# The time evolution equation for advective heat transport as a constraint for optimal bounds in Rayleigh-B\'enard convection

## TL;DR

This paper introduces a new constraint based on the time evolution of advective heat transport to improve bounds on heat transfer in Rayleigh-Bénard convection, refining previous theoretical limits.

## Contribution

It presents a novel constraint from advective heat transport evolution, enhancing the accuracy of bounds on heat transfer in convection models.

## Key findings

- Improved bounds on heat transport in Rayleigh-Bénard convection.
- Enhanced understanding of the role of advective heat transport constraints.
- Refinement of theoretical limits for convective heat transfer.

## Abstract

Upper bounds on the heat transport and other quantities of interest in Rayleigh-B\'enard convection are derived in previous work from constraints resulting from the equations of time evolution for kinetic energy, the root mean square of temperature, and the temperature averaged over horizontal planes. Here, we investigate the effect of a new constraint derived from the time evolution equation for the advective heat transport. This additional constraint leads to improved bounds on the toroidal dissipation.