The Prandtl number (most commonly denoted by the symbol Pr) is a dimensionless physical quantity used in fluid mechanics and heat transfer. It defines the ratio of momentum diffusivity to thermal diffusivity in a given medium, meaning it compares how quickly velocity disturbances spread in a fluid compared to temperature. At first glance, it sounds complicated.
In mathematical terms, the Prandtl number is defined as:
Pr = ν / α
where
The Prandtl number indicates how boundary layers behave in liquid or gas flow – for example in heat exchangers or condensers used in heat pumps. In practice, it shows whether momentum or heat spreads faster in a given fluid – which is important when improving devices associated with the heating industry revolution brought about by heat pumps. And not only heat pumps – also less advanced devices.
In practice:
Thanks to this, the value makes it possible to predict the nature of heat transfer in laminar and turbulent flows, and to better match system components in order to maximize efficiency. Seemingly an unnecessary detail, in practice it is another building block in improving heating systems.
As is often the case with such discoveries and phenomena, it is named after one of its first researchers and essentially its discoverer. This was the German scientist Ludwig Prandtl, who lived from 1875 to 1953.
He conducted research on fluid flow, heat transfer, and boundary layers. He introduced a number of concepts into physics that are still used today, mainly in hydrodynamics and thermodynamics. One of them is the Prandtl number, which describes the ratio of momentum diffusivity to thermal diffusivity in a fluid.
Different media have characteristic Prandtl number values:
These differences are extremely important when designing heating, cooling, and industrial systems – depending on the medium they are intended to work with.
The Prandtl number is widely used in engineering calculations, especially in issues related to heat transfer and fluid flow – but rest assured, it is not necessary to know this topic in detail to be a good professional in hydraulics. It is rather knowledge useful for designers.
It is used, among others, in:
It is often used together with other dimensionless numbers, such as the Reynolds number or the Nusselt number.
In the context of heat exchangers, the Prandtl number helps determine the efficiency of heat transfer between the fluid and the heat transfer surface. It affects the thickness of the thermal boundary layer and the selection of appropriate calculation correlations.
By taking the Prandtl number into account, it is possible to design devices more precisely that are more energy-efficient and better suited to operating conditions. This makes it possible to manufacture a heat exchanger that is small yet very efficient – such as today’s plate heat exchangers.
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