Tailoring the first law of thermodynamics for convective flows.

This article focuses on extending the first law of thermodynamics to nonequilibrium systems, specifically analyzing global energy exchanges during transitions between steady states in closed hydrodynamic systems exhibiting macroscopic motion, such as Rayleigh–Bénard convection. It demonstrates that the total energy balance in these nonequilibrium states retains the same formal structure as in equilibrium thermodynamics, with energy changes accounted for by heat exchange, mechanical surface work, and work done by external potential fields like gravity. While local processes such as viscous dissipation and heat flux occur in nonequilibrium steady states, their net global contributions vanish, making the system's global energy behavior analogous to equilibrium. This framework offers a foundation for developing a thermodynamic-like description of nonequilibrium steady states, with potential applications in atmospheric science and industrial chemical reactors, and highlights the unexplored nature of heat exchange in heat-driven convection systems.