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Avoid Convection Errors in Measuring the Thermal Conductivity of Liquids

A common question raised in testing the thermal conductivity of liquids is how does the method deal with the concern of convection?  Convection is commonly described as another form of energy transfer of heat from one place to another by the movement of fluids.   Heat transfer via convection in liquids is not the same as conductivity and in fact is a source of error in the measurement of thermal conductivity.  Convection takes place when heated molecules move from one place to another, taking the heat with them. In better understanding how this is different from how heat energy is transferred in thermal conductivity please see this helpful exlpanation provided by Dr. Jack Josefowicz.

Traditional methods (e.g. Guarded Hot Plate, Guarded Heat Flow Meter and Laser Flash Diffusivity) for thermal conductivity measurement are limited to solids due this additional impact of heat transfer through convection of the liquids.  Some of these traditional techniques employ much longer test times -  in the case of GHP and GHF the test times are typically in the range of hours.  While some methods such as ASTM E1530 attept to to calibrate out the impact of convection - the corrections are highly susceptible to changes in the viscosity of the materials tested.  ASTM E1530 can be very useful in testing pastes, but the challenge is very different in testing lower viscosity materials.  

Laser Flash Diffusivity Analysis is also unsuitable for different reasons.  Although LFD emlpoys a short test time - its high power density and sample coating requirements effectively prohibit the practical application of this technique for such liquid materials.  LFD's ineffectiveness in testing the thermal conductivity of liquids is well documented.  

C-Therm’s TCi Thermal Conductivity Analyzer was however specially engineered to handle both liquids and solids.  Employing the Modified Transient Plane Source (MTPS) technique, the TCi negates the impact of convection by employing a very short-test time (0.8 seconds) and lower power setting (37 mA).  The effectiveness of the MTPS method in dealing with convection is widely confirmed both experimentally as illustrated in the graph below and theoretically with sophisticated simulation. The simulation on ANSYS software animated below was developed to model the possible effects, if any,  convection would have by modeling a measurement of water with the standard 1-second duration measurement and comparing to a measurement done with exagerated test durations to see how it impacts the temperature profile in the liquid sample to be tested


Figure 1.  C-Therm TCi Thermal Conductivity Analyzer, Standard 0.8-second Measurement

0.8 Second Measurement Temperature Profile

Figure 2.  Exagerated 14-Second Measurement Illustrating the Impact of Convection

Exagerated 14-Second Measurement Demonstrating Impact of Convection


Figure 1 shows no significant natural convection has taken place while Figure 2 shows how natural convection starts to develop over time as illustrated at 14-second test time.  The 20 second test time animated in the GIF below illustrates how the convection eventually completely dominates the measurement.  The short time duration of the standard 0.8 second experiment done by the MTPS negates the effect of natural convection and the simulations clearly show the phenomenon only coming into play at times much exagerated than the standard testing technique employs.


Figure 3.  ANSYS Temperature Modeling of Thermal Conductivity Test of Water with MTPS Sensor with Exagerated 20-Second Test Time

Importance of Keeping Thermal Conductivity Test Times Short in Negating Convection Error

In reviewing the above animated GIF, one can easily see the impact of longer test times on the temperature profile.  The simulation is based on a MTPS sensor employing a low power pulse in contact with water.  The animation is run over an exagerated test time of 20 seconds to highlight the impact that test time has on convection.  The "mushroom" pattern that emerges with the longer test time is caused by convection.  It is important to note that for approximately the first 5 seconds of the measurement the temperature profile lines are parrallel and the impact of convection in this phase of the measurement is negligible.  This is why C-Therm's TCi MTPS sensors for measuring thermal conductivity employ very short test times in testing liquids of 0.8 seconds in negating the impact of convection.  

Ultimately, the "proof is in the pudding" and testing results confirm the accuracy of the method in being uniquely suitable for testing liquids.  The chart below higlights performance on the testing of distilled water.  

Chart 1.  C-Therm TCi Thermal Conductivity Test Results on Distilled Water, Employing the Modified Transient Plane Source (MTPS) Method

Thermal Conductivity of Water
Measuerment Thermal Conductivity (W/mK)
1 0.613
2 0.619
3 0.618
4 0.622
5 0.616
6 0.622
7 0.621
8 0.621
9 0.618
10 0.620
AVG (W/mK): 0.619
RSD (%): 0.5%


Note the high precision and repeatability of the measurement in testing the thermal conductivity of water - high precision is a hallmark of a suitable and appropriate method. The relative standard deviation is 0.5%.  This falls in line with expectations as the precision is stated as better than 1%.  Simliarly, in comparing the results to published values for water the results fall within better than 5%.  

The TCi's wide application and history in testing the thermal conductivity of liquids establishes it is at the most effective tool of choice for testing liquids across a broad temperature range.   While traditional steady-state heat flow methods have many advantages, the inherent long test-time to their measurements make them completely unsuitable for liquids and researchers are cautioned to exercised caution in their application accordingly.  

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