Relation between the Nusselt and Bejan numbers in natural convection
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 Nub 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.
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