What is sommerfeld number?

The Sommerfeld number is a dimensionless value used in fluid mechanics to describe the ratio of the thermal boundary layer to the hydrodynamic boundary layer on a heated or cooled surface. It is named after the German physicist Arnold Sommerfeld.

The Sommerfeld number is calculated as:

S = λ/Dh

Where λ is the thermal conductivity of the fluid, and Dh is the hydraulic diameter of the channel or pipe through which the fluid is flowing.

The Sommerfeld number is related to the Nusselt number and the Reynolds number, which are also commonly used in fluid mechanics. A high Sommerfeld number indicates a larger thermal boundary layer and a smaller hydrodynamic boundary layer, which is typically observed in situations where heat transfer is the dominant process. A low Sommerfeld number indicates a smaller thermal boundary layer and a larger hydrodynamic boundary layer, which is typically observed in situations where fluid flow is the dominant process.

In practical applications, the Sommerfeld number is often used to determine the heat transfer coefficient from a heated or cooled surface, which is important for designing heat exchangers, refrigeration systems, and other thermal management systems.