Heat conduction - flat wall/radial

As already mentioned on the previous page, the conducting cross-section area has a decisive influence on the heat flux.

If a small heat flux is desired, then if possible the heat-conducting cross-section area should be small too.
It is different if a large heat dissipation is desired. In this case the heat-conducting cross-section area should be as large as possible.

The heat-conducting cross-sectional area has an impact on the temperature profile within a body.
Two typical cases are highlighted in order to consider the reasons in more detail.

Flat wall:

The flat wall gives a straight line for the temperature profile. This requires a steady state at a constant heat flux.

On the left the image shows the temperature profile of a multi-layered wall.
The effects of different wall thicknesses and different materials can be seen in the temperature drop over the length.

The same heat flux flows through the entire wall. The heating surface load (heat capacity per area) is constant. It is not the level of the temperature that matters, but the temperature difference.

If the cross-section area of the wall is doubled, then twice as much heat flux is required for the same temperature difference.

If the cross-sectional area changes under a constant heat flux, the temperature drop deviates from the straight line.

Cylindrical wall:

In a cylindrical wall (e.g. the inside of a heated tube) the heat-transferring cross-sectional area increases with the radius. The constant heat flux is spread over an increasing area. The heating surface load falls as the radius increases.

The temperature profile therefore differs from a straight line.

In all processes the temperature difference is the cause of the heat fluxes.

If the direction of the heat flux QA-B changes to QB-A at the same temperature difference (TA-B => TB-A), then the temperature profiles are similar to those shown in the image. The temperature drop through the respective layer remains the same.