Important dimensionless numbers used in fluid mechanics and heat transfer are given below:-
Dimensionless Number |
Expression |
Significance |
Reynolds Number |
$Re =\frac{ρUD}{μ}$ |
|
Fourier Number |
$Fo = \frac{αt}{L^2}$ |
|
Biot Number |
$Bi = \frac{hL}{K_s} = \frac{L/K_s}{1/h}$ |
|
Nusselt Number |
$Nu = \frac{hL}{K_f} = \frac{h ΔT}{K_fΔT/L} = \frac{q_{conv}}{q_{cond}}$ |
|
Prandtl Number |
$Pr = \frac{ν}{α}= \frac{µC_p}{K}$ |
|
Grashof Number |
$Gr = \frac{gβΔTL^3}{ν^2}$ |
|
Peclet Number |
$Pe = Re*Pr = \frac{UL}{α}$ |
|
Stanton Number |
$St = \frac{h}{ρUC_p} = \frac{Nu}{Pe} = \frac{Nu}{RePr}$ |
|
Rayleigh Number |
$Ra = Gr*Pr = \frac{gβΔTL^3}{αν}$ |
|
Jakob Number |
$Ja = \frac{C_p(T_s - T_{sat})}{h_{fg}}$ |
|
Bond Number |
$Bo = \frac{gL^2Δρ}{σ}$ |
|
Froude Number | $Fr = \frac{U^2}{gL}$ |
|
Euler Number |
$Eu = \frac{Δp}{ρU^2}$ |
|
Weber number | $We = \frac{ρU^2L}{σ}$ |
|
Nomenclature:
μ → viscosity of fluid
ν → kinematic viscosity of fluid
ρ → density of fluid
U → characteristic velocity scale
D → characteristic Diameter = 4A/P
α → thermal diffusivity of fluid
t → time
L → characteristic length scale
Cp → specific heat at constant pressure
h → heat transfer coefficient
K → thermal conductivity of fluid
Kf → thermal conductivity of fluid
Ks → thermal conductivity of solid
g → gravitational acceleration
β → volumetric thermal expansion coefficient
ΔT → characteristic temperature difference
Tsat → saturation temperature
Ts → surface temperature
hfg → latent heat of condensation
Δρ → difference in density of the two phases
σ → surface tension
Δp → characteristic pressure difference of flow
δf → Fluid boundary layer thickness
δt → Thermal boundary layer thickness
δf → Fluid boundary layer thickness
δt → Thermal boundary layer thickness
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