Comparison of the quasi-steady-state heat transport in phase-change and classical Rayleigh-Bénard convection for a wide range of Stefan number and Rayleigh number

Abstract

We report the first comparative study of the phase-change Rayleigh–Bénard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height R a f is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters R a f (3.96 × 104 ≤ R a f ≤ 9.26 × 107) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate [Formula: see text] vs R a f for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nu h increase with the increase in Ste and R a f. There are two distinct RB flow configurations at low R a f independent of Ste. At low and moderate R a f, the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection [Formula: see text] is always greater than one. However, at higher R a f, the RB convection is turbulent, and [Formula: see text] can be less than or greater than one depending on the value of Ste. The results may turn out to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.

How the growth of ice depends on the fluid dynamics underneath

“…Various studies have been performed on the flow in the RB system with freezing or melting boundary conditions. The focus has been on the behaviors of global quantities such as the heat flux, the kinetic energy, and the dynamics of the ice-water interface morphology with a melting phase-change boundary in the RB system (21)(22)(23)(24); pattern selection and instability analysis with a moving solid-water interface (25,26); the bistability of the equilibria induced by different initial conditions (27,28); melting in double diffusive convection (29)(30)(31); and the influences of different container shapes on the melting and convection of phase change materials (32)(33)(34).…”

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

“…For vertical heating (no inclination), the average exponent is α ∼ 0.29 in n-octadecane melting 3 , in agreement with theoretical predictions of 2/7 32,44,45 . Also, it has been found in vertical heating of gallium that phase change induces a greater Nusselt number for small Rayleigh numbers 46 . Figure 15(b) shows the evolution of the Nusselt number as function of the Rayleigh number during melting in a log-log scale for θ < θ c .…”

Natural convection in phase change material: Experimental study

“…1) characterized by higher liquid depth in upward fluid regions and reciprocally. The interplay between convection and the topography has led to several studies [17,18,19,20,21].…”