Name  Formula  Ratio  Details 
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 L^{3} 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 c_{p} k 
Diffusion of Momentum Diffusion of Heat 
μ    viscosity of fluid 
c_{p}    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 c_{p} 
Heat Xfer at Wall Energy Xported by Stream 
h    heat xfer coefficient 
ρ    density of fluid 
V    far field fluid velocity 
c_{p}    specific heat of fluid 
