A2 Dimensionless Numbers

1 Introduction

The equations in the VDI-Heat Atlas are often given in dimensionless forms. The dimensionless numbers used in these equations are presented below in tabular form with notation, name, and definition, and by a numerical example for each of these numbers.

2 Dimensionless Numbers

Notation	Name	Definition
Ar	Archimedes number	gl 3Δρ/(ρν 2)
Bi	Biot number	α a l/λ i
Fo	Fourier number	κt/l 2
Fr	Froude number	w 2 /(gl)
Ga	Galilei number	g l 3 /ν 2
Gr	Grashof number	gβΔT l 3 /ν 2
Gz	Graetz number	l 2 /(κ t r)
Hg	Hagen number	(Δp/ΔL) l 3 /(ρν 2)
Ka	Kapitza number	gη 4 /(ρσ 3)
Le	Lewis number	κ/δ ij
Nu	Nusselt number	αl/λ
Pe	Péclet number	w l/κ
Pr	Prandtl number	ν/κ
Ra	Rayleigh number	gβΔT l 3/(νκ)
Re	Reynolds number	ρwl/η
Sh	Sherwood number	β l/δ ij
Sc	Schmidt number	ν/δ ij
St	Stanton number	α/(ρc p w)
We	Weber number	w 2 lρ/σ

3 Examples of Usage

The Archimedes number, Ar, is often used in equations describing the motion of particles (solid particles, drops, or bubbles) in gases...