Whether you want to keep heat in or keep it out, understanding thermal resistance helps.

    While not one of the more confusing concepts in physics, this can get tricky when it changing from one form of energy to the next.

    For challenging conversions, try our thermal resistance calculator. To get a break down of the basics and the typical formulas and calculations used by several analogies, check out the comprehensive Q&A below.


    What is thermal resistance?

    Thermal resistance can be simply described as the amount of temperature change across a surface.

    In this instance, a temperature change is noted as a decrease in heat energy as it is absorbed by the material.

    The opposite of thermal resistance is thermal conductance. This is how much temperature or heat energy is gained across a substance.

    The amount of heat lost through a surface can be calculated by knowing how much heat is lost through a specific substance.

    You measure the thickness of the substance and then calculate the heat change.

    This is often done in 2-dimensional structures with the assumption that size in width matters. The total volume of the substance is unimportant.

    This is because heat, like any energy, takes the path of least resistance to the point beyond.

    How is thermal resistance used in engineering?

    An important takeaway from thermal resistance work is that we're talking about a transfer of energy, not an elimination.

    The total amount of energy in the system remains the same, it just gets divided up and stored.

    Thermal Conductivity

    So, let's start with defining our terms. We start by working with the following formula for thermal conductivity:

    k = q * L / ΔT.

    That is, thermal conductivity (k) is equal to the heat flow (q in Watts/meter squared) multiplied by the thickness of the material (L) over the change in temperature (°T).

    This heat transfer equation tells us how energy gets moved through a material without resistance. Understanding this principle helps when we start with resistance.

    Thermal Resistance

    Now, we move the next equation:

    R = ΔT / q = L / k

    Resistance (R) is equal to the change in temperature divided by the flow rate (again in W/m2).

    This will also be equal to the thickness of the material divided by the conductivity of that material. So you need to know the conductivity of a material to understand it's resistance.

    That isn't too confusing as you need to understand the speed potential before a speed limit makes sense.

    You can find the known conductivity of a substance through various manuals or parts catalogs.

    Next, we'll look at the analogies for engineering issues that require an understanding of thermal resistance. We'll note the differences in their resistance formula and the resistance units.

    What is the ohm's law analogy?

    Currently, the most common place to see a discussion of thermal resistance is in electronics. So for that, we need to go to Ohm's Law:

    V = I * Relec

    This is the voltage (V) equal to the current (I) multiplied by the resistance (Relec for electrical resistance).

    Unlike in standard engineering, where understanding the heat resistance is often about keeping things at a steady temperature, in electrical work you have to consider both the temperature and the loss of power.

    You can certainly opt to keep something cool by insulating it heavily. But if you need power to flow, that won't do you much good.

    Flow Of Energy Across A System

    When the flow of energy across a system is required, and the temperature loss or gained must be controlled, you aren't looking at resistance in the form of thickness.

    You need to both understand the conductivity of the material and also the configuration.

    A short wire that is really thick will have less resistance than a very long thin wire.

    So we need to consider the heat flow (Q) and its direct relation to the thermal conductivity of our material (k) which we multiply by the area (A) and further modify that by the change in temperature (ΔT) over the change in distance (Δx).

    As an equation, it looks like this:

    Q = k * A * ΔT / Δx

    Remember that an analogy is an imperfect comparison. While these formulae work well for their intended purpose, heat and electricity behave differently in physical spaces.

    What is the fourier's law analogy?

    The last of the basics to go over is Fourier's Law.

    This rectifies the missing piece you may have noticed in our first set of equations that were pointed out in Ohm's equations. We need to calculate for the area of any material, not just the thickness.

    We'll use a derived version of Fourier's Law that functions with constant parameters to keep it simple.

    Rθ = x / A * k

    This gives us the relationship between the absolute thermal resistance (Rθ) and the length of our material (x) which is divided by the area (A) and multiplied by the conductivity (k) as we've seen before.

    Heat energy will try to spread out across any surface it comes into contact with. This is unlike an electrical current, which takes the shortest possible path to complete a circuit.

    Even though heat will dissipate across a whole surface, it still moves a distance over time. This means that a long piece of metal in contact with a flame will be cool at the opposite end but will still be quite hot across the width.

    The transfer of heat from one surface to another will prevent a total heating of a material across its entire area. This is because the heat is still moving.

    If heat were to have no place to go put into the resistance material, the entire material would eventually normalize at a temperature.

    Bottom Line

    Understanding any concept starts with the basics. There will always be exceptions and further complexity to find.

    A solid grasp on the fundamentals makes adapting to these real-world changes easier to do and makes finding mistakes intuitive.

    For help converting between thermal resistance units, it helps to work with our thermal resistance calculator.

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