Bejan number#

Named after: Adrian Bejan (1948-).

$$\text{Be} \stackrel{\text{def}}{=} \frac{(p_1 - p_2) L^{2}}{\mu \alpha} \sim \frac{\text{pressure driving}}{\text{viscous thermal diffusion}}$$

Description#

Measures pressure driving relative to viscous and thermal diffusion. It characterizes forced-convection strength in pressure-driven heat-transfer problems.

Quantities#

Name	Symbol	SI units	Dimension
pressure drop	$p_1 - p_2$	$\mathrm{Pa}$	$\text L^{-1}\,\text M\,\text T^{-2}$
characteristic length	$L$	$\mathrm{m}$	$\text L$
dynamic viscosity	$\mu$	$\mathrm{Pa}\,\mathrm{s}$	$\text L^{-1}\,\text M\,\text T^{-1}$
thermal diffusivity	$\alpha$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$

Regimes#

Forced convection

Range	Regime	Description
0 – 1	diffusion limited	Pressure work is small relative to viscous and diffusive transport. Flow forcing has a weak effect on thermal transport.
1 – ∞	pressure driven	Pressure work strongly drives transport. Forced convection and pressure losses are central to the thermal behavior.

Name	Symbol	SI units	Dimension
pressure drop	\(p_1 - p_2\)	\(\mathrm{Pa}\)	\(\text L^{-1}\,\text M\,\text T^{-2}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)
dynamic viscosity	\(\mu\)	\(\mathrm{Pa}\,\mathrm{s}\)	\(\text L^{-1}\,\text M\,\text T^{-1}\)
thermal diffusivity	\(\alpha\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)