January 1970 Dimensionless Numbers in Heat Transfer
It is almost impossible to read an article or listen to a lecture on heat transfer without hearing names like Reynolds. Nusselt, Rayleigh, etc. These names refer to very specific dimensionless numbers that are used to characterize and classify the heat transfer problems. This article attempts to explain the meaning and significance of these numbers and help you to get used to them.
But first, why do we need dimensionless numbers anyway? Well, we actually don't need them but they are useful tools. The nature itself does not have a clue about these numbers. It is not like the air says to itself " boy,my Reynolds number is exceeding 2500 and I am in a pipe so I better switch to my turbulent mode or all the fluid dynamics textbooks will be wrong". We have invented dimensionless numbers to be able to take our knowledge from experimenting with one system to learning about another system with different dimensions. If I have come up with some neat formula for calculating the pressure drop in a 2 inch pipe, can I use that formula for a 4 inch pipe? In a way, we are trying to get rid of dimensions in order to extend our knowledge beyond its source of acquisition. Mr. Osborne Reynolds experimented with pipes of different diameters and discovered that, regardless of the pipe diameter, if the ratio of UD/ exceeds 2500 or so, the flow no longer stays nice and laminar. This ratio is what we call Reynolds number and is probably the most commonly used dimensionless group in fluid dynamics.
Dimensionless numbers allow us to experiment with model cars, airplanes and ships and predict the behavior of the big thing under actual conditions. All we have to establish is to make sure that there is similarity between the model and the actual thing. But, this is beyond the scope of this article.
The Dimensionless numbers we will describe in this article are the most common numbers used in heat transfer:
1. Reynolds Number
2. Nusselt Number
3. Prandtl Number
4. Grashof Number
5. Rayleigh Number