Heat Transfer Conduction Calculator + Formula, Examples & Applications

If your actuator motor is running hot and you need to estimate how much heat is being conducted through an aluminium plate into a chassis, this is a straightforward conduction problem. Problems like this come up often in motion system work. This calculator is based on Fourier's Law, giving you heat flow rate in watts and BTU/hr, along with the thermal resistance of whatever material you use. Pick a material, enter its thickness, area, and the temperature difference across it. You’ll get numbers you can work with for practical design. There are examples and more details further down.

What Is Heat Transfer by Conduction?

Conduction is the transfer of heat through a solid, from the hotter side to the colder side. The speed of this process depends on the material’s conductivity, how thick the material is, the area of the contact, and the temperature difference you’ve got across it.

Simple Explanation

You can think of a metal plate as a physical path for heat—if the path is wide and short, more heat goes through, just like more water through a wide, short pipe. Aluminium behaves like a wide-open pipe for heat, while a plastic like ABS is more like a pinhole. The bigger the temperature difference, the harder heat “pushes” to move through, similar to how voltage pushes current through a resistor.

Heat Transfer (Conduction) Calculator

🎥 Video — Heat Transfer (Conduction) Calculator

How to Use This Calculator

This isn't complicated. Here’s what you do:

1. Select your material from the dropdown. The calculator fills in the thermal conductivity for standard choices. If your material isn’t there, use “Custom” and enter the value directly.
2. Enter the material thickness in inches. For a bracket or a plate, use the actual physical thickness the heat needs to cross.
3. Enter the surface area in square inches. This should be the area touching both sides that is actually conducting heat—not the total part surface.
4. Enter the temperature difference in °F. Subtract the cold side temperature from the hot side to get ΔT. For example, if one side is 160°F, the other is 120°F, ΔT is 40°F.
5. Hit Calculate. You'll see the heat flow (watts and BTU/hr) and the thermal resistance. If resistance is low, the material is a good heat path. If it’s high, it’s not.

Heat Transfer (Conduction) Formula

This is all based on Fourier’s Law—the workhorse for steady-state conduction through solids:

Where Q is how much heat flows, in watts. For BTU/hr, just multiply by 3.412:

Thermal resistance tells you how much the material slows down heat flow:

This calculator handles the unit conversions, but these are the conversions used:

Simple Example

Engineering Applications

Actuator Motor Heat Management

Whenever you see a hot actuator mounted to a colder chassis, the heat mostly moves by conduction through the mounting plate or bracket. The step that often causes trouble is using a thick steel plate with a small contact area. This ramps up total resistance, so the motor runs hotter. I've seen a lot of early failures traced back to small or poorly-conducting mounting details. The practical fix is to use the largest contact area you can, go for better-conducting materials, or keep that plate as thin as structural strength allows.

Why Aluminium Wins for Heat Spreading

Aluminium is popular in mechanical work for good reason. At 205 W/m·K, it moves heat much faster than mild steel (about 4×), and absolutely dwarfs stainless. Copper is technically better at 385 W/m·K, but it’s heavy, expensive, and awkward to machine for most brackets or enclosures. Aluminium holds a good balance—strong, lightweight, cheaper, and adequate for almost any actuator-mounting job that needs good heat flow.

The Thickness Relationship

Thick material slows heat, thin material helps it move. If you cut plate thickness in half and leave everything else the same, you double your heat transfer rate. If your part can be thinner and still support the load, this is the easiest way to upgrade your thermal path for free.

Plastic Enclosures Are Near-Insulators

Plastics like ABS barely let any heat through—thermal conductivity is less than 1/1,000th of typical metals. If you put electronics in a plastic box, almost no heat leaves by conduction. You're relying mostly on airflow (convection) or radiation. If overheating is on your radar, switch to an aluminium box or at least use an internal plate to get heat to the outer wall.

Thermal Resistance — The Design Number That Matters

Thermal resistance is your main metric for comparing heat paths. Think of it like electrical resistance, only for heat. Lower R means less temperature rise for the same heat flow—better cooling. Every layer in your heat path (metal, interface, etc.) adds up like resistors in series. The highest R usually chokes the system. If you do the math and see a high R somewhere, that's the weak link to redesign.

Advanced Example

Frequently Asked Questions

In practice, thermal management comes down to managing the main conduction path. Choose the right material, give the heat somewhere to go, make the path as short and wide as practical, and let the math confirm you’re on track. If your calculations say it won't handle your motor heat, adjust thickness, area, or material. That way you catch problems before they cause a hardware failure.

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