This document discusses four non-dimensional numbers that are used in heat transfer analysis: The Nusselt number relates convective heat transfer to conductive heat transfer through a characteristic length and thermal conductivity. The Grashof number compares buoyancy and inertia forces to viscous forces in natural convection. The Prandtl number is the ratio of momentum diffusivity to thermal diffusivity, relating how a fluid conducts momentum and heat. The Reynolds number compares inertial to viscous forces, indicating flow regime from laminar to turbulent. These non-dimensional numbers provide insight into dominant transfer mechanisms in heat transfer problems.

1. HEAT TRANSFER
PHYSICAL SIGNIFICANCE OF NON-
DIMENSIONAL NUMBERS

2. NUSSELT NUMBER(Nu)
• It shows relation between convective hear transfer co-officient
h, thermal conductivity k and characteristic length L.
• Thus, it shows the comparison between convection in the fluid
and conduction at the plate.
• It may also be defined as temperature gradient at the solid
surface to the overall temperature gradient.
L
K
h
K
hL
Nu 

3. Grashoff Number(Gr)
• It shows relative dominance of inertia and buoyant force over
viscous force.
• It is used in free convection similarly as Reynolds No. is used in
forced convection. Chances of free convection is very less,at
very low value of Gr,at some critical value of Gr,free convection
starts it increase as value of Gr increases

4.   
 2
ceviscousfor
cebuoyantforceinertiafor
Gr 
 
 2
322
VL
LtgVL

 
2
23

 tLg
Gr



5. Prandtl number(pr)
• It is the ratio of kinematic viscosity to thermal diffusivity.
• Kinematic viscosity indicates energy transport due to friction.
• Thermal diffusivity shows energy transport due to conduction.














cp
k





k
cp


6. • It shows relative comparison of energy transport due to
viscous action and conduction.
• It shows comparison between velocity and thermal boundary
layer.
• For gases value of number is almost unity,but for liquids metals
pr=0.003 to 0.1 which shows that energy transport due to
thermal conduction is more as compared to viscous action.

7. Reynolds number(Re)
• It is a ratio of the inertia force ton the viscous force.
• Inertia force= mass x acceleration
=density x volume x acceleration
2
3
T
LL 
22
LV

8. • Viscous force= shear stress x area
• Reynolds number is,
• It shows magnitude of inertia force compared to viscous force.if Re
value is high ,inertia force is more as compared to viscous force and
turbulence in flow will be higher.
• If Re value is low viscous force has dominance over inertia force,
thus turbulence in the flow will be low. it is mostly used for force
convection process.
VLL
L
V
L  





 22



 VL
VL
VL

22

9. Thank you