All About Thermal Conductivity

Thermal conductivity is one important material property that allows engineers to select the correct material for an application. It defines how easily heat can move through a material. For example, a highly heat-conductive material, like copper, is ideal for a heat sink, whereas a low thermal conductivity material like ceramic is ideal for thermal insulation.

This article will explore the concept of thermal conductivity, how it works, how it is calculated, and various factors that can influence this property. 

What Is Thermal Conductivity?

Thermal conductivity can be defined as how easily a material can transmit heat in the presence of an applied temperature gradient. The thermal conductivity of a material is often determined experimentally. It is used to characterize the thermal transfer behavior of a material at various temperatures. Thermal conductivity is often used to describe whether a material is an insulator or a conductor. In the case of an insulator, the term thermal resistivity is often used to describe how a material resists the flow of heat.  

Thermal conductivity is important because it is a measure of how well a material aids (conducts) or resists (insulates against) the flow of heat. In practice, this allows engineers to select the appropriate material for an application. For example, in a heat exchanger, a good thermal conductor is ideal. For a furnace lining, a good insulator is ideal. 

In 3D printing, thermal conductivity is important for a number of reasons. Firstly, the bed of the 3D printer must be kept hot to ensure that the first layer sticks to it. Bed plates for 3D printing are usually made of aluminum plate with a heating element attached to the underside. Aluminum is a good heat conductor, so a heated aluminum printer bed will transfer heat evenly throughout the print deposition target area. Secondly, thermal conductivity inside the extruder assembly can cause print failures due to heat creep. Finally, thermal conductivity is important as the heat in the hot end must be transferred from the thermistor to the plastic in order to melt it effectively. 

How Thermal Conductivity Works

Thermal conductivity relates to the ability of a material to transfer heat down a gradient from high temperature to low temperature. What we perceive as "heat" when we touch an object is the macroscopic effect of atomic-scale vibrations within the material. When heat energy is absorbed by a material, that energy is transformed into kinetic energy of the atoms. Atoms in solids cannot move around much, so they vibrate. The vibrating atoms directly exposed to the heat energy collide with their neighbors. This transfers the kinetic energy to the neighbors, which then excites atoms even further downstream from the heat source. The vibrations induced by the heat energy move through the material to colder areas, somewhat like a ripple spreading from a pebble hitting the surface of a pond.

Thermal Conductivity of Different 3D Printing Materials

Table 1 below lists the thermal conductivities of a range of 3D printing materials:

Importance of Thermal Conductivity in Laser Cutting and Plastic Injection Molding

Thermal conductivity in laser cutting is important for a number of reasons. First, highly thermally conductive materials need more energy in order for the laser to cut through them. For that reason, materials such as aluminum or copper can be more difficult to cut. Secondly, materials with low thermal conductivity will localize the heat near the cut edge. The uneven heating can result in residual stresses which can cause warping or cracking after the material cools.

Thermal conductivity is important in plastic injection molding to produce quality injection molded parts. It is important that the mold is kept at the optimal temperature during molding and cooled down quickly after molding to reduce cycle time. Molds with high thermal conductivity allow for quick heating and quick cooling to ensure optimal quality and minimal cycle time. 

Thermal Conductivity Formula

Thermal conductivity can be calculated by making use of a simplified form of Fourier's law for heat transfer. It is important to note a few assumptions used when employing this equation:

1. Steady State: Heat transfer can be classified as a “steady state” if the temperature on the hot side does not change. 
2. One-Dimensional Heat Transfer: Heat is transferred in only one direction.
3. Constant Thermal Conductivity: A material's thermal conductivity value will change depending on the temperature. In general, thermal conductivity will increase with increased temperature.

The equation for heat transfer is shown below in Equation 1: 

Equation 1: One-Dimensional, Steady-State Heat Transfer

Where:

k: Thermal conductivity

Q: Heat flux

A: Cross-sectional area

ΔT: The difference in temperature (T1-T2) between the hot side (T1) and the cold side (T2) of the material

d: This refers to the length of the piece of material

The equation can be rearranged such that the value for thermal conductivity is on the left-hand side of the equation as per Equation 2:

Equation 2: Mathematical Formula for Thermal Conductivity

It must be noted that this is not an efficient method of determining a material's thermal conductivity. Thermal conductivity is usually determined experimentally under controlled conditions, according to an internationally accepted standard method. Most material data sheets will indicate thermal conductivity at a specific temperature or in a range of temperatures. 

Examples of Calculating Thermal Conductivity

Thermal conductivity is not calculated but determined via experimental means. However, to illustrate the effect of a material’s thermal conductivity on the heat flux magnitude, three examples are presented below using experimentally determined thermal conductivities of common materials. The plate is assumed to be 1 m thick with a length and breadth of 1 m, and T1 equal to 250 °C and T2 equal to 25 °C. 

Factors That Affect the Thermal Conductivity of Materials

Listed below are some factors that can affect the thermal conductivity of a material:

1. Temperature

With conductive materials like metal, thermal conductivity generally decreases with increased temperature. As the metal heats up, the atoms and phonons will begin to vibrate more vigorously. This will reduce the mean free path for free electrons via a mechanism called electron phonon-scattering. For nonmetals, the relationship between temperature and thermal conductivity is more complex, and rising temperature can either increase or decrease thermal conductivity.

2. Density

Higher density in a  material can generally be related to a higher packing density of atoms within the crystal lattice or molecular structure of a material. This higher packing density will increase heat conductivity by improving the efficiency of heat transfer via phonons or free electrons. 

3. Pressure

When a material is exposed to sufficiently high pressure, there is a possibility that its density can be increased. This can result in an increase in thermal conductivity due to the tighter packing of atoms or molecules. Another potential effect of pressure is a change in the phase of the material, i.e. from a solid to a liquid. This phase change can affect the thermal conductivity of the material.  

4. Composition

The types of atoms, molecules, or ions in a material can affect its thermal conductivity. For example, metals tend to have high thermal conductivity because their electrons can move freely and transfer heat easily. Nonmetallic materials such as polymers or ceramics, however, tend to have lower thermal conductivity due to their more rigid and less mobile molecular structures.

5. Structure

The lattice structure of a material can affect its thermal conductivity because some structures are more efficient at heat transfer than others. For example, materials with larger crystals can transfer heat more effectively as there are fewer grain boundaries that can act as obstacles to the flow of free electrons. In addition to this, the form of the crystal structure can have an effect, for example, FCC (face-centered cubic) structures like those found in copper have better thermal conductivity than BCC (body-centered cubic) structures like those found in iron.

6. Porosity

Porosity refers to the presence of voids or gas pockets within the structure of a material. These voids can be a natural occurrence, deliberately added, or due to poor processing methods. The thermal conductivity through these gas pockets is significantly reduced when compared to the base material. This will then reduce the overall thermal conductivity of the material.

7. Impurities

Impurities within a material can affect thermal conductivity through a mechanism called electron impurity scattering. Impurities can create local anomalies in the electric potential within the crystal lattice. This can impede or deflect the motion of free electrons, thereby reducing the thermal conductivity of a material.

Benefits and Limitations of Thermal Conductivity

Both materials with very high thermal conductivities and those with very low conductivities can provide benefits to an application, depending on whether heat transfer or heat retention is the more important characteristic.

The benefits of using excellent conductors and insulators are listed below:

1. Conductors: Materials with high thermal conductivity can efficiently transfer heat from a heat source to a heat sink, keeping equipment cool. Alternatively, conductors can transfer heat from a heat source to cooler fluid in order to heat it up as well as allow for even heat transfer to prevent warping. 
2. Insulators: Materials with low thermal conductivity can prevent the transfer of heat away from a heat source. This can improve the efficiency of an oven, for example, as it keeps the heat inside where it is needed. Another example would be to keep heat from entering a temperature-sensitive environment like the inside of a spacecraft during atmospheric reentry. 

Listed below are some limitations of measures of thermal conductivity:

1. Not Precise: The thermal conductivity of materials changes with temperature. For that reason, calculations based on thermal conductivity measured under a particular set of conditions may not be accurate when used to estimate heat transfer at other conditions.
2. Primarily Conduction Based: Thermal conductivity generally only covers heat transfer via conduction and does not address convection or radiative heat transfer. 

Examples of Thermal Conductivity of Different Materials

Table 2 below lists the thermal conductivities of a range of common materials:

High vs. Low Thermal Conductivity

Whether high or low thermal conductivity is better depends entirely on the application. In heat transfer applications like heat exchangers, high thermal conductivity is ideal, since it improves the rate of heat transfer to the heat transfer fluid. In cases where heat must be prevented from moving to surrounding components like in a furnace, for example, lower thermal conductivity is preferred.

Summary

This article presented thermal conductivity, explained what it is, and discussed its various calculations. To learn more about thermal conductivity, contact a Xometry representative.

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