The document defines and provides physical significance for several dimensionless numbers used in heat transfer: - The Reynolds number (Re) gives the ratio of inertial to viscous forces, indicating laminar or turbulent flow. - The Prandtl number (Pr) is the ratio of momentum diffusivity to thermal diffusivity, depending on the fluid properties. - The Nusselt number (Nu) is the ratio of convective to conductive heat transfer across a boundary layer.

1. Some Dimensionless Numbers in Heat Transfer
Reynolds Number
Nusselt Number
Stanton Number
Peclet Number
Prantdl Number
Reynolds Number
The dimensionless number that gives the measure of theratio of inertial forces toviscous forces for a
particular fluid stream.
Re = ρuL/µ
Where:
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
o It is the ratio of inertial forces to viscous forces in a fluid.
o If Re is smaller, the fluid will be more viscous & 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 = cpµ/k
Where:

2. Pr = Prantdl number
ν = momentum diffusivity
α = thermal diffusivity
µ = viscosity
ρ = density
k = thermal conductivity
cp = specific heat capacity at constant pressure
Physical significance
o It is the ratio of momentum diffusivity of fluid to its thermal diffusivity.
o If a fluid has low Pr, its thermal diffusivity will be higher and momentum diffusivity will be lower.
o If a fluid has higher Pr, its thermal diffusivity will be lower and momentum diffusivity will be
greater.
o It depends on only the state of fluid and the type of fluid, it is independent of any length
dimension (as Re depends).
Nusselt Number
The dimensionless number which gives the ratio of convective heat transfer across (normal to) the
boundary layer of the fluid to the conductive heat transfer.
Nu = hL/k
Where:
Nu = Nusselt number
h = convective heat transfer coefficient of fluid
k = thermal conductivity of fluidL = characteristic length (outer diameter of cylinder, length of vertical
plate, diameter of sphere, volume of fluid object per surface area for complex shapes).
Physical significance