# Thermal convection with mixed thermal boundary conditions: Effects of insulating lids at the top

## TL;DR

This study experimentally investigates how insulating lids affect thermal convection, revealing that insulating area influences heat transfer and flow dynamics, with pattern symmetry impacting flow structure and strength.

## Contribution

It provides new insights into the effects of insulating boundary conditions on convection flow patterns and heat transfer efficiency, highlighting the roles of insulating area and pattern symmetry.

## Key findings

- Insulating lids reduce heat transfer efficiency, mainly depending on insulating area.
- Flow strength increases with larger insulating area, regardless of pattern.
- Symmetric insulating patterns produce symmetric flow, asymmetric patterns cause asymmetry and stronger flow.

## Abstract

The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3\times10^{9}\leq Ra_F \leq 1.8\times10^{11}$ and cylindrical cells in the range $1.4\times10^{10}\leq Ra_F \leq 1.2\times10^{12}$ with the Prandtl number Pr fixed at 4.3. It is found that the presence of the insulating lids leads to reduction of the global heat transfer efficiency as expected, which primarily depends on the insulating area but is insensitive to the detailed insulating patterns. At the leading order level, the magnitude of temperature fluctuation in the bulk fluid is, again, found to be insensitive to the insulating pattern and mainly depends on the insulating area; while the temperature probability density function (PDF) in the bulk is essentially invariant with respect to both insulating area and the spatial pattern of the lids. The flow dynamics, on the other hand, is sensitive to both the covering area and the spatial distribution of the lids. At fixed $Ra_F$, the flow strength is found to increase with increasing insulating area so as to transfer the same amount of heat through a smaller cooling area. Moreover, for a constant insulating area, a symmetric insulating pattern results in a symmetric flow pattern, i.e. double-roll structure; whereas asymmetric insulating pattern leads to asymmetric flow, i.e. single-roll structure. It is further found that the symmetry breaking of the insulating pattern leads to a stronger flow that enhances the horizontal velocity more than the vertical one.