters, which makes it is possible to develop a unified correlation formula of total melting time. The melting process of a vertical single-pass shell-and-tube LHTESU is numerically studied to build a half-analytical correlation of total melting time proposed by this paper. Boussinesq approximation is used to investigate the effects of natural convection on the melting characteristics. The proposed correlation has an extensible format and includes five dimensionless parameters: Stefan number, dimensionless initial temperature, Reynolds number, diameter ratio, and length-to-diameter ratio. The results show that the non-dimensional total melting time has a lower-order nonlinear-relationship with its influence parameters compared with the existing concept of total melting time. The common reason for these five concerned parameters affecting the dimensionless total time is that they all have effects on the inhomogeneous temperature distribution in LHTESU. The half-analytical correlation of dimensionless total time developed in this study has acceptable accuracy. The deviation between the total melting time predicted by empirical correlation and the numerical result is less than 5%.