Heat Transfer Conduction Calculator + Formula, Examples & Applications

Your linear actuator motor is running hot, and you need to figure out how much heat actually flows through that aluminium mounting plate into the chassis. That's a conduction problem — and it's one of the most common thermal questions we see in motion system design. This calculator uses Fourier's Law to give you the heat flow rate in watts and BTU/hr, plus the thermal resistance of your material. Just pick a material, enter thickness, area, and temperature difference, and you'll get answers you can design around. We've included worked examples, application notes, and a full formula breakdown below.

What Is Heat Transfer by Conduction?

Conduction is heat moving through a solid material from a hot side to a cold side. The rate depends on the material's thermal conductivity, its thickness, the contact area, and the temperature difference across it.

Simple Explanation

Think of a metal plate as a pipe for heat — wider pipe and shorter length means more flow. A material with high thermal conductivity (like aluminium) is a fat pipe. A material with low conductivity (like ABS plastic) is a pinhole. The bigger the temperature difference between the 2 sides, the harder heat pushes through — just like voltage drives current through a resistor.

Heat Transfer (Conduction) Calculator

🎥 Video — Heat Transfer (Conduction) Calculator

How to Use This Calculator

Getting a result takes about 15 seconds. Here's the process:

1. Select your material from the dropdown. The calculator auto-fills the correct thermal conductivity value. If your material isn't listed, choose "Custom" and enter k manually.
2. Enter the material thickness in inches. This is the distance heat has to travel through the solid — for a mounting plate, it's the plate thickness.
3. Enter the surface area in square inches. This is the contact area through which heat flows, not the total surface area of the part.
4. Enter the temperature difference in °F between the hot side and the cold side. If you know your motor housing runs at 160°F and the chassis sits at 120°F, ΔT is 40°F.
5. Hit Calculate. You'll get heat flow in watts and BTU/hr, plus the thermal resistance of that material path. Lower resistance means a better heat path.

Heat Transfer (Conduction) Formula

Everything in this calculator comes from Fourier's Law of heat conduction — the foundational equation for steady-state heat flow through a solid:

Where Q is the heat flow rate in watts. To convert to BTU/hr:

Thermal resistance — the key design number that tells you how hard it is for heat to get through:

And the unit conversions the calculator handles for you:

Simple Example

Engineering Applications

Actuator Motor Heat Management

Conduction is how heat moves through solid material — the mounting plate between a hot actuator motor and a cold chassis is a textbook conduction problem. Every linear actuator generates waste heat in its motor, and that heat needs to go somewhere. If the motor sits on a thick steel plate with minimal contact area, thermal resistance climbs and the motor runs hotter. We see this cause premature failures in high-duty-cycle applications all the time. The fix is usually straightforward: increase the contact area, choose a more conductive material, or reduce the material thickness between the heat source and the heat sink.

Why Aluminium Wins for Heat Spreading

Aluminium is the best practical choice for heat spreading in motion system designs. At 205 W/m·K, it conducts heat roughly 4 times better than mild steel and about 12 times better than stainless steel. Yes, copper at 385 W/m·K beats it handily — but copper costs significantly more, weighs more, and is harder to machine. For actuator mounting brackets, electronics enclosures, and heat sink plates, aluminium gives you the best balance of thermal performance, weight, machinability, and cost. We use it extensively in our own product designs for exactly these reasons.

The Thickness Relationship

Thinner material conducts more heat — halve the thickness and you double the heat flow rate. This is one of those relationships that catches people off guard. If you're designing a mounting plate and you want maximum heat transfer, make it as thin as structural requirements allow. Of course, you can't sacrifice mechanical strength — but the point is that a 0.125-inch aluminium plate transfers twice as much heat as a 0.25-inch plate, all else being equal. That's a free thermal upgrade if the thinner plate still meets your load requirements.

Plastic Enclosures Are Near-Insulators

Here's one that surprises a lot of people. ABS plastic has a thermal conductivity of just 0.17 W/m·K — that's roughly 1,200 times worse than aluminium. If your control electronics sit inside a plastic enclosure, you're relying almost entirely on convection (air movement) and radiation to get heat out. Conduction through the enclosure walls is doing almost nothing for you. This matters for actuator controllers, relay boxes, and any electronics in sealed enclosures. If heat is a concern, consider an aluminium enclosure or at least aluminium mounting plates that create a conductive path to the outside.

Thermal Resistance — The Design Number That Matters

Thermal resistance R is the single most useful number for comparing heat paths. Lower R means a better heat path — think of it like electrical resistance, but for heat instead of current. A good conductive path might have R of 0.01 °C/W, meaning for every watt of heat flowing through, the temperature only drops 0.01°C across the material. A bad path — like an air gap or plastic wall — could have R of 100 °C/W or more. When you're designing a thermal management system, you calculate R for each element in the heat path and add them up, just like resistors in series. The element with the highest R is your bottleneck.

Advanced Example

Frequently Asked Questions

Thermal management doesn't have to be complicated. Start with the conduction path — it's the one you have the most control over in your mechanical design. Pick the right material, size the contact area, and keep the path short. If the numbers from this calculator show your mounting setup can handle the heat, you're in good shape. If they don't... now you know exactly what to change.

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