Universal Relation between Nusselt Number and Bejan Number in Natural Convection
Fluid Dynamics
2026-04-13 v1
Abstract
We propose a universal scaling law linking the Nusselt number (Nu) and the Bejan number (Be) in natural convection. Using entropy generation analysis and boundary-layer scaling, we demonstrate that Be^-1 - 1 = a Nu^b emerges independently of geometry and boundary conditions when transport is governed by a single control parameter. The relation is validated using a canonical square cavity. This result establishes a direct connection between heat transfer and thermodynamic irreversibility, revealing a fundamental constraint in convective transport.
Cite
@article{arxiv.2604.08848,
title = {Universal Relation between Nusselt Number and Bejan Number in Natural Convection},
author = {Takuya Masuda and Toshio Tagawa},
journal= {arXiv preprint arXiv:2604.08848},
year = {2026}
}