Dimensionless Numbers


NameFormulaRatioDetails
Bi

Biot
h L
k
Surface Conductance
Internal Conductance of Solid
h-heat xfer coef at surface
L-characteristic length of conduction. Ex: radius.
k-thermal conductivity of solid
Gr

Grashof
g β L3 Δ T
ν 2
Bouyancy Force
Viscous Force
g-acceleration of gravity
β -coef of thermal expansion of fluid
L-characteristic length of object
Δ T-wall temp - ambient temp
ν -kinematic viscosity
Nu

Nusselt
h L
k
Convection at Surface
Conduction at Surface
h-heat xfer coef at surface
L-characteristic length of object
k-thermal conductivity of fluid
Pr

Prandtl
μ cp
k
Diffusion of Momentum
Diffusion of Heat
μ -viscosity of fluid
cp-specific heat of fluid
k-thermal conductivity of fluid
Re

Reynolds
ρ V L
μ
Intertial Force
Viscous Force
ρ -density of fluid
V-far field fluid velocity
L-characteristic length of object
μ -viscosity of fluid
St

Stanton
h
ρ V cp
Heat Xfer at Wall
Energy Xported by Stream
h-heat xfer coefficient
ρ -density of fluid
V-far field fluid velocity
cp-specific heat of fluid