Dimensionless Number &It's significant

There are four types of dimension less No. 

 

1.) Reynolds No.:- It is ratio of inertia force to viscous force. 

                  

                                        

Significant:

• It is used for determined types of flow for example if, 
• Reynold No. (Nre) <2100 then flow is laminar flow
• Reynold No. (Nre) >2100 then flow is turbulent flow
• Reynold. No. is 2100<Nre<2100 then it is transient flow

2.) Grashof No.:- It is ratio between product of buoyancy force and inertia force to square root of viscous force.

 

                                                            

Significant:

• Behavior of fluid flow

                                                    

3.) Prandtl No.:- It is ratio of molecular diffusivity of momentum to molecular diffusivity of heat. 

                        

Significant: 

• It can be used to determine the thermal conductivity of gases at high temperatures
• It is found that the temperature decreases as the Prandtl no. increases. 
• Physically, the increase of Pr means the decrease of thermal conductivity of fluid.

4.) Nusselt No.:- It is ratio of wall heat transfer rate to the heat transfer by conduction.

                 

Significant:

• The physical interpretation of Nusselt number is the enhancement of heat transfer due to convection over conduction alone. 
• If Nu=1, then, than your fluid is stationary and all heat transfer is by conduction.
• ifNu>1, the fluid motion enhances heat transfer by convection