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

Thermodynamics

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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:

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

where

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

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

Fluid mechanics and heat transfer

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

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

where

: $\backslash mu$ is the dynamic viscosity
: $\backslash alpha$ 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)

See also

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Adrian Bejan

Entropy

Exergy

Thermodynamics

Constructal theory

References

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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 Transfer and Mass Transfer, Vol. 37, 1994, p. 1283.

Category:Thermodynamics
Category:Fluid dynamics
Category:Convection