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.

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.

See also

• Adrian Bejan
• Entropy
• Exergy
• Thermodynamics
• Constructal theory

Further reading

• Petrescu, S. (1994). "Comments on ‘The optimal spacing of parallel plates cooled by forced convection’". Int. J. Heat Mass Transfer 37 (8): 1283. doi:10.1016/0017-9310(94)90213-5.