Dimensionless Numbers in Heat Transfer

[kundukoustav]

Firstly, my question is - why do we use dimensionless quantities?
Next question, I would like to know the physical significance of Nusselt number, Prandtl Number, Sherwood Number, Scmidt Number, Peclet Number and Gratez Number!
Thanks in advance!

 

[kundukoustav]

I hope this question can be answered! Thanks in advance!

 

[Studiot]

1) Why do we use dimensionless quantities?

Well here is a simple example : pi is a dimensionless quantity (can you see why?) that is the same for all circles.

So it is scale invariant or independent of size.

Dimensionless quantities are all independent of some physical quantity.

For your list have you tried Google?

A while back I posted this list here in a discussion about the difference between constants and dimensionless quantities.
Perhaps some will be here.

https://www.physicsforums.com/attachment.php?attachmentid=28382&d=1284989819

go well

 

[kundukoustav]

Thanks! :)

 

[Studiot]

I should perhaps add that pi is a very very simple dimensionless number that is also a constant ie it does not vary.

Dimensionless numbers that vary are used to compare and standardise situations. This is useful in making physical scale models. One of the most common dimensionless numbers is Reynolds Number which is the ration of inertial to viscous forces acting on a body in a fluid. It has a range from a few units to hundreds of thousands. By taking suitable model dimensions and the test fluid viscoscity to make the Reynolds Number the same, we can model the fluid flow in large river channels or in wind tunnels over aircraft bodies without creating full scale models.

 

[kundukoustav]

exactly! But, Can you specially mention some practical point of stanton number? and where can it be used? some idea would be welcome!

 

[Studiot]

The Stanton Number (the reciprocal of the Prandtl No) is used by Chemical Engineers in heat and mass transfer calculations in chemical plant process theory. It is one of many such dimensionless numbers and appears in the dimensionless equation for energy transfer in forced convection.

Are you aware that this type of calculation is normally carried out by rewriting standard energy and mass balance equations in terms of dimensionless variables?

For more detail I recommend consulting

p338 - 339 of 'Transport Phenomenon' by messers Bird, Stewart and Lightfoot.

p310 - 313 of 'Introduction to Heat Transfer' by messers Incropera and DeWitt

 

[AlephZero]

The Stanton Number (the reciprocal of the Prandtl No)

Not qute. St = Nu / (Re Pr).

 

[Studiot]

Not qute. St = Nu / (Re Pr).

I think that depends upon your authority.

That is also why I gave two references. The second reference has a detailed description of your definition also calling it "a modified Nusselt No".

Either way it is about comparing the thermal to diffusive driving force for heat transfer in a fluid.

We use reciprocal numbers in this case because the Prandtl No is often near unity.