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Bejan number

There are two Bejan numbers (Be) in use, named after Duke University professor Adrian Bejan in two scientific domains: thermodynamics and fluid mechanics.

Thermodynamics

In the context of thermodynamics, the Bejan number is the ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction:

$Be=\frac{\dot S'_{gen, \Delta T}}{\dot S'_{gen, \Delta T}+ \dot S'_{gen, \Delta p}}$

where

$\dot S'_{gen, \Delta T}$ is the entropy generation contributed by heat transfer
$\dot S'_{gen, \Delta p}$ is the entropy generation contributed by fluid friction.

This definition was introduced by Paoletti et al. (see reference).

Fluid mechanics and heat transfer

In the context of fluid mechanics and heat transfer. the Bejan number is the dimensionless pressure drop along a channel of length L:

$Be=\frac{\Delta P . L^2} {\mu \alpha}$

where

μ is the dynamic viscosity
α is the thermal diffusivity

The Be number plays in forced convection the same role that the Rayleigh number plays in natural convection. The Be number was introduced by Bhattacharjee and Grosshandler (see references)