Temperatures and velocities

Boundary layer:

Boundary layers are the outer layers of a fluid (gas or liquid) on which the wall has an effect. Outer layers are localised areas. In the case of convection a distinction is made between temperature boundary layer and velocity boundary layer.

Temperature boundary layer:

In convection there is an exchange of heat between a surface and the surrounding fluid. This exchange of heat can be perceived as a temperature difference. In order for convection to occur, there must be a temperature difference between the surface and the surrounding fluid.

The boundary layer is as thick from the surface as it takes until the ambient temperature is reached. The thickness of the boundary layer can vary. Depending on the location and geometry of the body, as well as flow velocity, it is more or less pronounced.

Velocity boundary layer:

The velocity of a fluid around a body depends on a number of factors. However, an independent common feature exists in the first layer, which wets the surface of the body.

In this first layer of the fluid is the so-called no-slip condition. The fluid is practically stationary at the surface. This is why, for example, it is impossible to clean dust of glasses by blowing them.
The other layers slide in parallel to this adhesive layer.

The thickness of the boundary layer is reached where 99% of the undisturbed flow velocity is present. This undisturbed state can be found at a sufficient distance from the undisturbed surface.

Free convection:

The influence of the flow around the wall with free convection is only dependent upon the added heat and the rising fluid. The fluid always flows up due to the density change (water between 0...4°C is an exception).

Perpendicular to the wall, the heat is passed through the layers by heat conduction.

The image shows a vertical plate which at increased surface temperature (TW) dissipates heat to the environment (Tamb).

On the right in the image are magnified extracts from the top and bottom section.
Temperature distribution (left) and velocity distribution on the surface are shown at these extracts.

Forced convection:

Since in forced convection the flow velocity is generated by a technical device (e.g. a fan), the heat-dissipating body is subjected to incident flow at an even velocity.

The non-slip condition means the fluid is decelerated to zero at the surface. The higher velocity of the flow means the velocity drop in the fluid near the wall is much greater than in the case of free convection.

At the same time the outflowing layers give off heat. Consequently, a larger temperature gradient is generated in the vicinity of the wall, which means a greater equalisation effort for the heat. The heat transfer increases.

How well or how poorly the heat transfer of a surface works depends on the boundary layers, the given geometry and the fluid. All of the factors are reflected in two variables:

The heat transfer coefficient 'Alpha':
This indicates how large the heat flux that is transferred per area and temperature difference.

The Nusselt number 'Nu':
This is a dimensionless value and indicates the improvement of the heat transfer compared to pure heat conduction of the non-moving fluid.

Both parameters are linked to each other via the variable of the relevant geometry.