Relation between the Nusselt and Bejan numbers in internal natural convection

This Letter proposes a scaling relation between the Nusselt number Nu and Bejan number Be in internal natural convection. Entropy generation analysis and boundary-layer scaling show that Be−1 − 1 = a Nub emerges when heat transfer and entropy generation are governed by a common control parameter. The coefficients are not universal constants but depend on geometry, boundary conditions, Prandtl number, the irreversibility distribution ratio, nondimensionalization, and so on. Numerical results for side-heated cavities, Rayleigh–Bénard convection, and concentric cylinders support the proposed relation, suggesting a robust link between heat-transfer enhancement and thermodynamic irreversibility.