2-D numerical investigation of melting of an impure PCM in the arbitrary-shaped annuli

A transient numerical study is carried out using a boundary-fitted coordinate (BFC) technique to model the melting characteristics of an impure phase-change material (PCM) in the annular gap formed by an inverse outer equilateral triangular-shaped enclosure and various shaped inner tubes. A control-volume based finite difference method is used to solve the non-dimensional transformed curvilinear conservation equations for mass, momentum, and energy in terms of the physical variables. An enthalpy-porosity scheme is used to model the mushy region melting problem. The developed code is verified with the available experimental data. The effects on the melting characteristics of the PCM of the inner tube wall temperature (Rayleigh number), the initial condition of the PCM, the cross-sectional shape as well as the vertical position of the inner tube inside the annulus are ascertained. The velocity and temperature fields, the total and complete melt fractions, and the latent and total stored energies as a function of the melting time are reported. From the predicted results it is found that the heat exchanger with a vertically placed eccentric inner circular tube provides the maximum energy storage capacity. The wall temperature of the inner tube, as well as the initial temperature of the solid PCM, both has a significant influence on the melting rate of the impure PCM.