Thermal energy storage in a confined cylindrical heat source filled with phase change materials

Abstract

Thermal energy storage in the phase change materials (PCMs) around a confined heated cylindrical heat source has been investigated numerically. This work aims to explore three major objectives namely; evolution of melting front around the cylindrical heat source, quantification of overall rate of heat transfer and identifying the factors to maximize the energy storage. The enthalpy-porosity formulation is utilized to model melting of PCMs. The flow and energy equations with relevant boundary conditions have been solved using finite element method for range of parameters as Rayleigh number (102 ≤ Ra ≤ 106 ), Prandtl number (102 ≤ Pr ≤ 103 ), Stefan number (0.01 ≤ Ste ≤ 0.5) and aspect ratio (0.1 ≤ AR ≤ 0.5). The evolution of melting front and melt fraction, streamlines, isotherms, Nusselt number and thermal energy storage are reported as a function of Rayleigh number (Ra), Prandtl number (Pr), Stefan number (Ste), and aspect ratio (AR). Stefan number and the aspect ratio have shown to be a positive influence on the amount of thermal energy absorbed during the melting of PCMs. At low Rayleigh and Stefan number, melting kinetics is shown to be sluggish. All else being equal, the energy storage exhibits three distinct regimes depending upon the Fourier number namely, the lag phase, the exponential phase and stationary phase. For process design calculations, the gross engineering parameters like Nusselt number and steadystate melt fraction are often required, and therefore a predictive correlation for the value of the average Nusselt number is proposed to facilitate the estimation of average Nusselt number at intermediate values of dimensionless numbers for a given practical application.