Relation between the Nusselt and Bejan numbers in natural convection
Fluid Dynamics
2026-04-28 v1
Abstract
This study derives a scaling law connecting the Nusselt (Nu) and Bejan (Be) numbers in natural convection. Combining entropy generation analysis with boundary-layer scaling, the relation Be^-1 - 1 = a Nu^b naturally emerges without explicit dependence on geometry or boundary conditions. This is achieved within the present scaling framework when transport is governed by a single control parameter. Numerical validation against several cases corroborates this scaling. This finding reveals a direct, quantitative link between heat transfer efficiency and thermodynamic irreversibility, suggesting a potentially universal constraint that governs convective transport.
Cite
@article{arxiv.2604.23736,
title = {Relation between the Nusselt and Bejan numbers in natural convection},
author = {Takuya Masuda and Toshio Tagawa},
journal= {arXiv preprint arXiv:2604.23736},
year = {2026}
}