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What exactly is this simulator showing? It looks like a colorful grid that changes when I paint on it.
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Basically, it's simulating how heat spreads and settles in a flat object, like a metal plate. The colors represent temperature. When you paint a red "heat source" with the slider set to, say, 100°C, you're adding energy. The simulator then calculates how that heat diffuses until it reaches a steady state where temperatures don't change anymore. Try painting a hot spot and watch the heat bleed into the cooler areas.
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Wait, really? So the blue "cold sinks" I can paint are like holding parts of the plate at a fixed cold temperature?
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Exactly! In practice, a cold sink could be a cooling pipe or the edge of the plate touching ice. The simulator fixes those cells at the temperature you set with the "Cold sink" slider. The "insulator" brush is just as important—it creates barriers heat can't cross. For instance, try drawing an insulating wall between a hot and a cold spot; you'll see a sharp temperature gradient form.
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What does the "Iterations" slider do? When I increase it, the colors seem to smooth out more.
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That's the core of the calculation! The simulator uses a method called Jacobi iteration. Each "iteration" is one step where every cell updates its temperature by averaging its four neighbors. More iterations let the simulation run longer, getting closer to the final, perfectly smooth steady state. If you set iterations to 1 and click "Solve," you'll see just one averaging pass—it's very blocky. Crank it up to see it converge.
At steady state (when temperatures no longer change with time), heat conduction in a solid without internal heat generation is governed by Laplace's equation. This means the net heat flow into any tiny region is zero.
$$\nabla^2 T = \frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial y^2}=0$$
Here, $T$ is temperature, and $\nabla^2$ is the Laplace operator. The equation states that the second spatial derivatives (a measure of curvature) of temperature sum to zero, leading to smooth, harmonic temperature distributions.
To solve this equation numerically on a pixel grid, we use the Jacobi iteration method. We discretize the domain into cells and repeatedly update each cell's temperature based on its neighbors.
$$T_{i,j}^{n+1}= \frac{T_{i+1,j}^n+T_{i-1,j}^n+T_{i,j+1}^n+T_{i,j-1}^n}{4}$$
Here, $T_{i,j}^{n+1}$ is the new temperature at grid position (i,j), calculated as the average of its four orthogonal neighbors' temperatures from the previous iteration step $n$. Cells marked as heat sources, cold sinks, or insulators are held fixed and do not update.
Common Misunderstandings and Points to Note
There are a few key points you should be especially mindful of when starting to use this tool. First, understand that "the simulation results are not absolute temperature values." The "100°C" or "0°C" on the tool are relative benchmarks. In reality, the actual heat generation (wattage) of a source and the thermal conductivity of materials significantly alter the outcome. For instance, the same "100°C" setting will have a completely different thermal impact on the surroundings for a small LED versus a large CPU. Think of this tool as a way to see "relatively where temperatures are high and how heat tends to spread."
Next, be aware of boundary condition setup errors. In this simulator, the four edges of the board are treated as "adiabatic walls" (no heat escapes). However, a real PCB is exposed to air, and building walls are in contact with outside air. Therefore, if heat appears excessively trapped in the simulation, the real-world temperature is likely lower. In practice, figuring out how to model this "heat exchange with the surroundings" is often the most challenging part.
Finally, consider the interpretation of "steady state." The tool calculates a steady state through iteration, but the time it takes for a real product to reach "steady state" is not negligible. For example, a smartphone heats up rapidly right after launching a heavy game, but what you see on a thermogram is the state a moment later. Since the simulation results show the "final stabilized temperature distribution," this tool alone cannot evaluate the risk of transient thermal runaway. Use it as a first step in your basic design process.
Related Engineering Fields
The concepts behind this 2D thermal distribution simulator are actually the very fundamentals of Computational Fluid Dynamics (CFD). To be more specific, analyzing cooling for complex 3D shapes or forced air cooling with fans can be thought of as extending this tool's calculations to three dimensions and coupling them with airflow (fluid equations). For example, optimizing the fin shape of a heat sink is a technology precisely on this extended path.
Furthermore, the "Laplace's equation" used in the calculation appears in electrostatic and magnetostatic field analysis in exactly the same form. In other words, calculating electric potential distribution and calculating temperature distribution are mathematically like siblings. Therefore, if you think of "heat sources" as "positive charges" and "cooling plates" as "negative charges" in this tool, it can also help you intuitively understand how electrostatic fields spread. The reason CAE engineers can relatively quickly master software for different physics fields is due to this mathematical commonality.
Looking at other application fields, subsurface heat conduction and groundwater flow (groundwater flow analysis) also fall under the same equation. Finding isothermal lines in the ground is essentially the same problem as finding isothermal lines on this board. Deeply understanding one tool can unexpectedly reveal a wide world—that's the interesting part of engineering.
For Further Learning
If you get comfortable with this tool and think, "I want to know more," I recommend taking the following steps. First, try searching for introductory books using keywords like "numerical heat transfer and fluid dynamics" or "numerical analysis." An initial goal could be to learn about solvers other than the "Jacobi method" used by this tool, such as the faster-converging "Gauss-Seidel method" or "SOR method." Understanding why they converge faster will give you insight into the depth of computational algorithms.
For the mathematical background, learning the basics of partial differential equations is the best shortcut. Laplace's equation, which falls under the classification of "elliptic partial differential equations," has the elegant property that its solution is determined solely by boundary conditions. To understand this, starting with the one-dimensional heat conduction equation and solving a simple equation like $$ \frac{d^2 T}{dx^2} = 0 $$ by hand is good practice. Once you can solve this, extending to two dimensions will make much more sense.
As a natural next practical topic, moving to "transient (time-dependent) thermal analysis" is a good step. While this tool looks at the state "after things have settled over time," in product design, temperature changes over time, like "one minute after switch-on," are crucial. For this, you need to learn the "heat conduction equation," which adds a time derivative term to Laplace's equation: $$ \frac{\partial T}{\partial t} = \alpha \left( \frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial y^2} \right) $$. Here, $\alpha$ is the thermal diffusivity. Knowing this next step will completely change your perspective on thermal design.