Heat Conduction Through a Wall: Fourier's Law Simulator
Change a wall's thickness, area and material, or stack layers of brick and insulation in series, and watch the heat flow and temperature gradient update live using Fourier's law.
Set the hot-side and cold-side temperatures and pick a wall material. Turn on multi-layer mode to stack up to three materials (like brick + insulation) and watch how much adding insulation cuts the heat loss.
About the Heat Conduction Through a Wall: Fourier's Law Simulator
Free heat conduction through a wall: fourier's law simulator. Change a wall's thickness, area and material, or stack layers of brick and insulation in series, and watch the heat flow and temperature gradient update live using Fourier's law. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for engineering, the heat conduction through a wall: fourier's law simulator runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Change a wall's thickness, area and material, or stack layers of brick and insulation in series, and watch the heat flow and temperature gradient update live using Fourier's law. Use it to explore engineering ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Heat Conduction Through a Wall: Fourier's Law Simulator
- Use the controls to change Hot-side temperature, Cold-side temperature, Cross-sectional area, Surface film coefficient h, Electricity rate, and more. The simulation reacts instantly.
- Press "Reset" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Set a single copper wall and a single fiberglass wall of the same thickness and area, and compare the heat transfer rate Q.
- Turn on multi-layer mode and build a wall of brick plus a thin layer of fiberglass insulation. Watch how much Q drops compared with brick alone.
- With multi-layer mode on, make the insulation layer thicker and thinner and see how much of the total resistance it controls even when it is much thinner than the brick layer.
- Increase the hot-side to cold-side temperature difference and check that Q scales in direct proportion, exactly as Fourier's law predicts.
- Toggle the surface air film checkbox on and off and see how much Q and the seasonal energy-cost estimate change for the same wall.
- Compare the seasonal energy-cost estimate for a brick-only wall versus brick plus a thin fiberglass layer, at the same electricity rate.
Key ideas you can learn
- Steady-state 1D conduction follows Fourier's law: Q = kA(T1-T2)/L, where k is the thermal conductivity of the material, A is the cross-sectional area, and L is the thickness.
- Thermal resistance R = L/(kA) plays the same role as electrical resistance: a bigger R means less heat gets through for the same temperature difference.
- When layers are stacked (like brick plus insulation), heat has to cross each one in series, so the resistances simply add: R_total = R1 + R2 + R3, and Q = ΔT / R_total.
- A material with a very low thermal conductivity (like fiberglass insulation, k ≈ 0.04 W/m·K) can add far more resistance in a few centimeters than many meters of a good conductor like copper or steel.
- Each layer's own temperature drop is proportional to its own resistance: the layer with the highest resistance always carries the biggest share of the total temperature difference, even if it is the thinnest layer in the wall.
- Real walls lose heat by convection at each surface too, not just conduction through the material: a thin film of still air clings to every surface with a typical film coefficient h ≈ 10 W/m²K, adding a surface resistance R = 1/(hA) in series on both the hot and cold face.
- Multiplying the steady heat-loss rate Q by time and a typical electricity rate turns the abstract W/m²K numbers into a real cost, which is a quick way to see why upgrading insulation often pays for itself over a heating season.
Where this is used in the real world
Building insulation, refrigerator and oven walls, pipe lagging, spacecraft thermal protection tiles, and industrial furnace linings are all designed using this same steady-state conduction and thermal-resistance-in-series analysis to control how fast heat is gained or lost.
Who is this simulation for?
Engineering and technology students, makers, robotics clubs and teachers of design and technology. It gives a hands-on feel for how machines behave before you build a real one.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
Why does adding insulation cut heat loss so much more than adding more brick or concrete?
Because insulation has a much lower thermal conductivity, so a thin insulation layer already adds a large thermal resistance. Since resistances in series simply add, that one thin low-k layer can dominate the total resistance and choke off most of the heat flow, while a thick layer of a good conductor barely slows it down.
What is the difference between thermal conductivity (k) and thermal resistance (R)?
Thermal conductivity k is a property of the material itself (how easily it conducts heat, in W/m·K). Thermal resistance R = L/(kA) also depends on how thick and how wide the actual piece of material is, so the same material can have a high or low resistance depending on its shape.
Why is the temperature line straight through each layer but bends at the layer boundaries?
Within a single uniform material at steady state, the temperature drops at a constant rate, so it is a straight line. At the boundary between two different materials the slope has to change because a different k means a different temperature drop per unit of thickness for the same heat flow.
What is the surface air film (convection) toggle doing?
It adds a small extra resistance, R = 1/(hA), on the hot and cold faces of the wall to represent the still air that clings to any real surface, in series with the wall's own conduction resistance. With it on, R_total = R_film,hot + R_wall + R_film,cold, so Q is a little lower than pure conduction alone would predict, which matches how real buildings actually behave.
How is the energy-cost estimate calculated?
It multiplies the steady heat-loss rate Q by an assumed 120-day (2,880 hour) heating season to get kWh, then multiplies by the editable electricity rate to get an approximate cost. It is meant as a rough, order-of-magnitude teaching estimate, not a real utility-bill prediction, since real weather and indoor temperatures vary.
Is the Heat Conduction Through a Wall: Fourier's Law Simulator free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Heat Conduction Through a Wall: Fourier's Law Simulator work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.