Universal Relation between Nusselt Number and Bejan Number in Natural Convection

TL;DR

This paper introduces a universal scaling law linking heat transfer and thermodynamic irreversibility in natural convection, validated across different geometries and boundary conditions.

Contribution

It proposes a new universal relation between Nusselt and Bejan numbers based on entropy analysis, independent of geometry and boundary conditions.

Findings

The relation Be^-1 - 1 = a Nu^b holds universally in natural convection.

Validated using a canonical square cavity.

Connects heat transfer with thermodynamic irreversibility.

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.