Stochastic parametric excitation of convective heat transfer

TL;DR

This paper investigates how random vertical vibrations can induce convective heat transfer in fluid layers, deriving excitation thresholds and comparing stochastic effects to periodic modulation.

Contribution

It introduces a mathematical framework for analyzing stochastic parametric excitation of convection and identifies thresholds for heat transfer onset under random vibrations.

Findings

Excitation thresholds for velocity and temperature perturbations are derived.

Stochastic excitation of heat transfer differs significantly from high-frequency periodic effects.

The heat flux relates directly to the second moment of temperature perturbations.

Abstract

We study the parametric excitation of the free thermal convection in a horizontal layer and a rectangular cell by random vertical vibrations. The mathematical formulation we use allows one to explore the cases of heating from below and above and the lowgravity conditions. The excitation threshold of the second moments of the current velocity and the temperature perturbations is derived. The heat flux through the system quantified by the Nusselt number is reported to be related to the second moment of temperature perturbations; therefore, the threshold of the stochastic excitation of second moments gives the threshold for the excitation of the convective heat transfer. Comparison of the stochastic parametric excitation to the effect of high-frequency periodic modulation reveals dramatic dissimilarity between the two.