Particle Thermal Inertia Delays the Onset of Convection in Particulate Rayleigh-B\'enard System

TL;DR

This study analyzes how thermal inertia of particles in a fluid layer delays the onset of convection in a particulate Rayleigh-Bénard system by stabilizing the system through heat exchange effects.

Contribution

It introduces a linear stability analysis of a particulate Rayleigh-Bénard system considering thermal coupling, revealing how particle thermal inertia influences stability.

Findings

Increasing thermal coupling enhances system stability.

Stabilization saturates when particle heat capacity matches fluid.

Interphase heat exchange modifies temperature profile, reducing buoyancy.

Abstract

We investigate the linear stability of a thermally stratified fluid layer confined between horizontal walls and subject to continuous injection of dilute thermal particles at one boundary and extraction at the opposite, forming a particulate Rayleigh-B\'enard (pRB) system. The analysis focuses on the influence of thermal coupling between the dispersed and carrier phases, quantified by the specific heat capacity ratio $\epsilon$. Increasing $\epsilon$ systematically enhances stability, with this effect persisting across a wide range of conditions, including heavy and light particles, variations in volumetric flux, injection velocity and direction, and injection temperature. The stabilizing influence saturates when the volumetric heat capacity of the particles approaches that of the fluid, $\epsilon = O(1)$. The physical mechanism is attributed to a modification of the base-state temperature profile caused by interphase heat exchange, which reduces thermal gradients near the injection wall and weakens buoyancy-driven motion.