Relation between the Nusselt and Bejan numbers in natural convection

TL;DR

This paper derives a universal scaling law linking the Nusselt and Bejan numbers in natural convection, revealing a fundamental thermodynamic constraint on convective heat transfer.

Contribution

The study introduces a new scaling relation between Nu and Be numbers based on entropy analysis, independent of geometry or boundary conditions.

Findings

Derived the relation Be^-1 - 1 = a Nu^b without geometry dependence

Validated the scaling law with numerical cases

Linked heat transfer efficiency to thermodynamic irreversibility

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.