What do Rayleigh and Nusselt numbers tell us about heat transfer?

In summary, the Rayleigh number and Nusselt number are important in thermal convection. The Rayleigh number determines when natural convection occurs, while the Nusselt number is used to calculate heat transfer at a solid-fluid interface. They both have different dependencies and interpretations, and are commonly used in different types of convection.
  • #1
billiards
767
16
Hi

Can anyone tell me anything about these numbers. I know the formulae I just want a qualitative description.

As far as I have it the Rayleigh number tells you if you can have convection and how vigorous that convection is, and the Nusselt number tells you how efficient that convection is in transporting heat.

I could well be wrong...

Cheers
 
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  • #2
Check out the following reference:

Natural Convection in Enclosures
Book: Free-Convective Heat Transfer
Publisher: Springer Berlin Heidelberg
Pages: 279-343
 
  • #4
sorry, I had a brain fart ...

Here's something I compiled for work:

Rayleigh Number:
Important in natural (free) convection
Onset of natural convection occurs when the Rayleigh number reaches a critical value (~1700)

Nusselt number:
Ratio of convective to conductive heat transfer across a solid-fluid interface
Used to calculate heat transfer coefficient at the interface
Depends upon Re and Pr in forced convection
Depends upon Gr and Pr in natural convection
Sometimes also interpreted as the dimensionless temperature gradient at the surface.
 

FAQ: What do Rayleigh and Nusselt numbers tell us about heat transfer?

1. What are Rayleigh and Nusselt numbers?

Rayleigh and Nusselt numbers are dimensionless parameters that are commonly used in heat transfer and fluid mechanics to characterize the flow of a fluid. They are named after Lord Rayleigh and Wilhelm Nusselt, two influential scientists in the field.

2. How are Rayleigh and Nusselt numbers related?

The Rayleigh and Nusselt numbers are related through the Prandtl number, which is the ratio of momentum diffusivity to thermal diffusivity. This relationship is expressed as Nu = Ra * Pr^(1/3), where Nu is the Nusselt number, Ra is the Rayleigh number, and Pr is the Prandtl number.

3. What is the significance of the Rayleigh number?

The Rayleigh number is a measure of the relative importance of buoyancy-driven convection compared to other forms of heat transfer in a fluid. A high Rayleigh number indicates that convection is the dominant mode of heat transfer, while a low Rayleigh number indicates that other forms of heat transfer, such as conduction, are more significant.

4. How is the Nusselt number used in practical applications?

The Nusselt number is used to determine the heat transfer coefficient, which is a measure of how well a fluid can transfer heat. It is often used in the design and optimization of heat exchangers, as well as in the analysis of natural convection phenomena such as geothermal energy systems.

5. What factors affect the values of Rayleigh and Nusselt numbers?

The values of Rayleigh and Nusselt numbers are affected by various factors, including fluid properties (such as density and viscosity), temperature gradients, and geometric parameters (such as the size and shape of the system). Additionally, the type of fluid flow (such as laminar or turbulent) can also impact these numbers.

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