Thermal heat storage and convective melting dynamics of phase change materials in inclined square enclosures: Effect of the Prandtl number

Abstract

We study numerically the effect of the Prandtl number on the thermal heat storage, heat flux, and melting dynamics in phase change materials enclosed in square geometries inclined from 0° (bottom horizontal heating) to 180° (top horizontal heating) at increments of at least 5°. Chosen phase change materials are representative of very low, moderate, and high Prandtl numbers: gallium ( P r = 0 . 021 ), water ( P r = 13 . 5 ), and erythritol ( P r = 201 ). The Stefan number is fixed to 0.5, and the Rayleigh number to R a ∼ 1 0 8 . Water and erythritol exhibit a global bifurcation angle at θ c = 3 0 ∘ , separating the liquid phase dynamics from turbulent to laminar. Gallium exhibits stages of turbulent behavior up to 165°. The optimum tilt for harvested thermal energy corresponds to 95° for water and erythritol, and 100° for gallium. The maximum energy efficiency in harvesting thermal energy corresponds to small inclinations within the turbulent region, and 50° for water and erythritol, and the region about 45° for gallium. The maxima at 50° and 95° are very close to those values of the most frequent inclinations 45° and 90° investigated in the experimental literature. There is a power-law dependence between the Nusselt and Rayleigh number N u ∼ R a α for all the Prandtl numbers. Power-law exponents for water and erythritol exhibit a global upward trend with the inclination and undefined for gallium. • Simulations on erythritol (Pr=201), water (Pr=13.5), gallium (Pr=0.021) for Rã10̂8. • Power-law with inclination between Nusselt and Rayleigh numbers for all the Prandtl. • Similar melting time, energy storage and efficiency curves for all Prandtl. • Exists a critical inclination splitting laminar from turbulent flow for all Prandtl. • Optimal inclination for energy storage: 95° water and erythritol, 100° for gallium.