Selecting the Right Method: Transient vs Steady-State for Thermal Conductivity Measurement

May 14, 2024

Imagine holding a cup of fresh, hot coffee. The warmth seeps through the mug, radiating a pleasant heat to your hands – or maybe it’s too hot to hold. Have you ever wondered why some mugs offer a more comforting embrace than others? The answer lies in a fascinating property called thermal conductivity.

Thermal conductivity is like a material’s superpower for transferring heat. It dictates how efficiently a substance, whether a cozy mug or a cutting-edge spacecraft component, can move heat through its core. Understanding a material’s thermal conductivity ensures we build comfortable and energy-efficient buildings, manufacture high-performance electronics that don’t overheat, and craft mugs that feel comfortable in your hands.

In this blog, we’ll explore the two main methods for measuring thermal conductivity: transient and steady-state. By the end, you’ll be equipped with the knowledge to choose the right method for your specific needs, whether you’re a seasoned researcher or simply curious about the intriguing world of heat transfer.

So, grab your metaphorical cup of knowledge and let’s dive in!

Understanding Thermal Conductivity

Thermal conductivity (k), measured in Watts per meter per Kelvin (W/mK),  signifies a material’s ability to transfer heat through its core. Imagine a hot cup of coffee – the higher the thermal conductivity of the mug, the faster the heat will travel from the hot beverage to your hands. Conversely, a low thermal conductivity material, like a wooden spoon, will keep your hand comfortable despite being submerged in the hot liquid.

Understanding this property is essential for various applications:

• Construction and Building Materials: Selecting appropriate insulation materials for homes and buildings relies heavily on thermal conductivity. Low thermal conductivity materials like fiberglass or rock wool help maintain comfortable indoor temperatures and reduce energy consumption.
• Electronics: Efficient heat dissipation is paramount in electronic devices like computer chips and LEDs. Knowing the thermal conductivity of electronic components allows engineers to design optimal heat management systems.
• Textiles: Thermal conductivity plays a vital role in clothing comfort. Wool, for example, has low thermal conductivity, which keeps you warm in cold weather. Conversely, cotton, on the other hand, has a higher thermal conductivity, which allows heat to escape and keeps you cool in warmer temperatures.

Now that you understand thermal conductivity let’s explore the difference between the transient and steady-state methods for measuring it.

Exploring Transient Methods for Thermal Conductivity Measurement

Transient methods offer a powerful approach to measuring thermal conductivity by analyzing a sample’s response to a heat pulse. Unlike steady-state methods, they focus on the time-dependent energy dissipation process within the material.

Here’s how transient methods work:

• Heat Pulse Delivery:  A short burst of heat or a periodic heat source is applied to the sample. This initial jolt disrupts the thermal equilibrium within the material.
• Temperature Response Monitoring: The sample’s crucial temperature response is meticulously recorded over time. This data captures how efficiently heat travels through the material.
• Thermal Conductivity Calculation:  Scientists can calculate the sample’s thermal conductivity using the recorded temperature changes and a specific equation (k = q/4πa).

Figure 1. Equation to calculate thermal conductivity using transient methods. Where k is the thermal conductivity in W/mK, q is the heating power of the sensor, and a is the slope of the line for temperature rise over the log of time.

Common Transient Techniques

There are three main types of transient methods, each using a slightly different sensor configuration:

• Transient Plane Source (TPS) ISO 22007-2, ISO 22007-7 / GB/T 32064:  This technique involves “sandwiching” a sensor between two flat surfaces of the sample. Ideal for solid materials, pastes, and powders, TPS offers a versatile and user-friendly approach.
• Transient Hot Wire (THW) ASTM D7896-19: The sensor is embedded directly within a sample cell. This method excels at measuring liquids and phase change materials (PCMs) because it can interact directly with the fluid.
• Transient Line Source (TLS) ASTM D5334-22a, D5930: The TLS method excels at testing soil, rocks, concrete, and polymers. It involves inserting a sensor line into the sample to measure thermal conductivity.

Figure 2. Heat flow during asymmetric TPS test.

Figure 3. Heat flow during symmetric TPS test.

Advantages of Transient Methods

Transient methods boast several advantages over steady-state techniques:

• Faster Results:  The shorter test duration translates to quicker turnaround times for your thermal conductivity measurements.
• Reduced Heat Loss:  The rapid nature of transient methods minimizes heat loss to the surroundings, leading to more accurate results.
• Material Versatility:  These methods can handle a broader range of materials, including liquids and those with high thermal conductivity.
• Sample Size Flexibility:  Transient methods often work well with smaller sample sizes, which can be beneficial when there is limited availability.
• Contact Resistance Correction:  Advanced transient techniques can account for contact resistance between the sensor and the sample, leading to more precise thermal conductivity measurements.

Considerations for Transient Methods

While transient methods offer numerous benefits, it’s important to consider these points:

• Data Processing:  Extracting thermal conductivity data from transient methods often involves more complex mathematical analysis than steady-state methods.
• Material Limitations:  Measuring materials with extremely low thermal conductivity or high thermal resistance might present challenges for some transient techniques.

Examining Steady-State Methods for Thermal Conductivity Measurement

Steady-state methods are used to determine a sample’s thermal properties. These methods establish a constant temperature difference across the sample and measure the thermal properties by keeping the temperature difference constant over time. A constant heat flux is applied to the sample, and the resulting temperature difference is measured. The temperature, thickness, and heat input are then used to calculate the thermal conductivity using the following equation:

Figure 4. Equation to calculate thermal conductivity, where Q = heat flow (W), L= length or thickness of the material (m), A = surface area of material (m²) and T2-T1 = temperature gradient (K).

Here’s a closer look:

• Constant Heat Flux: A steady heat flux is applied to the sample.
• Temperature Difference Measurement: The resulting temperature difference across the sample is measured.
• Thermal Conductivity Calculation: Thermal conductivity is calculated based on Fourier’s Law of heat conduction.

Figure 5. Experimental variables for steady-state thermal conductivity tests.

Common Steady-State Techniques

Guarded Heat Flow Meter (ASTM E1530-19): A sample with fixed dimensions is placed between two temperature-controlled plates. One plate is heated, while the other is cooled. The heat flux is recorded until a steady-state condition is reached, and thermal conductivity is calculated based on the measured temperature difference, sample thickness, and heat input.

Advantages of Steady-State Methods

• Accuracy for Specific Materials: Steady-state methods can be highly accurate for construction and insulation materials.
• Simpler Calculations: Analysis and calculations are often more straightforward.
• Full Thickness Measurement: Steady-state methods provide a complete measurement of the sample’s thermal conductivity throughout its thickness.

Considerations for Steady-State Methods

• Long Testing Times: Reaching a steady-state condition can be time-consuming, leading to longer test durations.
• Large Sample Sizes: Steady-state methods typically require larger sample sizes than transient methods, which may not be feasible when availability is limited, or the sample is delicate.
• Destructive Sample Preparation: On some occasions, steady-state methods might require altering the sample’s shape or dimensions, making them destructive testing techniques.
• Parasitic Heat Loss: Heat loss to the surroundings can occur during testing, potentially impacting the accuracy of the results. Steady-state methods need to be meticulously designed to minimize this effect.
• Contact Resistance Challenges: Similar to transient methods, contact resistance between the sensor and the sample can influence the measured thermal conductivity.

Pros and Cons of Transient and Steady-State Methods

Both methods have pros and cons and depend on the material you’re testing.

Steady-State Methods

Steady-state methods offer several key advantages:

• Construction and Insulation Expertise:  When it comes to measuring the thermal conductivity of construction and insulation materials, steady-state methods excel. Their ability to provide a full-thickness measurement of the sample’s thermal conductivity makes them a valuable tool for ensuring energy efficiency in buildings.
• Accuracy Advantage:  For specific materials, particularly construction and insulation materials, steady-state methods can deliver highly accurate thermal conductivity measurements, making them a reliable choice for applications where precise thermal performance data is critical.
• Keeping it Simple:  Compared to transient methods, steady-state methods often involve more straightforward analysis and calculations. This can be advantageous if you need straightforward results without the complexities of advanced data processing.
• Seeing the Whole Picture:  Unlike transient methods that offer localized readings, steady-state methods provide a complete picture. They measure the thermal conductivity of the entire sample thickness, giving you a comprehensive understanding of the material’s heat transfer properties.
• Heterogeneity Hero:  For heterogeneous materials with non-uniform composition throughout, steady–state methods can be a superior choice. Since they measure the average thermal conductivity of the entire sample, they account for these variations and provide a representative value.

While steady-state methods have their merits, they also come with some drawbacks to consider:

• Time is of the Essence:  Reaching a steady-state condition can take time, leading to longer testing duration; this might not be ideal if you require quick results for your thermal conductivity measurements.
• Heat Loss Challenges:  Maintaining a steady state often involves bulky setups, which can make these methods more susceptible to radiative and conductive heat losses to the surroundings, potentially impacting the accuracy of the results.
• The Sensor Squeeze: Steady-state techniques are typically designed for bulk materials, often requiring larger sample sizes and sensor areas. This can be a limitation if you have limited sample material available.
• Contact Concerns:  Imperfect contact between the temperature sensor and the sample can introduce “contact resistance.” Contact resistance can obscure the measurement of the material’s intrinsic thermal conductivity.
• Sample Sacrifice:  Destructive sample preparation might be necessary for some steady-state techniques. This involves altering the sample’s shape or dimensions, which wouldn’t be ideal if the sample is delicate or irreplaceable.

Figure 6. Comparison of volume measured – GHFM vs TPS

Pros and Cons of Transient Methods

Pros:

• Speed Demons:  Transient methods boast a significant advantage in test times. Their rapid heat pulse approach delivers quicker results compared to steady-state methods, making them ideal for situations where time is a constraint.
• Minimizing Heat Loss:  The shorter test duration associated with transient methods minimize heat loss to the surroundings. This translates to more accurate thermal conductivity measurements by reducing the influence of external factors.
• Sample Size Savvy:  These methods offer greater flexibility regarding sample size. They can often work effectively with smaller samples, which can be beneficial in scenarios where sample availability is limited or the material is scarce.
• Accounting for Contact:  Advanced transient techniques have the capability to account for contact resistance between the sensor and the sample. This resistance can affect the measured thermal conductivity, and transient methods can compensate for it, leading to more precise results.
• Direct Measurement Powerhouse: Unlike steady-state methods that rely on established temperature differences, transient methods involve directly measuring the sample’s response to a heat pulse. This can be advantageous for certain materials or applications.
• Material Menagerie:  Transient methods shine in their versatility regarding material compatibility. They can effectively measure thermal conductivity in a wider range of materials, including solids, liquids, pastes, and powders. This makes them a valuable tool for researchers and engineers working with diverse materials.

Cons:

• Data Delving:  Extracting thermal conductivity data from transient methods can involve more complex mathematical analysis than steady-state methods. This can require additional expertise or software to process the data accurately.
• Material Matchmaking:  While transient methods offer a broader material range, measuring materials with extremely low thermal conductivity or high thermal resistance might present challenges for some techniques. Construction and building materials like insulation often fall into this category.
• Planar Perfection:  Transient methods often require samples with at least one flat planar surface for optimal contact with the sensor. This can limit their applicability in situations where samples have irregular shapes.
• Partial Picture:  Unlike steady-state methods that provide a thermal conductivity measurement for the entire sample thickness, transient methods might offer localized readings depending on the specific technique. This can be a drawback if you need a complete understanding of the material’s heat transfer properties throughout its entire volume.

Choosing the Right Method for Your Thermal Conductivity Measurement Needs

Understanding the strengths and weaknesses of both transient and steady-state methods empowers you to select the most appropriate technique for your specific thermal conductivity measurement needs.

Here’s a breakdown to guide you:

Matching the Method to Your Needs:

• Material Matters: Your sample’s thermal properties play a crucial role. Steady-state methods excel for construction and building materials, where a full-thickness measurement is essential. Steady-state methods might better suit materials with low thermal conductivity or high thermal resistance (like some insulators). However, transient methods can still be valuable for a broader range of materials, including liquids, pastes, powders, and even high-conductivity materials like copper.
• Sample Size Considerations: Transient methods often shine if you have limited sample availability. Their ability to work effectively with smaller samples makes them viable in these scenarios. Steady-state methods typically require larger sample sizes, which may necessitate destructive sample preparation techniques.
• Time Constraints:  Speed is a factor! Transient methods boast significantly faster test times than steady-state methods if time is of the essence. Their rapid heat pulse approach delivers quicker results, making them ideal for situations where time is a constraint.

Both transient and steady-state methods offer valuable tools for measuring thermal conductivity. By carefully considering the material properties, sample size constraints, and desired testing time, you can select the most appropriate method to meet your specific needs. If you still need to figure out the best method for your application, consulting with a thermal conductivity expert can provide valuable guidance.

Conclusion

Don’t let the world of thermal conductivity leave you feeling burnt out! At Thermtest, we’re passionate about helping you navigate these methods. Our team of specialists can guide you through the selection process, ensuring you choose the technique that perfectly aligns with your project’s needs.

Understanding both transient and steady-state methods empowers you to make informed decisions. It’s about the “how” of measuring thermal conductivity and the “why.” By considering your project’s specific demands, you can choose the method that maximizes efficiency, effectiveness, and, ultimately, the success of your thermal management strategies. Remember, the right tool in the right hands can unlock a world of thermal possibilities.

FAQs

1. What is a transient method?

Transient methods measure thermal conductivity by analyzing a material’s response to a short burst of heat or a periodic heat source. Imagine poking a fire – the initial jolt of heat disrupts the thermal equilibrium, and the transient method is like carefully monitoring how the warmth spreads through the surrounding materials. Scientists can calculate the material’s thermal conductivity by recording the temperature response over time.

2. What is the steady-state method?

Steady-state methods establish a constant temperature difference across a sample and measure the thermal conductivity by maintaining that temperature difference over time. It’s like setting your oven to a specific temperature and measuring how much heat it takes to keep it there. Based on the heat input, temperature difference, and sample thickness, researchers can calculate the material’s thermal conductivity using Fourier’s Law.

3. What is the difference between transient methods and steady-state methods?

The key difference lies in how they approach heat transfer. Transient methods involve a short-duration heat pulse, while steady-state methods rely on maintaining a constant temperature difference. This translates to several key advantages for each method:

• Transient methods: Faster test times, minimal heat loss, work with a wider range of materials (including liquids) and can handle smaller samples.
• Steady-state methods: Highly accurate for specific materials (like construction materials), simpler calculations, provide a full-thickness measurement for the entire sample, and excel with heterogeneous materials (non-uniform composition).

4. What are the methods of determining thermal conductivity?

The two main methods for determining thermal conductivity are transient and steady-state, as explored throughout this blog. However, various techniques depend on the sample type and desired measurements within these categories. Some common examples include:

• Transient Methods: Transient Plane Source (TPS), Transient Hot Wire (THW), Transient Line Source (TLS)
• Steady-State Methods: Guarded Heat Flow Meter (ASTM E1530-19)

5. What is steady-state in thermal conduction?

Steady-state, in thermal conduction, refers to a condition where the temperature at any point within a material remains constant over time. Imagine a well-insulated cup of hot coffee – once it reaches a specific temperature, it stays that way for a while, representing a steady-state condition.

6. What is an example of a transient conduction?

Transient conduction occurs when a sudden temperature change causes heat to flow within a material until a new equilibrium is reached. A simple example is touching a hot stovetop. The initial contact creates a transient heat flow from the hot stove to your cooler finger until a somewhat balanced (hopefully less painful) temperature is achieved.

References

Trevisan, O. V., Mohanty, S., & Miller, M. A. (1993). Transient method for measuring thermal properties of saturated porous media. International Journal of Heat and Mass Transfer, 36(10), 2565-2573. https://doi.org/10.1016/S0017-9310(05)80194-2

Zhao, D., Qian, X., Gu, X., Jajja, S. A., & Yang, R. (2016). Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials. arXiv. https://arxiv.org/pdf/1605.08469

Thermtest Inc. (n.d.). Transient vs. steady-state for concrete materials. Thermtest. Retrieved May 14, 2024, from https://thermtest.com/application/transient-vs-steady-state-for-concrete-materials

Braun, J. L., Olson, D. H., Gaskins, J. T., & Hopkins, P. E. (2019). A steady-state thermoreflectance method to measure thermal conductivity. Review of Scientific Instruments, 90(2), 024905. https://doi.org/10.1063/1.5056182