Bejan number

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

Contents

1 Thermodynamics

2 Fluid mechanic and heat transfert

3 See also

4 References

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 mechanic and heat transfert

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

References

S. Paoletti, F. Rispoli, E. Schiubba, Calculation of exergetic losses in compact heat exchanger passager, ASME AES-Vol. 10-2, 1989, pp. 21-29.
S. Bhattacharjee and W.L. Grosshandler, The formation of wall jet near a high temperature wall under microgravity environment, ASME MTD-Vol. 96, 1988, pp. 711-716.
S. Petrescu, Comments on the optimal spacing of parallel plates cooled by forced convection, International Journal of Heat Transfert and Mass Transfer, Vol. 37, 1994, p. 1283.