Nusselt Number dimension question

In summary, The Nussult number (Nu) is calculated by dividing the heat transfer coefficient (h) by the diameter (D) of the pipe. The dimensions of k, the thermal conductivity, are expressed in terms of mass (M), length (L), time (T) and temperature (\theta). The units for h are J/(m2 hr C) and potentially could be expressed as W/(m2 K). The Nussult number is dimensionless, so the units of k should be obvious. Pi theorem can also be used to find the dimensions of k.
  • #1
Jasones
2
0
So, in

Nu=[itex]\frac{hD}{k}[/itex]

h is the heat transfer coefficient, and D is the diameter of the pipe in which heat transfer takes place...

..but what are the dimensions of k in terms of mass (M), length (L), time (T) and temperature ([itex]\theta[/itex])?

So far, I've worked out that the units for h are J/(m2 hr C), but I'm having difficulty expressing k in terms of what is given.

Am I wrong is thinking that J/(m2 hr C) can be expressed as W/(m2 K)? I'm thinking that this is relevant to the end units of k, but I am unsure if the dimensions are correct.
 
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  • #2
The Nussult number is dimensionless, so if you already know the units of h and D, then the units of k should be obvious: J/(m hr C)
 
  • #3
We could do some major dimensional analysis with this to prove it, but I really don't feel like it. I'm guessing you've done the old pi theorem already though?
 

FAQ: Nusselt Number dimension question

What is the Nusselt Number dimension?

The Nusselt Number dimension is a dimensionless quantity used in heat transfer to characterize the ratio of convective to conductive heat transfer across a boundary. It is defined as the ratio of the convective heat transfer coefficient to the conductive heat transfer coefficient.

How is the Nusselt Number dimension calculated?

The Nusselt Number dimension can be calculated using the following formula: Nu = hL/k, where h is the convective heat transfer coefficient, L is the characteristic length, and k is the thermal conductivity of the fluid.

What is the significance of the Nusselt Number dimension?

The Nusselt Number dimension is significant because it indicates the efficiency of heat transfer between a fluid and a solid surface. A higher Nusselt Number indicates a more efficient transfer of heat, while a lower Nusselt Number indicates a less efficient transfer.

In what situations is the Nusselt Number dimension used?

The Nusselt Number dimension is commonly used in situations where there is convective heat transfer, such as in heat exchangers, flow over a surface, and natural convection. It is also used in the analysis of heat transfer in liquids and gases.

How does the Nusselt Number dimension relate to other heat transfer coefficients?

The Nusselt Number dimension is closely related to other heat transfer coefficients, such as the Prandtl Number and the Reynolds Number. It is often used in conjunction with these coefficients to analyze and predict heat transfer in various systems.

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