STL View Factor
- Francesco Lena
- 1 day ago
- 9 min read
This blog post will be a little different. Sometimes I'll not only show travels and photographs, but also some of my experiences with engineering and development.
In 2019 I began my internship at LNLS, the synchrotron light laboratory of CNPEM, in Campinas, where I worked until 2024. Among the various projects in the beamlines where I worked – laboratories that use synchrotron radiation to study matter – one theme was recurrent: Cryogenics.
What is cryogenics?
Cryogenics is the branch of physics and engineering that studies the production and behavior of materials at extremely low temperatures. Although there is no strict definition, the cryogenic regime is generally considered to be for temperatures below -150°C (123 K). It is a domain where gases that we are accustomed to breathing, such as nitrogen and oxygen, become liquids, and the properties of materials can change drastically.
In this context, the very laws of physics that govern our world begin to be a little different. Not in a constitutive sense, of course, but things we take for granted seem to stop working. The concept is essentially simple: a cold source, be it a cryostat, a heat pump, or a cryogenic liquid bath (e.g., nitrogen or helium), cools a chain of components leading to the object of interest.
In the synchrotron context, this object is usually the sample of interest or some special optic subjected to high thermal loads (e.g., silicon mirrors or monochromator crystals). Since we are dealing with very low temperatures, where even atmospheric oxygen condenses (approx. 90K), we cannot work in a normal atmosphere. Often, we cannot even be in an atmosphere (due to the absorption of the X-rays themselves), so a vacuum is often mandatory.
The Challenge of Thermal Contacts
This is where the first problem arises: thermal contact. We don't stop to think about it in our daily lives, but every part in contact with another has varying levels of imperfections. These imperfections on the surfaces, sometimes pressed against each other, result in a heterogeneous distribution of physical contact. In our atmospheric world, this isn't even perceptible. Speaking of heat exchange by conduction, small distances without direct contact between these surfaces are filled with air. Even though it's a very poor thermal conductor, this layer of air is so thin, on the order of a few micrometers, that thermal contact is guaranteed. Imagine it as if all the surfaces you know were covered by a "thermal paste," only made of air.
In a vacuum, this is gone. These small gaps no longer contribute to heat exchange. Suddenly, any contact between the parts becomes a major problem. The use of thermal interface materials (TIMs ) becomes mandatory. For cryogenics, we cannot use simple thermal pastes or greases, but rather other soft metals that deform under the pressure of the clamping between the surfaces. Silver or indium foil – an extremely malleable metal – is commonly used.
From a design perspective, these surfaces become critical, as they can represent significant thermal resistance, resulting in large "deltas" between parts. Maximizing contact areas and optimizing the clamping with TIMs is mandatory.
With the contact resolved, another problem arises: thermal conduction itself. In the ambient temperature world, vibrations quantized in phonons dominate conduction transfers. As temperatures decrease, these phonons represent less and less of the material's conductivity, which then becomes dominated by electronic conduction. Suddenly, the problem of thermal conduction becomes intertwined with the electrical properties of materials – and small impurities become quite significant. I will delve into this topic further at another time.
The Invisible Source of Heat: Radiation
Poorly behaving contacts, low extraction capacity, and poor heat conduction are part of the challenge. If there were no heat, there would be no concern. However, there is an invisible source: radiation.
As the surrounding environment gets warmer, a radiative heat flow in the form of infrared waves will be present, worsening the situation by transporting heat to the cold parts. This exchange is governed by Stefan-Boltzmann's Law, which states that the total power radiated per unit area is proportional to the fourth power of the temperature ( P ∝ T^4 ). This means that small temperature differences can generate large heat flows, especially when there is a large gradient between the environment (300K) and the cryogenic part.
P = ϵ ⋅ σ ⋅ A ⋅( T^ 4− Also^ 4)
Where:
P is the radiated power (Watts);
ϵ is the emissivity of the surface (0 to 1);
σ is the Stefan-Boltzmann constant (5.67×10−8W/m2*K4);
A is the surface area (m2);
T and Tamb are the body and ambient temperatures (Kelvin).
This relationship governs what we call a black body. A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle. As a thermodynamic consequence, it is also the perfect emitter of thermal radiation.
However, in practice, the perfect black body does not exist, as all surfaces are capable of reflecting, to some extent, part of the radiation that reaches them, or even preventing some of it from being emitted. This relationship is simplified by what we call emissivity (ε ) . Emissivity is a dimensionless factor that varies from 0 to 1, representing the ratio between the radiation emitted by a real surface and that of a black body at the same temperature. The lower the emissivity, the less heat the surface exchanges through radiation.
A classic and extreme example of this application is the James Webb Space Telescope (JWST). Because it observes the universe in the infrared spectrum (which is essentially heat), its instruments need to operate at extremely low temperatures, below 50 K (-223°C), to avoid being "blinded" by their own heat. To achieve this, in addition to a massive five-layer sunshield, its primary mirrors are made of beryllium and coated with a very thin layer of pure gold. Gold is chosen not for aesthetics, but because it has exceptional reflectivity in the infrared (very low emissivity), ensuring that incident heat is reflected and not absorbed by the mirrors, keeping the optics cool and stable.
Therefore, controlling emissivity is important. With it, we can limit how much of the heat radiated into the environment will be coupled and will actually heat the parts we want to keep cool. Generally, what we can do is simply cover the surface of the parts – usually metallic – with a thin film of another metal with very low emissivity. There is nothing better than gold for this: a metal with low emissivity at cryogenic temperatures (<5%), which does not oxidize easily, remaining stable, and which can be deposited by inexpensive methods such as electrochemical deposition, CVD, or even foil.
Radiation Shields
In addition to treating surfaces, a key strategy is the use of radiation shields . These are physical barriers, usually made of polished (or gold-plated) copper or aluminum, placed between the hot source (the environment or vacuum chamber) and the cold part. The shield intercepts thermal radiation from the environment and reaches an intermediate temperature. By doing so, it re-radiates only a fraction of the energy to the cold part, drastically reducing the final thermal load. In complex systems, multiple shields can be nested like layers of an onion.
By controlling the materials, contacts, and emissivities, we can understand the problem well and design systems to achieve the desired temperatures. However, in the simplified Stefan-Boltzmann relationship, we only consider the heat exchange between the part and the environment. In practice, several parts make up a system, each at a different distance, temperature, and even worse, with a different geometry. Therefore, modeling the heat transfer between multiple parts is essential to understanding the problem. We can rewrite the relationship by considering a geometric factor called the View Factor .
The Sighting Factor ( F 1→2) represents the fraction of radiation that leaves surface 1 and directly reaches surface 2. It is a purely geometric value that depends on the orientation, size, and distance between the surfaces involved.
With the Sight Factor known, we can finally calculate the net heat exchange by radiation between two gray (with emissivity ϵ <1) and diffuse surfaces. The equation, often represented by an electrical analogy of resistances, is given by:
This formulation is extremely powerful because it separates the geometric problem ( F 1→2) from the material properties ( ϵ ), allowing engineers to optimize geometry and materials independently.
For simplified, flat surfaces, it's possible to solve the sighting factor analytically. However, the problem becomes extremely complex when we move to the real world, where irregular, three-dimensional geometries represent the parts. Thus, numerical methods are necessary. Techniques such as the Monte Carlo Method (Ray Tracing) are frequently used, where millions of virtual "rays" are randomly fired from the surfaces to statistically calculate how many hit the target, allowing the solution of arbitrary geometries.
During my time working at LNLS, we developed some tools based on Ansys' FLUENT finite element software. Essentially, we solved the problem of heat transfer between two parts and, knowing the boundary conditions, it was possible to extract the line-of-sight factor between them. This process, however precise, is extremely slow, with each simulation easily taking more than an hour from setup to results. This makes an iterative workflow impossible, hindering the process of optimizing geometries.
Inspired by this problem, I created the STL View Factor tool, initially in Matlab, capable of simulating and calculating the line-of-sight factor between two or more parts in a lightweight, fast, and accurate way. Recently, using a good amount of generative AI, I ported this tool to a web version. Basically, the user can upload STL files representing the bodies involved in the heat exchange (Emitter, Receiver, and Obstacle). The interface allows adjusting the positioning of the parts, defining the unit system, and configuring the number of radii for the simulation. All this with real-time 3D visualization in the browser, without the need for complex installations.
Regarding its physical operation, the tool uses the Monte Carlo method for ray tracing. Unlike analytical methods restricted to simple geometries, Monte Carlo fires thousands of virtual "photons" from the emitting surface. The emission follows a probabilistic distribution based on Lambert's Law, where the direction of the rays is weighted by the cosine of the angle with the surface normal (pΩ( ω ) = cos θ / π ). The origin point of each ray is sampled uniformly over the mesh area of the emitting body. For each ray fired, the algorithm calculates the intersection with other surfaces using the Möller–Trumbore algorithm.
The Aiming Factor ( FA → B ) is then statistically approximated by the ratio between the number of rays that hit the target ( Nhits ) and the total number of rays fired ( Ntotal ):
FA → B ≈ Ntotal / Nhits
The tool addresses three main calculation scenarios:
Between Two Bodies (2 Parts): Calculates the fraction of radiation that leaves Body A and reaches Body B. Rays that collide with Body A itself (self-occlusion) are discarded, and only those that directly hit B are counted.
Between Two Bodies with Obstacle (2 Parts with Obstacle): Adds a third body to the simulation that acts as a barrier. If a beam strikes the Obstacle before reaching Body B, it is counted towards the obstacle's line-of-sight factor ( FA → Obs ) and does not contribute to FA → B. This is essential for sizing radiation shields.
Part-to-World: Estimates the fraction of radiation that escapes to the infinite environment. Any ray that is not blocked by the geometry of the emitting body itself (self-occlusion) is considered lost to the "World". Useful for calculating overall heat losses.
How to Use the Tool
The tool was designed to be intuitive and run directly in the browser.
Upload Files: Select the STL files for "Body A" (Transmitter) and "Body B" (Receiver). If using obstacle mode, also upload the obstacle file.
Configure Units: Define whether your model was designed in millimeters, meters, or inches. This is crucial for the correct calculation of areas and offsets.
Adjust Position (Optional): If the parts are not aligned correctly at the origin of the STL file, use the "Offset" fields to translate each body independently in 3D space.
Set Precision: Choose the number of rays for the simulation (e.g., 10,000 for quick tests, 100,000+ for accurate final results).
Calculate: Click on "Calculate View Factor" and follow the progress. At the end, the result will be displayed along with the processing time.
Report: You can generate a complete PDF report with the configuration image and the results obtained.
This tool drastically simplifies what previously required heavy engineering software and hours of configuration, facilitating access to complex thermal radiation calculations. However, I must disclaim that this is only a personal project, not intended to be an absolute and precise tool in all cases. I recommend its use as a quick and iterative reference, not as a replacement for more complex finite element software. If you see any problems, or have suggestions for improvement, please get in touch!
The tool is available at the link below:
(Under construction)
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