Effect of the inclination angle on the transient melting dynamics and heat transfer of a phase change material

Abstract

We report two-dimensional simulations and analytic results on the effect of the inclination on the transient heat transfer, flow, and melting dynamics of a phase change material within a square domain heated from one side. The liquid phase has Prandtl number Pr = 60.8, Stefan number Ste = 0.49, and Rayleigh numbers extend over eight orders of magnitude 0≤Ra≤6.6·108 for the largest geometry studied. The tilt determines the stability threshold of the base state. Above a critical inclination, there exists only a laminar flow at the melted phase, irrespective of the Rayleigh number. Below that inclination, the base state destabilizes following two paths according to the inclination: either leading to a turbulent state for angles near the critical inclination or passing through a regime of plume coarsening before reaching the turbulent state for smaller angles. We find that the Nusselt and Reynolds numbers follow a power law as Nu∼Raα, Re∼Raβ in the turbulent regime. Small inclinations reduce very slightly α and strongly β. The inclination leads to subduction of the kinematic boundary layer into the thermal boundary layer. The scaling laws of the Nusselt and Reynolds numbers and boundary layers are in agreement with different results at high Rayleigh convection. However, some striking differences appear as the stabilization of turbulent states with further increasing of the Rayleigh number. We find as well that the turbulent regime exhibits a higher dispersion in quantities related to heat transfer and flow dynamics on smaller domains.