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Thermal Resistance: Definition, How It Works, Importance, Calculations, and Factors

Learn more about what thermal resistance is and its importance in 3D printing, laser cutting, injection molding, and more.

Xomety X
By Team Xometry
April 28, 2023
 13 min read
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Thermal resistance is the ability of substances or systems to fend off heat flow. It is a crucial parameter in many disciplines, including engineering, physics, and thermodynamics. The amount of heat energy needed to raise a material's or a system's temperature by a specific amount is determined by the material or system's thermal resistance. This ability to conduct or resist heat transfer is difficult to calculate accurately because it depends on the material's composition, structure, and other elements.

You must understand thermal resistance to design and optimize heat transfer systems such as electronic devices, insulation materials, and building envelopes. The temperature difference, the area and thickness of the material, the material's type, and the item’s shape all affect thermal resistance. We’ll cover the definition, operation, significance, and variables influencing thermal resistance calculations in this article. We will also discuss thermal conduction and how it relates to our understanding of thermal resistance as a whole.

What Is Thermal Resistance?

A system's or material's capacity to impede the transfer of heat is referred to as thermal resistance. It is described as the relationship between the temperature difference across a substance or object and the rate of heat flow through it. K/W, or Kelvin per watt, is the SI unit for thermal resistance. Some building materials are defined by their resistance to heat transfer. Insulation materials should have a high thermal resistance or insurance values because they reduce the amount of heat that is transferred through a building envelope. In contrast, materials used for heat exchangers or heat sinks, where the objective is to transfer heat as effectively as possible, are preferred because they have low thermal resistance values.

How Does Thermal Resistance Work?

A material's thermal resistance is a measure of how difficult it is for heat to pass through it. It is determined by the thermal conductivity and thickness of the material. Highly resistive materials, like insulators, slow the transfer of heat while those with low thermal resistance, like metals, facilitate it.

What Is the Importance of Thermal Resistance?

Thermal resistance is significant because it represents a material's or system's capacity to hinder the flow of heat. It is a key factor in the development and improvement of thermal management systems meant to avoid overheating and boost energy effectiveness.

What Is the Importance of Thermal Resistance in 3D Printing?

Thermal resistance is a critical part of a 3D printer’s design because it influences the melting and cooling of the print material, which in turn influences the final object's quality. Prints can be enhanced and errors avoided with proper thermal management and an understanding of thermal resistance. For more information, see our guide on 3D Printing.

What Is the Thermal Resistance of Different 3D Printing Materials?

The thermal resistance of some popular 3D printing materials can only be determined by calculating it using the formula below:

R = L / kA

To calculate the thermal resistance of an item, you first need to know the thickness of the material (L), its cross-sectional area perpendicular to the heat flow (A), and the material’s thermal conductivity (k). 

Important Thermal Resistance in Laser Cutting?

Thermal resistance is important because it affects a material's capacity to withstand the high temperatures produced by the laser-cutting process. While materials with low thermal resistance may need to be cut slowly to avoid material damage, materials with high thermal resistance can be cut at higher speeds with little distortion or melting. For more information, see our guide on What is Laser Cutting? Process, Uses, Types, and Materials.

How Important Is Thermal Resistance in Plastic Injection Molding?

Thermal resistance is crucial to the process of plastic injection molding because it impacts the functionality and quality of the finished product. It calls attention to the material's capacity to withstand high temperatures without deteriorating or deforming. Plastic with the wrong thermal qualities may warp, crack, or lose its shape during the molding process, producing faulty products. It is important to choose a plastic material with the right thermal resistance to ensure consistent quality and production efficiency.

What Is the Formula for Thermal Resistance?

The formula for thermal resistance is:

R = L / kA

Where:

  1. k = Material's thermal conductivity (measured in units of W/mK)
  2. L = Material's thickness parallel to heat flow (measured in units of m)
  3. A = Cross-sectional area perpendicular to heat flow (measured in units of m^2)
  4. R = Thermal resistance (measured in units of K/W)

What Is the Symbol for Thermal Resistance?

Thermal resistance is denoted by the letter "R." It serves as a symbol for a system's or material's capacity to impede the transfer of heat. This resistance represents the ratio of temperature difference to heat flow rate between two points.

What Is the Unit for Thermal Resistance?

Thermal resistance is expressed in K/W or Kelvin (temperature) per watt (power). Since the degree values on the Kelvin and Celsius scales are identical, they may also be listed in °C/W.

How To Calculate the Thermal Resistance of a Material?

Here is a step-by-step explanation of how to determine an item’s thermal resistance:

  1. Use a caliper or a ruler to determine the material's thickness in the direction of expected heat flow. The thermal resistance of a material depends on its thickness. 
  2. Calculate the material's cross-sectional area perpendicular to heat flow. 
  3. Look up the material's thermal conductivity in its Material Safety Data Sheet (MSDS). 
  4. Apply the above values to this formula and solve: Thermal resistance = thickness / (area x thermal conductivity). 
  5. Note: make sure the thickness, area, and thermal conductivity are all expressed in the same unit (e.g., all in meters or all in inches), and that the units cancel out properly in the formula. Thermal resistance is typically expressed in degrees Kelvin per watt (K/W) or degrees Celsius per watt (°C/W).

What Are Examples of Calculating Thermal Resistance?

Here are a few examples:

1. A steel plate with a thickness of 2 cm and a thermal conductivity of 50 W/mK has an area of 0.5 m².

Thermal resistance = thickness / (area x thermal conductivity)

Thermal resistance = 0.02 m / (0.5 m² x 50 W/mK)

Thermal resistance = 0.0008 K/W

2. A window has a thickness of 3 mm and thermal conductivity of 0.8 W/mK. The window has an area of 2 m². 

Thermal resistance = thickness / (area x thermal conductivity)

Thermal resistance = 0.003 m / (2 m² x 0.8 W/mK)

Thermal resistance = 0.001875 K/W

3. A 2-meter pipe with a diameter of 10 cm and a thickness of 5 mm is made of copper, which has a thermal conductivity of 400 W/mK.

First, we need to calculate the area of the pipe's cylindrical surface:

Area = π x diameter x length

Area = π x 0.1 m x 2 m

Area = 0.628 m²

Then, we can use the thermal resistance formula:

Thermal resistance = thickness / (area x thermal conductivity)

Thermal resistance = 0.005 m / (0.628 m² x 400 W/mK)

Thermal resistance = 0.0000199 K/W

What Are the Factors That Affect the Thermal Resistance of Materials?

Several factors affect the thermal resistance of a material, including:

1. Pressure

By changing a material's thermal conductivity (capacity to transfer heat), pressure can have an impact on thermal resistance. Higher pressure results in lower thermal conductivity and, consequently, higher thermal resistance.

2. Surface Area

Surface area influences the rate of heat transfer between the material and its surroundings and thus affects the thermal resistance of materials. The part can be made more effective at transferring heat by increasing surface area and lowering thermal resistance.

3. Porosity

One of the elements that affect a material's ability to resist heat is its porosity. The air within the pores transfers heat convectively, making a porous item’s thermal conductivity different from that of a non-porous version of the same material. Particularly for materials used as insulation, where high thermal resistance is desired, this difference in thermal resistance may be significant.

4. Material Composition

The chemical makeup of a material is known as its composition. This has a large influence on the material's capacity to conduct heat. Parts made with materials with poor thermal conductivity typically have a high thermal resistance. A material's composition thus has a direct impact on its thermal resistance.

5. Temperature Difference

Temperature difference affects thermal resistance because its tendency to transfer heat depends on the temperature difference between one surface and the other.

6. Material Thickness

A material's thermal resistance rises along with its thickness because there is more material for heat to pass through. Thicker materials generally resist heat transfer better than thin ones. Nevertheless, the precise relationship between thickness and thermal resistance depends on the characteristics of the material and the mode of heat transfer.

What Are the Benefits of Thermal Resistance?

High thermal resistance can be valuable for several reasons: 

  1. Energy Efficiency: Thermally resistant insulation helps lower the amount of energy required to maintain a proper temperature in a building or other enclosed space by restricting the flow of heat. That can lower energy costs and give the building a smaller carbon footprint.
  2. Temperature Control: Thermal resistance can help maintain a steady temperature in an enclosed area. It makes the space more comfortable for its occupants and less likely to cause damage to machinery or other contents that may be sensitive to temperature fluctuations.
  3. Fire Protection: High-thermal-resistance materials can slow the spread of fire, giving occupants more time to flee and minimizing property damage.

What Are the Limitations of Thermal Resistance?

Listed below are some of the imperfections regarding thermal resistance:

  1. Limited Effectiveness: High thermal resistance materials can reduce the speed of heat transfer, but they cannot completely prevent it. No matter how resistant a material is, heat will always travel from warmer to cooler regions.
  2. Moisture /issues: Many materials gradually absorb moisture. This is true of some materials with high thermal resistance such as fiberglass insulation. It may also result in problems like mold growth and a reduction in their insulating effectiveness.
  3. Insufficient /insulation: In some circumstances, even excellent insulation might not be sufficient to stop heat gain or loss in a building or other enclosed space. Temperature variations may also be caused by other factors such as air leakage and inadequate ventilation.

What Are Examples of Thermal Resistance of Different Materials?

To determine the thermal resistance of an item, you will need to determine its area, thickness, and thermal conductivity first. Once you know these values, compute its thermal resistance using the following formula below:

R = L / kA

For example: Consider that we have two flat plates, one made of steel and the other of copper. Both plates have a 0.02-meter thickness and a 0.1 m2 cross-sectional area.

The thermal conductivity of copper is approximately 401 W/mK, while the thermal conductivity of steel is approximately 50 W/mK.

Using the formula R = L / kA, we can calculate the thermal resistance of each plate:

For the copper plate:

R = 0.02 m / (401 W/mK * 0.1 m^2)

R = 0.0005 K/W

For the steel plate:

R = 0.02 m / (50 W/mK * 0.1 m^2)

R = 0.004 K/W

The copper plate has significantly less thermal resistance than the steel plate, which means it will conduct heat more effectively.

What Does High Thermal Resistance Mean?

A material with high thermal resistance does not easily allow heat energy to travel through its thickness. This property is crucial in industries like electronics or aerospace where heat management is fundamental.

Does Higher Resistance Mean More Heat?

No, increased thermal resistance does not equate to increased heat. The capacity of a material to withstand the transfer of heat is referred to as thermal resistance. Although a material with greater thermal resistance slows the transfer of heat, it says nothing about the absolute amount of heat in total. Additionally, other elements like temperature difference and surface size affect how much heat is produced or transferred.

Does High Resistance Increase Heat?

No, high thermal resistance does not increase heat. Items of high thermal resistance obstruct the movement of heat between two surfaces. This is why materials with high thermal resistance, like insulation, are frequently used to impede heat transfer and keep internal temperatures stable. 

Does High Resistance Increase Temperature?

No, a high thermal resistance does not raise the temperature. Thermal resistance is a measure of the substance’s tendency to withstand the flow of heat. High-thermal-resistance materials will stop heat from moving quickly, but they won't raise the temperature on their own.

What Material Has Highest Thermal Resistance?

Tantalum carbide has the ability to withstand extremely high temperatures, almost reaching 4000 °C, making it known as the material with the highest thermal resistance in the world. Due to its exceptional heat resistance, it has found use in many industrial applications, including as a ceramic reinforcement in high-entropy alloys (HEAs) and a sintering additive for ultra-high temperature ceramics (UHTCs).

What Does Low Thermal Resistance Mean?

Low thermal resistance is a descriptor for items that allow heat energy to easily pass through or across them. A material or structure that has a low thermal resistance is likely to be a good heat conductor, enabling heat to move through it quickly and easily. Many electronic devices, for instance, need to enhance heat transfer away from hot components in order to optimize their performance. They use conductive materials with low thermal resistance to do so. 

What Material Has Lowest Thermal Resistance?

Graphene, an effectively two-dimensional material made of a single layer of carbon atoms arranged in a hexagonal lattice, is currently thought to have the lowest thermal resistance in the world. Though largely experimental thus far, graphene shows promise for applications that need, particularly speedy heat transfer. 

Is Higher or Lower Thermal Resistance Better?

Both situations have their uses. Insulating materials need to exhibit high thermal resistance to slow heat infiltration or exfiltration from insulated regions. On the flip side, devices like radiators need to be made of materials with low thermal resistance because their purpose is to transfer heat away from themselves and their associated devices. 

What Is the Difference Between Thermal Conductivity and Thermal Resistance

Thermal resistance quantifies the resistance to heat flow in a particular item whereas thermal conductivity quantifies a material's inherent capacity to conduct heat. While high thermal resistance indicates poor heat transfer, high thermal conductivity does the opposite.

Summary

This article presented thermal resistance, explained what it is, and discussed its importance in various capabilities. To learn more about thermal resistance, contact a Xometry representative.

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Xomety X
Team Xometry
This article was written by various Xometry contributors. Xometry is a leading resource on manufacturing with CNC machining, sheet metal fabrication, 3D printing, injection molding, urethane casting, and more.