English

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.

Keywords

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}
}