Dimensionless number in heat transfer
. Reynolds Number

The dimensionless number that gives the measure of the
ratio of inertial forces to viscous forces for a particular fluid
Re = ρuL/μ
Re = Reynolds number
ρ = Density of the fluid
u = mean velocity of fluid object
L = is a characteristic length or linear dimension (internal
diameter for flow in pipe or sphere moving in pipe, length or
width for aircraft or ship moving in fluid, equivalent diameter
for rectangular pipe and non-spherical object in fluid)
μ = viscosity of fluid

Physical significance

It is the ratio of inertial forces to viscous forces in a fluid.
o If Re is smaller, the fluid will be more viscous and less
inertial forces will exist in the fluid inverse will be true for
greater value of Re.
o At low Re, the flow will be smooth, continuous, streamline,
laminar flow due to higher viscosity
o For higher Re, the flow will be turbulent with eddies,
vortices, and discontinuous as inertial forces are higher.
o It is also considered as the ratio of total momentum
transferred to the molecular momentum transferred because
at higher Re and velocity the momentum of the fluid will be
greater from one point to another but at lower Re the
momentum distribution between the molecules due to higher
viscous forces will be greater and consequently velocity will
be lower, the flow will be laminar.

Prantdl Number

The dimensionless number that gives the ratio between
momentum diffusivity to thermal diffusivity.
Pr = ν/α = μ/ρ/k/ρcp = cpPμ/k