Numerical simulations are typically validated either experimentally or analytically, using simplified benchmark cases that can be solved with classical methods.
This study starts exactly from that point:
Can the temperature field obtained from a 2D thermal simulation be validated analytically?
Under the same boundary conditions, we examined two different façade scenarios. To model heat transfer through the building envelope, boundary conditions were defined as 20°C indoor temperature with 60% relative humidity (RH) and -5°C outdoor temperature with 80% RH.
Scenario 1: A 500 mm thick reinforced concrete wall.
Scenario 2: The same 500 mm wall with an additional 50 mm stone wool insulation layer.
First, we established the analytical solution using the layered thermal resistance method, and then solved the same problem using a 2D thermal simulation to compare the results.
The outcome was quite clear.
For the reinforced concrete only case:
- U-value: 2.58 W/m²K
- Internal surface temperature: 11.6°C
- External surface temperature: -2.42°C
For the reinforced concrete + stone wool case:
- U-value reduced to 0.563 W/m²K
- Internal surface temperature increased to 18.2°C
- External surface temperature: -4.44°C
- Heat flux decreased from 64.5 W/m² to 14.1 W/m², corresponding to approximately 78% reduction
In other words, the stone wool layer provided a highly effective thermal insulation.
When we examine the simulation results, we observe that the outputs match the analytical calculations almost exactly for both scenarios. The internal surface temperature, external surface temperature, and overall heat transfer coefficient are consistent with the analytically derived values.
The key takeaway is this:
The analytical solution and the simulation validate each other.
This means we are not only looking at visually appealing temperature contours, but at a model that has been verified against physical equations. This is a critical step before moving on to more complex 2D/3D junctions, thermal bridges, and real façade details.
The visual results also tell a compelling story. In the uninsulated concrete case, the temperature gradient is distributed across the entire wall thickness. In contrast, when insulation is added, the gradient is largely concentrated within the insulation layer. In other words, the low-conductivity layer absorbs most of the thermal resistance, allowing the concrete mass to remain much closer to indoor temperature. The result is not only a lower U-value, but also a significantly warmer internal surface.
Another critical outcome of this comparison is the dew point behavior.
Assuming indoor conditions of 20°C and 60% RH, the dew point temperature is approximately 12.0°C. This means that if the internal surface temperature drops below this value, condensation—and therefore mold risk—can occur.
From both analytical and simulation results:
- In the uninsulated concrete scenario, the internal surface temperature is 11.6°C, which is already below the dew point. This indicates a high risk of condensation.
- In contrast, in the insulated scenario, the internal surface temperature rises to 18.2°C, well above the dew point.
This clearly shows that insulation not only reduces heat loss, but also eliminates condensation risk, leading to a healthier and more durable building envelope.
This simple comparison reminds us of an important principle:
The true value of simulation lies in how well it aligns with analytical physics.
Colorful contours only become meaningful when they are backed by equations.
For anyone working on façade performance, building physics, and energy efficiency, the key mindset is:
Validate first, then refine.
