# Bejan number (modified form)

## Description

The modified form of the Bejan number, riginally proposed by Bhattacharjee and Grosshandler for momentum processes, by replacing the dynamic viscosity appearing in the original proposition with the equivalent product of the fluid density and the momentum diffusivity of the fluid. This modified form is not only more akin to the physics it represents but it also has the advantage of being dependent on only one viscosity coefficient. Moreover, this simple modification allows for a much simpler extension of Bejan number to other diffusion processes, such as a heat or a species transfer process, by simply replacing the diffusivity coefficient. Consequently, a general Bejan number representation for any process involving pressure-drop and diffusion becomes possible. It is shown that this general representation yields analogous results for any process satisfying the Reynolds analogy (i. e., when Pr = Sc = 1), in which case the momentum, energy, and species concentration representations of Bejan number turn out to be the same.

Related formulas## Variables

Be | Bejan number (dimensionless) (dimensionless) |

Δ_{P} | pressure drop (Pa) (dimensionless) |

L | channel of length (m^2) (dimensionless) |

ρ | fluid density (kg/m^3) (dimensionless) |

δ | corresponding diffusivity of the process in consideration (m^4/s^2) (dimensionless) |