Physical mechanism of the convective heat flux increasing in case of mixed boundary conditions

TL;DR

This study uses numerical simulations to explore how mixed boundary conditions and the spatial frequency of conducting plates influence the thermal boundary layer structure and heat flux in Rayleigh-Bénard convection.

Contribution

It reveals the physical mechanisms behind increased heat flux due to higher spatial frequency of conducting-adiabatic patterns in mixed boundary conditions.

Findings

Thermal boundary layer becomes highly non-uniform under mixed boundary conditions.

Smaller conducting plates lead to thinner boundary layers and higher heat flux.

The effect is consistent across a range of Rayleigh numbers from 10^7 to 2×10^9.

Abstract

A series of numerical simulations of Rayleigh-B{\'e}nard convection in a cubic cavity are conducted in order to examine the structure of the thermal boundary layer in case of mixed boundary conditions. The main goal of the study is the physical mechanism which provides increasing of heat flux with spatial frequency of conducting-adiabatic pattern. Different spatial configuration of conducting plates, including the fractal one, are considered for Rayleigh numbers from $\Ray=10^{7}$ to $\Ray=2.0\times 10^{9}$. We have shown that the temperature boundary layer in case of mixed boundary conditions at the bottom is strongly non-uniform. This non-homogeneity is a result of several factors such as conducting-adiabatic pattern, large-scale circulation and small-scale motions over conducting plates. The thickness of the thermal boundary layer strongly depends on the size of the conducting plates and can be substantially smaller than for a classical Rayleigh-B{\'e}nard convection. This effect increases the heat flux with decreasing the size of hot plates, which corresponds to the increasing of spatial frequency of conducting-adiabatic pattern.