Systems and methods for measuring thermal behaviour of materials

Abstract

Systems and methods are disclosed for determining thermal behaviour of a material. A method includes: receiving measured temperatures of the material, times of the measured temperatures, a volumetric heat capacity of the material, and a heat flux, wherein the flux provides a temperature response in the material; and applying a non- linear fitting technique to determine a time-dependent thermal property of the material. Applying the non-linear fitting technique includes: computing estimated temperatures using an initial estimate of the time-dependent thermal property and a temperature function; and iterating values of the time-dependent thermal property to minimize an error between the measured temperatures and estimated temperatures computed using the iterated values of the time-dependent thermal property, wherein the time- dependent thermal property is determined as a value that results in a minimum error measure between the measured temperatures and the estimated temperatures.

Description

SYSTEMS AND METHODS FOR MEASURING THERMAL BEHAVIOUR OF MATERIALSTECHNICAL FIELD

[0001] The present disclosure relates to measuring thermal behaviour of materials, and in particular to measuring time-dependent thermal behaviour of materials.BACKGROUND

[0002] Existing thermal conductivity measurement methods fall into two categories: transient methods, which are time-dependent measurements and steadystate methods which are time-independent measurements. Both methods assume that the sample is homogeneous. That is to say, transient and steady-state methods assume that the sample is made of the same material all throughout its given dimensions.

[0003] The performance of both transient and steady-state methods has been tested in heterogeneous materials in the work of Kubicar (Kubicar, L. et al. "Thermophysical Parameters Measured by Classic and Transient Methods."), Araki (Araki, N., Tang, D.W., Makino, A. et al. “Transient Characteristics of Thermal Conduction in Dispersed Composites.”), and Obori (Obori, M., Nita, S., Miura, A., and J. Shiomi. “Onsite synthesis of thermally percolated nanocomposite for thermal interface material”). All papers measured a significant difference in transient and steady-state thermal conductivity values for the same material with a high degree of heterogeneity. These papers state that discrepancies between results obtained from transient and steady-state methods appear when measuring thermal conductivity of heterogeneous materials as a consequence of heterogeneity and measurement error.

[0004] Composite and heterogeneous materials have spatial variations in thermal conductivity which would be difficult to measure when using only one temperature sensor and one heat source, as most of existing thermal conductivity measurement methods only have one heat source and one temperature sensor. Multiple temperature sensors have to be placed across the length of the material to measure the spatial variations in thermal conductivity.

[0005] Indeed, Sizov (Sizov, A., D. Cederkrantz, L. Salmi, A. Rosen, L. Jacobson, S. E. Gustafsson, and M. Gustavsson. “Thermal Conductivity versus Depth Profiling of Inhomogeneous Materials Using the Hot Disc Technique.”) proposed a solution of profiling the thermal conductivity with probing depth for heterogeneous materials on a transient plane source (TPS), and found that conductivity does not stay constant. However, Sizov uses Gustafsson’s mathematical model for the TPS, which assumes that conductivity is constant regardless of time or probing depth, limiting the applicability of their approach.

[0006] Therefore, there is a need for a system and a method for determining thermal conductivity of a material, especially a heterogeneous (e.g., composite) material, using a simple setup.SUMMARY

[0007] In accordance with a first aspect of the present disclosure, a method for determining thermal behaviour of a material includes: receiving measured temperatures of the material, times of the measured temperatures, a volumetric heat capacity of the material, and a flux supplied by a heat source, wherein the flux supplied by the heat source over a measurement period provides a temperature response in the material; and applying a non-linear fitting technique to determine a timedependent thermal property of the material. In some embodiments, applying the nonlinear fitting technique includes: computing estimated temperatures using an initial estimate of the time-dependent thermal property at measurement times and a temperature function that is a function of the volumetric heat capacity, time, the flux, and the time-dependent thermal property; and iterating values of the time-dependent thermal property to minimize an error between the measured temperatures and estimated temperatures computed using the iterated values of the time-dependent thermal property, wherein the time-dependent thermal property is determined as a value that results in a minimum error measure between the measured temperatures and the estimated temperatures.

[0008] In some embodiments, computing the estimated temperature at each measurement time takes into account an estimated temperature of at least one previous measurement time.

[0009] In some embodiments, the method further includes determining the temperature function by solving a heat equation that is a function of the volumetric heat capacity, time, the flux, and the time-dependent thermal property.

[0010] In some embodiments, the temperature function is a solution to the heat equation of a physical system with boundary conditions describing a thermal contact resistance and / or a heat capacity of the heat source and / or a temperature sensor.

[0011] In some embodiments, solving the heat equation when absent information on any analytical form of the time-dependent thermal property includes: dividing the measurement into a transient region and a steady-state region; and representing the time-dependent thermal property as a piecewise function wherein a constant value of the time-dependent thermal property is assigned at the steady-state region and a linear combination of splines is assigned at the transient region.

[0012] In some embodiments, the time-dependent thermal property has a constant term and a time dependent term, wherein the time dependent term is a product between a constant parameter and a time dependent function, wherein the time dependent function is finite and positive at all times and has a finite positive limit as time goes to infinity.

[0013] In some embodiments, the method further includes determining the initial estimate of thermal property of the material by: dividing the measurement into transient and steady-state regions when a function representing the time-dependent thermal property is known; determining a short-time behaviour of the function representing the time-dependent thermal property by selecting an initial subset of measured temperatures from the transient region and using a linear fit of temperature to root time; determining a long-time behaviour of the function representing the timedependent thermal property from the steady-state region using Fourier’s law; and determining unknown parameters using a nonlinear fitting procedure with the short- time and long-time behaviours of the function representing the time-dependent thermal property being fixed.

[0014] In some embodiments, absent information on the analytical form of the time-dependent thermal property, the method further includes, prior to applying thenon-linear fitting technique to determine the time-dependent thermal property: creating a set of cardinal times from which spline basis functions can be constructed.

[0015] In some embodiments, the spline is a cubic spline.

[0016] In some embodiments, the time-dependent thermal property is one of: thermal conductivity, thermal effusivity, thermal diffusivity, and volumetric heat capacity.

[0017] In some embodiments, the material is heterogenous.

[0018] In some embodiments, the material is homogeneous, and the timedependent thermal property is constant with time.

[0019] In accordance with a second aspect of the present disclosure, a system for measuring thermal behaviour of a sample material over a measurement period includes: a first heatsink and a second heatsink; and a vertical stack for receiving the sample material, the vertical stack is arranged between the first heatsink and the second heatsink. The vertical stack includes a heat source configured to supply a heat flux that provides a temperature response in the sample material over the measurement period, and a temperature sensor for measuring temperature of the sample material, the temperature sensor. The first and second heatsinks are configured to pull away heat from the sample material during the measurement period.

[0020] In some embodiments, the system further includes a heat flux sensor for detecting a steady state flux of the heat source. The heat flux sensor is located under the first heatsink. The sample material is located between the temperature sensor and the heat flux sensor.

[0021] In some embodiments, the vertical stack further includes a block material located between the second heatsink and the heat source.

[0022] In some embodiments, the block material is a thermal insulating material.

[0023] In some embodiments, the thermal insulating material has a thermal conductivity of less than about 0.1 W / mK.

[0024] In some embodiments, the block material is a supplementary sample material identical to the sample material.

[0025] In some embodiments, the vertical stack further includes the sample material.

[0026] In some embodiments, the heat source and the temperature sensor are combined into a transient plane source.

[0027] In some embodiments, a center of each component of the vertical stack is aligned.

[0028] In some embodiments, each component of the vertical stack has an identical shape.

[0029] In some embodiments, each component of the vertical stack has a cylindrical shape.

[0030] In some embodiments, the system further includes a movable contraption configured to bring the first heatsink in contact with the heat flux sensor for the measurement.

[0031] In some embodiments, the first heatsink is further configured to apply a pressure onto the vertical stack to maintain the vertical stack in a locked configuration during the measurement.

[0032] In some embodiments, a force sensor is attached above the first heatsink to measure the pressure applied onto the vertical stack.

[0033] In some embodiments, the heat source provides a constant heat flux to the sample material over the measurement period.

[0034] In some embodiments, the second heatsink is further configured to pull away the heat from the block material.

[0035] In some embodiments, at least one of the first and the second heatsinks includes a passive heat sink.

[0036] In some embodiments, at least one of the first and the second heatsinks includes a liquid-cooled heatsink.

[0037] In some embodiments, a temperature of each of the first and second heatsinks is set by an electronic temperature control system for measurements above 100 °C.

[0038] In some embodiments, the system further includes a data acquisition device configured to collect heat flux sensor data and temperature sensor data.

[0039] In some embodiments, the system further includes a passive guard that wraps around the sample material.

[0040] In some embodiments, the passive guard is actively heated by an electronic temperature control system for measurements above room temperature.

[0041] In some embodiments, the height of the system is measured electronically using a linear variable differential transformer (LVDT).

[0042] In some embodiments, a levelling system is attached above the first heatsink to facilitate system alignment and parallelism.

[0043] In some embodiments, the system further includes a computer device including: a network interface for receiving temperature sensor data from the acquisition device; a processor; and a non-transitory computer-readable memory storing computer-executable instructions which, when executed by the processor, configure the system to perform the method of the first aspect based on the temperature sensor data.BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Further features and advantages of the present disclosure will become apparent from the following detailed description, taken in combination with the appended drawings, in which:

[0045] FIG. 1 shows an example homogeneous material on the left and an example heterogeneous material on the right and respective isotherms in grayscale;

[0046] FIG. 2 shows a system for measuring a time-dependent thermal behaviour of a material;

[0047] FIG. 3 shows a close-up view of the sensor-sample system in FIG. 2.

[0048] FIG. 4 shows an example of a method of determining thermal behaviour of a sample material;

[0049] FIG. 5 shows an example of a method to determine an initial estimate of a time-dependent thermal conductivity of the sample material;

[0050] FIG. 6 shows an example of a method to find transient and steady-state regions of measured temperatures;

[0051] FIG. 7 shows an example of a method to find an estimate of a short time behaviour of thermal conductivity of the sample material;

[0052] FIGs. 8A and 8B show the distinction between the transient and steadystate regions in a measurement;

[0053] FIGs. 9A and 9B show a graph of an example temperature graph obtained from measurement of a material and the computed time-dependent thermal conductivity for said material; and

[0054] FIGs. 10A and 10B show a heterogeneous material inserted in the asymmetric configuration of the system and the computed time-dependent thermal conductivity for said heterogeneous material.

[0055] It will be noted that throughout the appended drawings, like features are identified by like reference numerals.DETAILED DESCRIPTION

[0056] Transient and steady-state methods work by placing a heat source in contact with the sample. For a homogeneous material, the heat coming from the heat source is expected to travel at the same rate in all directions. In case of heterogeneous materials containing fillers which are more thermally conductive than the surrounding material, the embedded fillers would create heat paths where more heat travels at afaster rate. FIG. 1 shows an example of a homogeneous material 10 and an example of a heterogeneous material 11 with its fillers.

[0057] In heterogeneous materials, when a temperature sensor is placed right next to the heat source, at short timescales, the temperature sensor would see the more thermally conductive paths resulting in a higher thermal conductivity reading. For longer timescales, however, heat would start to saturate the thermally conductive and diffusive paths. Thus, more heat would start to flow on the less thermally conductive paths, resulting in a lowerthermal conductivity reading. This effect is called thermal shunting.

[0058] Spatial variations in thermal conductivity of a composite material lead to temporal variations in thermal conductivity when measured by transient and steadystate methods. Knowing how thermal conductivity of a composite material changes with time can be useful in applications where a material is subjected to transient and steady-state heating since the material or any design involving the material can be optimized for these two modes of heating.

[0059] An aim of the present disclosure is to allow characterization of heterogeneous (e.g., composite) materials with time-dependent expressions for thermal properties of the materials, such as thermal conductivity and / or other thermal behaviours such as thermal diffusivity, thermal effusivity, and volumetric heat capacity.

[0060] Another aim of the present disclosure is to allow for the thermal shunting phenomenon, as described above, to be observed with a single meter. Existing methods would require at least two methods, transient and steady-state, to observe said thermal shunting.

[0061] The present disclosure also provides systems and methods for determining whether a material is homogeneous or heterogeneous.

[0062] Advantageously, in accordance with the systems and methods described in the present disclosure, accurate time-dependent thermal behaviour can be obtained for heterogeneous sample materials. However, it should be noted that the systems and methods described in the present disclosure are not limited toapplications related to heterogeneous sample materials but can also be applied to homogeneous samples materials or other types of materials.

[0063] Embodiments are described below, by way of example only, with reference to FIGs. 2-1 OB.

[0064] In accordance with the first aspect of the present disclosure, a system is disclosed for determining thermal property of a heterogeneous material over a measurement period.

[0065] FIG. 2 shows a system 100 for determining thermal behaviour of a heterogeneous material over a measurement period. A close-up view of the samplesensor system 115 is shown in FIG. 3.

[0066] The system 100 comprises a measurement device 110 which is configured to perform thermal measurements of a sample material 202. The measurement device 110 comprises a first heatsink 114 and a second heat sink 116. Both, the first and second heatsinks (114 and 116) are configured to pull away heat from components of the measurement device 110, specifically the sample material 202. The measurement device 110 comprises a vertical stack of a heat source 204, a temperature sensor 203, and heat flux sensors 201 and 206.

[0067] The measurement device 110 is configured such that during the measurement, the sample material 202 is to be inserted between the temperature sensor 203 and the heat flux sensor 201 , and a block material 205 is to be inserted between the flux sensor 206 and the heat source 204. In some instances, measurements can be made without the heat flux sensors 201 , 206, in which case the sample material 202 is to be inserted between the first heatsink 114 and the temperature sensor 203, while the block material 205 is to be inserted between the second heatsink 116 and the heat source 204.

[0068] The heat source 204 is configured to supply a heat flux that provides a temperature response in the sample material 202 over the measurement period.

[0069] In practice the heat source 204 receives electrical power from a power supply system 207 and causes the sample material 202 to heat up.

[0070] The temperature sensor 203 is located on top of the heat source 204 and is configured to measure temperature of the sample material 202.

[0071] The heat flux sensor 201 located under the first heatsink 114 is configured to detect a steady-state flux.

[0072] In some embodiments, the first heatsink 114 is further configured to apply a pressure onto the vertical stack to maintain the vertical stack in a locked configuration during the measurement. That is to say, the first heatsink 114 may be used to ensure sufficient contact between the temperature sensor 203 and the sample material 202.

[0073] In some embodiments, the force applied onto the vertical stack can be measured by a force sensor 112 attached above the first heatsink 114.

[0074] The second heatsink 116 is further configured to pull away the heat from the block material 205.

[0075] In some embodiments, at least one of the first and the second heatsinks 114 and 116 is or comprises a passive heat sink such as a large thermally conductive material.

[0076] In some embodiments, at least one of the first and the second heatsinks 114 and 116 is or comprises a liquid-cooled heatsink. For instance, the heatsink may be a large thermally conductive material connected to a liquid cooling device configured to keep temperature of said heatsink constant. The liquid cooling device allows for an active temperature control. The liquid cooling device may be similar, but not limited to, a liquid recirculating chiller.

[0077] Anyhow, the heatsinks 114 and 116 may be of a thermally conductive material whose thermal conductivity is preferably greater than 50 W / mK.

[0078] In some embodiments where the system temperature needs to be above room temperature, a heated guard 141 is clamped onto the heatsinks to ensure the sample environment temperature is the same as the heatsink temperatures.

[0079] In some embodiments, the temperature of the heated guard 141 is maintained by an electronic temperature control system.

[0080] In some embodiments, the guard 141 is not heated but still serves the purpose of (1) preventing lateral heat loss and (2) minimizing fluctuations in ambient temperature.

[0081] In some embodiments, the measurement system will be used above 100 °C and would require the use of an electronic temperature control system 143 to control the temperature of the heatsinks.

[0082] In some embodiments, the heat source 204 and the temperature sensor 203 are combined into a transient plane sensor (TPS) that acts as both a heating and a temperature-sensing item (shown in FIG. 3). The electricity heats up the transient plane sensor and the surrounding sample material 202, and the transient plane sensor is configured to measure a temperature of the sample material 202. In particular, the resistance of the transient plane sensor is related to the temperature of the surrounding sample material 202, and a time-dependent temperature increase of the surface of the sample material 202 can thus be recorded.

[0083] However, it is to be understood that using a TPS sensor is not required. The embodiments described herein can be performed with the heat source 204 and the temperature sensor 203 being separate (e.g. using a thermocouple as the temperature sensor 203, placed directly on top of the heat source 204).

[0084] In some embodiments, the heat source 204 or the TPS sensor is configured to provide a constant heat flux to the sample material 202 over the measurement period.

[0085] If the block material 205 is identical to the sample material 202, this is referred to as a symmetric configuration. If the block material 205 is a thermal insulating material with a thermal conductivity of less than about 0.1 W / mK, this is referred to as an asymmetric configuration.

[0086] In some embodiments, the system 100 further comprises a movable contraption 111 configured to bring the first heatsink 114 in contact with the heat fluxsensor 201 for the measurement. The movable contraption 111 can be manually or automatically controlled.

[0087] As explained before, the sample material 202 may be a solid material, and may either be a bulk solid (non-symmetric setup) or comprise two solid slabs (symmetric setup), to be placed in the measurement device 110 for measuring its temperature response. Alternatively, the sample material 202 may be a liquid or gel, provided that the liquid or gel is placed inside a sample cell with the same cross- sectional area as the heat source to (1) prevent the material from squeezing out and (2) maintain a one-dimensional heat flow.

[0088] In one embodiment, each component of the vertical stack (of the measurement device 110) has an identical shape. Specifically, the materials 202, 205 (symmetric configuration) have essentially the same cross-sectional area as the heat source 204. The heat flux sensors 201 and 206 may also have identical shapes to the shape of the heat source 204. The heat flux sensors 201 and 206 and the heat source 204 may at least have an essentially identical cross sectional area.

[0089] In some embodiments, two sample materials located on both sides of the TPS sensor have an essentially identical height. The heights of the sample may be determined with a separate device, such as a caliper, or with the meter itself.

[0090] In some embodiments, the height of the system is measured in situ with a linear variable differential transformer (LVDT) 120. The height of the sample is related to the height of the system by the formula: height of the sample = 0.5*(height of the system - temperature sensor thickness).

[0091] Specifically, in the case of two sample materials (i.e., the symmetric configuration), the sample materials may have the same dimensions.

[0092] In some embodiments, the sample materials and the TPS sensor have an essentially identical cross section.

[0093] In one embodiment, a center of each component of the vertical stack is aligned. That is to say, the center of the TPS sensor, the heat flux sensors 201 and 206, the sample material 202 and the block material 205 are preferably all aligned.

[0094] In some embodiments, a levelling system (not shown) is attached above the first heat sink 114 to facilitate alignment and ensure the sample and heat sink surfaces are in perfect contact.

[0095] In some embodiments, each component of the vertical stack has a cylindrical shape. Specifically, the sample materials preferably have the same diameter as the diameter of TPS sensor.

[0096] The power supplied to the heat source 204 should be selected such that the temperature rise over the expected fit range is greater than some value that depends on the sensitivity of the system. As one example, it may be beneficial to control the power and operation time such that the increase in temperature is greater than 0.5°C. The selection of operation time should be in a way such that there is enough data points within the transient phase to ensure that all fit parameters or values required for curve fitting are clear and distinct from one another. In order for the system to reach steady-state, the condition Ksstmax / h2> 4 has to be satisfied, where KSSis the thermal diffusivity of the material at steady-state conditions, h is the height of the material, and tmaxis the maximum time.

[0097] In use, once the center of each component of the vertical stack is aligned, pressure is applied onto the stack by weight of the first heatsink 114. Power is then provided on the heat source 204 by the power supply system 207, delivering heat across the stack for a time defined by the user. As power is provided to the heat source 204, the heat source 204 heats up and its temperature becomes greater than the temperature of the first and second heatsinks 114 and 116. As a result, heat flows through the sample material 202 toward the first heatsink 114. Heat also flows through block material 205 toward the second heatsink 116. As a matter of fact, when the block material 205 is a thermal insulating material, significantly less heat flows through the thermal insulating material due to its lower thermal conductivity compared with the thermal conductivity of the sample material 202. Typically, thermal conductivity of the sample material 202 is ten times the thermal conductivity of the thermal insulating material.

[0098] The TPS sensor or the temperature sensor 203 records change in temperature over time. The heat flux sensor 201 records voltage proportional to heat flux through the sample.

[0099] The temperature and the flux readings from the temperature and heat flux sensors 203, 201 and 206 are then sent to a computer 130 as further discussed below. Once the data is collected, the data is then passed onto custom software that would perform the analysis thereof to determine thermal behaviour of the sample material 202.

[0100] The system 100 may comprise a first data acquisition system 208 configured to receive temperature sensor data comprising temperature measurements from the temperature sensor 203.

[0101] The system 100 may further comprise a second data acquisition system 209 configured to receive heat flux sensor data comprising heat flux measurements from the heat flux sensor 201 .

[0102] The first and the second data acquisition systems 208 and 209 may be combined into one data acquisition device configured to collect heat flux sensor data and temperature sensor data.

[0103] The temperature sensor data, the heat flux sensor data, the force sensor data, the height data from the LVDT, and the power supplied to the heat source 204 may all be communicated to the computer or a processing unit 130. The computer 130 shown in FIG. 2 comprises a processing unit, which may for example be a central processing unit (CPU), a microprocessor, field programmable gate array (FPGA), or an application specific integrated circuit (ASIC). The computer 130 also comprises a non-transitory computer-readable memory, a non-volatile storage, and an input / output interface. The computer 130 may be coupled to the power supply system 207, the temperature sensor 203, the heat flux sensor 201 , and / or the heat source 204 via an I / O interface, and is configured to receive measurement data from the sensors and to send commands to the power supply system 207 or to the heat source 204. The computer 130 may also be coupled to one or more external processing devices and / or displays, which may for example be a lab computer configured to send measurementcommands to the computer 130 (e.g. what parameters to use for the thermal measurements), and the computer 130 is configured to send measurement data to the lab computer. The memory of computer 130 stores non-transitory computer- readable instructions that are executable by the processing unit to configure the controller 130 to execute certain methods and to provide certain functionality as described herein. In particular aspects, the system 100 is configured to measure thermal properties of a heterogeneous sample materials and the memory has computer-executable instructions stored thereon for implementing measurement functionality, which when executed configure the controller 130 to perform certain functionality including control of the power supply system 207 and receiving the sensor measurements from sensors 201 and 206. It is also possible that the memory has computer-executable instructions stored thereon for implementing a fitting algorithm (described below) to analyze the measurement data and determine thermal property of the sample material. The results of the data analysis at the controller may be output to the external processing device or a display on the measurement device 110, for example.

[0104] As explained above, measurement data comprising temperature measurements with respect to time are received from the temperature sensor 203, and may be analyzed by the controller / computer 130 or be output for analysis, for example to a remote processing device. Note that in some embodiments, the controller / computer 130 may be part of the system 100 and sold with the measurement device 110, while in other embodiments the controller / computer 130 may be external to the measurement device 110, and may even be remote from the measurement device 110.

[0105] As is apparent from the disclosure, the system 100 for measuring thermal behaviour of a sample material provides the ability to detect the change in thermal conductivity of a material at different timescales with a single method and in a single measurement. As opposed to the state of the art systems where at least two thermal conductivity methods, transient and steady state, are required to observe this change.

[0106] Further, the system 100 for measuring thermal behaviour of a sample material 202 provides the ability to measure thermal conductivity with time.

[0107] In accordance with a second aspect, FIG. 4 shows a method 300 of determining thermal behaviour of the sample material 202. It will be appreciated that the sample material can be heterogeneous in some embodiments. The method 300 may for example be performed by the controller / computer 130 of the measurement system 100 or by an external processing device, as shown in FIGs. 2-3. The method 300 may be performed by a processor when executing computer-executable instructions stored in a non-transitory computer-readable memory.

[0108] The method 300 comprises receiving 302 measurement data comprising measured temperatures of the heterogeneous material collected using a temperature sensor, times of said measured temperatures, and a flux supplied by a heat source. The flux supplied by the heat source over a measurement period provides a temperature response in the heterogeneous material. The power supplied to the heat source over the measurement period may also be part of the measurement data. The volumetric heat capacity of the heterogeneous material may be known or received as part of the measurement data. The measurement data comprises a set of data obtained from the sensor comprising: a set of measured times t; a set of measured temperatures V, each corresponding to a specific measured timea set of measured heat flux Q, each corresponding to a specific measured time t^, and a power supplied to the heat source. FIG. 9A shows a graph of an example temperature obtained from measurement, which is over a measurement period of 1400s performed on a heterogeneous material.

[0109] Method 300 goes to determining 306 an initial estimate of thermal conductivity. A discussion on determining the initial estimate of thermal conductivity is held below with respect to FIG. 5. However, it is to be noted that the initial estimate of the thermal conductivity is time-dependent.

[0110] Once the initial estimate of thermal conductivity is determined 306, method 300 goes to applying 308 a non-linear fitting technique to determine an effective time-dependent thermal conductivity of the heterogeneous material. Applying 308 the non-linear fitting technique comprises: computing estimated temperatures for measurement times using the initial estimate of the time-dependent thermal conductivity and a temperature function. The temperature function is theresult of solving a heat equation representing the system. The temperature function is a function of the volumetric heat capacity, time, the flux, and the time-dependent thermal conductivity.

[0111] Applying 308 the non-linear fitting technique further comprises iterating values of the initial estimate to minimize an error measure between the measured temperatures and estimated temperatures computed using the iterated values of the initial estimate.

[0112] In other words, the non-linear fitting algorithm deploys an iterative process where it computes estimated temperatures using the initial estimate of the time-dependent thermal conductivity, and compares the estimated temperatures to the actual measured temperatures by computing an error measure therebetween. Once the error measure computed, values of the initial guess are changed (iterated) so that the error measure is minimized throughout the different iterations of the nonlinear fitting algorithm.

[0113] The effective time-dependent thermal conductivity results from a minimum error measure between the measured temperatures and the estimated temperatures.

[0114] In an example embodiment, the temperature residuals (i.e., the difference between the measured temperature and the final estimated temperatures), should be randomly distributed along the zero line. In some cases, a pattern in the residuals could indicate a deficiency of the measurement.

[0115] Once again, the iterative process of the non-linear fitting algorithm allows to change values of the initial estimate so that the estimated temperatures computed based on this iterating initial estimate are as close as possible to the measured temperatures.

[0116] In one implementation, the non-linear fitting algorithm may be the Levenberg-Marquardt fitting algorithm.

[0117] Different definitions can be used to set the error measure and are known to the person of skill in the art. One possible error measure is the sum of squaredresiduals, where the residual is calculated as the difference between the measured temperature and the predicted temperature.

[0118] Other effective time-dependent thermal behaviours such as thermal diffusivity, thermal effusivity, and volumetric heat capacity may be determined as part of the method. For example, time-dependent thermal diffusivity may be determined by taking the time-dependent thermal conductivity measured and dividing it by the volumetric heat capacity. Additionally or alternatively, time-dependent thermal effusivity may be determined by taking the square root of the product of the timedependent thermal conductivity and volumetric heat capacity. The volumetric heat capacity is defined as the product of the specific heat per unit mass and the density of the material, and is assumed to be known and constant.

[0119] In one embodiment, the heat equation representing the system comprising the heat source and the material sample (e.g., heterogeneous material) is solved 304 as part of method 300.

[0120] In another embodiment, solving the heat equation is performed outside of the method 300 and the resulting temperature function is provided and used by subsequent steps of method 300. Solving the heat equation is further discussed below.

[0121] Anyhow, the temperature function is a solution to the heat equation of a physical system with boundary conditions describing a thermal contact resistance and / or a heat capacity of the heat source 204 and / or the temperature sensor 203.

[0122] Back to determining 306 an initial estimate of thermal conductivity.

[0123] In some embodiments, determining the initial estimate of thermal conductivity of the heterogeneous material may be achieved by estimating the short and long-time behaviour of the thermal conductivity function. The short-time behaviour can be obtained through a linear fit of the first few temperature points with root time, where the short-time constant behaviour of the thermal conductivity can be obtained using the formula, Q2 / npCpm2, where Q is the heat flux, pCpis the volumetric heat capacity of the material, and m is the slope of the linear fit. The long-time behaviour can be obtained from the sample height, the heat flux and the net averagetemperature rise of the temperature sensor towards the end of the measurement, where the temperature rise is constant. Using Fourier’s law, the long-time behaviour of the thermal conductivity function is calculated as Q / / 2AT, where I is the sample height and AT is the net temperature rise. In some embodiments, the time dependent function comprises one or more parameters, and wherein determining the initial estimate of thermal conductivity further comprises determining said one or more parameters by fitting the solution of the heat equation to the measured temperatures.

[0124] FIG. 5 shows a method 400 of determining an initial estimate of the timedependent thermal conductivity of the heterogeneous material assuming an analytical form of the time-dependent thermal conductivity.

[0125] The time-dependent thermal conductivity is assumed to have a known analytical form that comprises a constant term and a time dependent term. The time dependent term is assumed to be a product between a constant parameter and a time dependent function. The time dependent function is assumed to be finite and positive at all times and has a finite positive limit as time goes to infinity. Here is an example analytical form of the time-dependent thermal conductivity:

[0126] Method 400 starts by dividing the measured temperatures into transient and steady-state regions 402. The procedure for finding the transient and steady-state regions are found in method 500. An average 502 of the last five temperature points Tend has to be determined first, then, a search 504 for the earliest temperature measurement Ttis performed wherein Tt> 0.999Tend. Measurements with timestamps less than ttis the transient region 506 while measurements with timestamps greater than or equal to ttis the steady-state region, where ttis the timestamp of the temperature measurement Tt.

[0127] Upon performing method 500, measurements from the temperature sensor and the time-dependent thermal conductivity can be divided into transient and steady-state regions, as shown by graphs 700 and 702 of FIGs. 8A and 8B.

[0128] Once the transient and steady-state regions have been divided, estimates of the short and long time behaviours 404 of the thermal conductivityfunction has to be estimated. Finding an estimate of the short time behaviour is found in method 600. The long-time behaviour can be estimated from the sample height, flux and the net temperature rise of the temperature sensor using Fourier’s law.

[0129] Often times when the analytical form 406 of the thermal conductivity function is known, it is dependent on the short and long-time behaviours, and some additional unknown parameters. A nonlinear fitting procedure 410 can be used to estimate the unknown parameters, while keeping the short time and long time behaviours fixed.

[0130] If there is absent information on the analytical form of the thermal conductivity function, then, a nonparametric representation 408 can be used to represent the thermal conductivity function. In some embodiments, the nonparametric representation of the thermal conductivity function is defined as a piecewise function which separates the constant and nonconstant behaviour of the thermal conductivity function. The constant behaviour is the steady-state behaviour of the function, while the nonconstant behaviour is the transient behaviour of the function. A constant thermal conductivity value is assigned to the steady-state behaviour of the function. In some embodiments, the transient behaviour is represented by a linear combination of cubic splines, whose value as it approaches steady-state is equal to the steadystate value, and whose derivative as it approaches steady-state is zero.

[0131] In some embodiments, absent information on an analytical form of the time-dependent thermal conductivity, the method further comprises, prior to applying the non-linear fitting technique to determine the time-dependent thermal conductivity: creating a set of cardinal times from which the spline basis functions can be constructed. The cardinal times can be as few as three and as many as the number of time points in the transient behaviour of the thermal conductivity function. The linear combination of the spline basis functions, along with the steady-state value, is considered as the initial estimate of the thermal conductivity function. During application of the non-linear fitting technique, computing estimated temperatures and iterating values of the initial estimate are performed for measurement times that are between cardinal times of the first subset of cardinal times. In some embodiments, the spline is a cubic spline. In some embodiments, the set of cardinal times covers the measurement times.

[0132] T o get the short-time behaviour of the thermal conductivity, method 600 in FIG. 7 should be followed. A time boundary 602 of, for example 20 seconds, is set. Then, the heat flux Q, volumetric heat capacity pc, and sample height I are obtained 604. A linear fit with root time 608 is performed from the subset 606 extracted from the measurement, where the timestamps are less than the time boundary t0. The preliminary estimate of the short-time behaviour 610 is then obtained from the slope of the linear fit, while the temperature offset from the linear fit can be attributed to the thermal resistance of the sensor. This preliminary estimate is used to determine the updated time boundary 612. The method 600 further includes a step 614 of determining if the updated time boundary is greater than the original time boundary. If the updated time boundary is greater than the original time boundary, then an accurate estimate of short-time behaviour of the thermal conductivity function is obtained, while the temperature offset from the linear fit is recorded (step 616). If the updated time boundary is less than the old time boundary, then we set the time boundary to be equal to the updated time boundary, and repeat 606 (step 618).

[0133] In embodiments where the time-dependent function (i.e., (t)) comprises one or more parameters, said one or more parameters may be determined by fitting 410 the solution of the heat equation to the measured temperatures.

[0134] Examples of the time-dependent function may comprise:

[0135] In the instances of time-dependent functions shown above, one or more parameters of the time-dependent functions may include n and a>.

[0136] When no information on the analytical form of the time-dependent thermal conductivity function is present, a nonparametric piecewise function of the thermal conductivity function can be defined, where,The thermal conductivity function is represented by l(t), the spline basis functions are representedfu f), while the spline coefficients are represented by l-t, 12, ■ ■ ■ . ^v- The steady-state thermal conductivity value is denoted by Ass. The transient and steady-state behaviour are divided by tss, where t < tssis the transient behaviour while t > tssis the steady-state behaviour.

[0137] The steady-state thermal conductivity value Asscan be estimated from the long time behaviour of the thermal conductivity function. In addition, if the spline basis functions are represented by cubic / W-splines (J. Ramsay. Monotone Regression Splines in Action. Statistical Science 3, 425-441 (1988). doi: 10.1214 / ss / 1177012761.), thencan be estimated from the short-time behaviour A0.To estimate the remaining unknown parameters 12, T3, ... ,a nonlinear fitting procedure is applied with fixed parametersand Ass. The best-fit parameters A2, 13, ... , along withand Assprovide a complete initial estimate of the time-dependent thermal conductivity function when there is no information on its analytical form.

[0138] FIG. 9A shows a graph 704 of an example temperature graph obtained from measurement of a heterogeneous material. In FIG. 9A, the measured temperatures where collected using the TPS sensor disclosed above with respect to the system 100 for measuring thermal behaviour of a heterogeneous material.

[0139] The heterogeneous material may be a composite material where the fillers are more thermally conductive than the matrix such as the composite material described with reference to FIG. 1.

[0140] FIG. 9B shows a graph 706 of the computed time-dependent thermal conductivity for said heterogeneous material using the methods 300 and 400.

[0141] As illustrated above, the heat flux sensor 201 would read heat fluxes that go across the sample material 202 and would eventually reach a steady-state value. It is worth noting that the steady-state thermal conductivity value inferred from the value of the heat flux at the steady-state agrees with the thermal conductivity computed using methods 300 and 400.

[0142] In the graph of FIG. 9B, the thermal conductivity of the composite material is high initially, due to the thermal shunting phenomenon described above. The thermal conductivity then decays to a lower value once the sample material reaches steady-state conditions. In fact, the thermal conductivity decays with time. This decaying thermal conductivity can be modelled by an exponential decay function such as :

[0143] It is to be noted that thermal shunting such as that displayed in FIG. 9B can also be described using functions that is finite at t = 0 and goes to a constant value as t goes to infinity. These functions include, but are not limited to: tanh(tot) , coth(to(t — t0)) , e~atn, (<o(t — t0))

[0144] FIG. 10A shows an example heterogeneous material 600 inserted in the asymmetric configuration of the system 100. In some embodiments, the heterogeneous material 600 includes a stainless steel 304 layer 610 between a first layer and a second layer of Delrin™ 606, 608. In some embodiments, the heterogeneous material 600 further includes a TPS sensor 612 connected to the second layer of Delrin™ 608, a backing layer 614 connected to the TPS sensor 612, and two heatsinks (e.g., aluminum heatsinks 602, 604) respectively connected to the first layer of Delrin™ 606 and the backing layer 614.

[0145] FIG. 10B shows a graph 708 the computed time-dependent thermal conductivity for said heterogeneous material.

[0146] In this case, no information on an analytical form of the time-dependent thermal conductivity of the heterogeneous was known or could be predicted. Therefore, method 300 was used in conjunction with method 500 to compute the timedependent thermal conductivity shown in FIG. 10B.

[0147] As shown in FIG. 10B, the thermal conductivity increases then starts to decrease, the thermal conductivity function in this case cannot be modelled by an exponential decaying function. This shows that the methods described herein, especially methods 300 and 500, can be used even for materials whose time-dependent thermal conductivities are complicated to predict. In fact, method 300 when used in conjunction with method 500 alleviate the need to guess or predict the analytical form of the time-dependent thermal conductivity of a heterogeneous material.

[0148] Reference is made again to solving 304 the heat equation representing the system comprising the heat source and the material sample.

[0149] When the thermal conductivity as a function of time for a given material is known, then the sensor temperatures over time can be determined with the heat equation. This is known as the direct problem. The direct problem has a solution for a one-dimensional heat flow, that is, the heat source and the material sample have the same cross-sectional area. To get the sensor temperatures, the following information is needed:- the heat flux (power per unit area) delivered by the heat source (referred to as Q in the equations);- The volumetric heat capacity pCpof the material sample, obtained from either a literature value or by directly measuring the volumetric heat capacity of the sample material;- the location of the heat source and the temperature sensor. For a TPS sensor, the heat source and the temperature sensor are both at the same location. In some embodiments, it is assumed to be at a location of z = 0; and- the boundary and initial conditions for the temperatures and heat fluxes on the sample. The first boundary condition would be the incoming flux from the heat source. If the temperature of the top surface of the material sample is kept at y0, the boundary conditions can be represented as: z = ) = V0(1) flux (constant (2) assuming the sample has thickness I, and l(t) is the time-dependent thermal conductivity of the sample material.

[0150] The heat equation for a one-dimensional heat flow is:where V = V(z, t) is the temperature field dependent on time and space.Mathematical Derivations

[0151] A system (e.g., the system 100) for measuring thermal conductivity allows for both symmetric setup (using identical samples) and asymmetric (using only a single sample) setup. Mathematical derivations of both setups are treated separately herein below.Symmetric Setup

[0152] For a symmetric test, two identical material samples of radii b and height I are placed on the opposite sides of a TPS sensor. Let z = 0 be the location of the sensor, and let the radius of the TPS sensor be a, where a < b. Let the power supplied by the sensor be P. Since the samples are placed on the opposite sides of the sensor, they would be located at 0 < z < I and at -I < z < 0. The two heat sinks are located at z = ±1.

[0153] The following assumptions are made to solve the heat equation:1 . the whole system 100 is at a temperature y0at the start of the measurement (t = 0);2. heat flows in one dimension (in the z-direction). This assumption requires a knowledge of the volumetric heat capacity of the material before the measurement;3. the heat sinks are kept at constant temperature, equal to the initial temperature y0all through-out the measurement. This translates to the following boundary condition:V(z = +l, ) = V0(4)4. the thermal conductivity of the sample is not constant but rather changes with time.

[0154] The corresponding heat equation can now be formed from the four assumptions above:

[0155] <5(z) is the Dirac delta function (since the source is only located at z =0) and u(t) is the Heaviside step function, since the power is turned on at t = 0 and is left on during the whole measurement. The equation is subject to the boundary condition V{z = ±1, t) = Vo. Because the setup is symmetric, the flux Q coming intothe material would be Q =However, because a < b, assumption no. 2 is not entirely correct. But as long as a / b is not far from 1 , then letting Q =would serve as a good approximation and would still allow us to use assumption no. 2. Thus, in full detail, equation (5) reads:subject to boundary conditions V(z = ±1, t) = y0. To solve this equation, we first divide (6) by l(t), thus

[0156] Let :T = fQ^T)dT (8) so that (7) becomes :where<p(T) = t.Equation (9) is subject to the boundary conditions V{z = ±1, T) = Vo. Since Vois constant, we can set V = V - Voand we get the following equation:subject to the boundary conditions V (z = ±1, T) = 0.

[0157] We then take the Laplace transform of (10) with respect to T, so that we get:where V is the Laplace-transform of V and S is the Laplace variable, andThe function (S) can be further simplified intoby making the substitution y = (p(l"). Note that equation (11 ) has the boundary conditionV(z = ±Z, T) = 0 (14)

[0158] From (11 ), (13) and (14), the Laplace-transformed temperature of the TPS sensor (V(z = 0,S)) can be obtained:

[0159] Taking the inverse Laplace transform of (15) gives the temperature of the TPS sensor. The inverse Laplace transform can be obtained numerically, or analytically. Analytically, the inverse Laplace transform of (15) is given by,Asymmetric Setup

[0160] For the asymmetric setup (as shown in FIG.4), the sample of radius b and height I is located at 0 < z < I. The insulative material of radius b and height ltis located at -lt< z < 0.

[0161] The following assumptions are made: (1) the insulative material is a perfect insulator, meaning, its thermal conductivity is zero, (2) the insulative material is thick enough that boundary effects from the insulative material can be ignored.

[0162] From the assumptions above, the sensor temperatures would be similar to (16), but <2 is multiplied by a factor of two.Contact Effects

[0163] In some cases, the effects of contact resistance and the heat capacity of the TPS sensor have an effect on the measurement. This would result in the addition of the following boundary conditions:

[0164] (z0) =is the flux at z0, the + superscript indicates the limit approaching from the right. Thus, V{z = 0+) is the limit of V(z) as z goes to zero approaching from the right (positive direction). Similarly, the - superscript indicates the limit approaching from the left (negative direction). The quantities R and Csrefer to the thermal contact resistance and the heat capacity of the sensor, respectively. Applying these boundary conditions on the symmetric test would yield the following Laplace-transformed temperature:Steady-State Constraint

[0165] When the asymptotic behaviour of (16) is taken, that is, (16) is evaluated as time approaches infinity, then the sensor temperature would approach a constant value yss. As time approaches infinity, the system reaches a steady state, thus, ysscan be obtained using Fourier’s law,<2°)

[0166] The asymptotic behaviour of (16) is given by,where yexptis the steady-state temperature rise of the TPS sensor obtained during the experiment, and y0= QR / 2. Since ensorC is dependent on the steady-state thermal conductivity Ass, (21 ) can be applied to (16), which means that one less parameter has to be determined with the nonlinear fitting procedure, leading to a better estimate of the time-dependent thermal conductivity function.

[0167] It would be appreciated by one of ordinary skill in the art that the system and components shown in the figures may include components not shown in the drawings. For simplicity and clarity of the illustration, elements in the figures are notnecessarily to scale, are only schematic and are non-limiting of the elements structures. It will be apparent to persons skilled in the art that a number of variations and modifications can be made without departing from the scope of the invention as described herein.

[0168] It is contemplated that any part of any aspect or embodiment discussed in this specification can be implemented or combined with any part of any other aspect or embodiment discussed in this specification.

[0169] It should be recognized that features and aspects of the various examples provided above can be combined into further examples that also fall within the scope of the present disclosure.

[0170] When used in this specification and claims, the terms "comprises" and "comprising" and variations thereof mean that the specified features, steps, or components are included. The terms are not to be interpreted to exclude the presence of other features, steps, or components.

[0171] The invention may also broadly consist in the parts, elements, steps, examples and / or features referred to or indicated in the specification individually or collectively in any and all combinations of two or more said parts, elements, steps, examples, and / or features. In particular, one or more features in any of the embodiments described herein may be combined with one or more features from any other embodiment(s) described herein.

Claims

CLAIMS:

1. A method for determining thermal behaviour of a material, the method comprising: receiving measured temperatures of the material, times of the measured temperatures, a volumetric heat capacity of the material, and a flux supplied by a heat source, wherein the flux supplied by the heat source over a measurement period provides a temperature response in the material; and applying a non-linear fitting technique to determine a time-dependent thermal property of the material, applying the non-linear fitting technique comprising: computing estimated temperatures using an initial estimate of the time-dependent thermal property at measurement times and a temperature function that is a function of the volumetric heat capacity, time, the flux, and the time-dependent thermal property; and iterating values of the time-dependent thermal property to minimize an error between the measured temperatures and estimated temperatures computed using the iterated values of the time-dependent thermal property, wherein the time-dependent thermal property is determined as a value that results in a minimum error measure between the measured temperatures and the estimated temperatures.

2. The method of claim 1 , wherein computing the estimated temperature at each measurement time takes into account an estimated temperature of at least one previous measurement time.

3. The method of any one of claim 1 or 2, further comprising: determining the temperature function by solving a heat equation that is a function of the volumetric heat capacity, time, the flux, and the timedependent thermal property.

4. The method of claim 3, wherein the temperature function is a solution to the heat equation of a physical system with boundary conditions describing a thermal contact resistance and / or a heat capacity of the heat source and / or a temperature sensor.

5. The method of claim 3 or 4, wherein solving the heat equation when absent information on an analytical form of the time-dependent thermal property, comprises: dividing the measurement into a transient region and a steady-state region; and representing the time-dependent thermal property as a piecewise function wherein a constant value of the time-dependent thermal property is assigned at the steady-state region and a linear combination of splines is assigned at the transient region.

6. The method of claim 5, wherein absent information on the analytical form of the time-dependent thermal property, the method further comprises, prior to applying the non-linear fitting technique to determine the time-dependent thermal property: creating a set of cardinal times from which spline basis functions can be constructed.

7. The method of claim 6, wherein the spline is a cubic spline.

8. The method of claim 3 or 4, wherein the time-dependent thermal property has a constant term and a time dependent term, wherein the time dependent term is a product between a constant parameter and a time dependent function, wherein the time dependent function is finite and positive at all times and has a finite positive limit as time goes to infinity.

9. The method of any one of claims 5 to 8, further comprising determining the initial estimate of thermal property of the material by:dividing the measurement into transient and steady-state regions when a function representing the time-dependent thermal property is known; determining a short-time behaviour of the function representing the time-dependent thermal property by selecting an initial subset of measured temperatures from the transient region and using a linear fit of temperature to root time; determining a long-time behaviour of the function representing the timedependent thermal property from the steady-state region using Fourier’s law; and determining unknown parameters using a nonlinear fitting procedure with the short-time and long-time behaviours of the function representing the time-dependent thermal property being fixed.

10. The method of any one of claims 1 to 9, wherein the time-dependent thermal property is one of: thermal conductivity, thermal effusivity, thermal diffusivity, and volumetric heat capacity.

11. The method of any one of claims 1 to 10, wherein the material is heterogeneous.

12. The method of any one of claims 1 to 10, wherein the material is homogeneous, and the time-dependent thermal property is constant with time.

13. A system for measuring thermal behaviour of a sample material over a measurement period, the system comprising: a first heatsink and a second heatsink; and a vertical stack for receiving the sample material, the vertical stack arranged between the first heatsink and the second heatsink, the vertical stack comprising :a heat source configured to supply a heat flux that provides a temperature response in the sample material over the measurement period; and a temperature sensor for measuring temperature of the sample material, the temperature sensor, wherein the first and second heatsinks are configured to pull away heat from the sample material during the measurement period.

14. The system of claim 13, further comprising a heat flux sensor for detecting a steady state flux of the heat source, the heat flux sensor being located under the first heatsink, the sample material being located between the temperature sensor and the heat flux sensor.

15. The system of claim 14, further comprising a movable contraption configured to bring the first heatsink in contact with the heat flux sensor for the measurement.

16. The system of any one of claims 14 or 15, further comprising a data acquisition device configured to collect heat flux sensor data and temperature sensor data.

17. The system of any one of claims 13 to 16, wherein the vertical stack further comprises a block material located between the second heatsink and the heat source.

18. The system of claim 17, wherein the block material is a thermal insulating material.

19. The system of claim 18, wherein the thermal insulating material has a thermal conductivity of less than about 0.1 W / mK.

20. The system of any one of claims 17 to 19, wherein the block material is a supplementary sample material identical to the sample material.

21. The system of any one of claims 13 to 20, wherein the vertical stack further comprises the sample material.

22. The system of any one of claims 13 to 21 , wherein the heat source and the temperature sensor are combined into a transient plane source.

23. The system of any one of claims 13 to 22, wherein a center of each component of the vertical stack is aligned.

24. The system of any one of claims 13 to 23, wherein each component of the vertical stack has an identical shape.

25. The system of any of claims 13 to 24, wherein each component of the vertical stack has a cylindrical shape.

26. The system of any one of claims 13 to 25, wherein the first heatsink is further configured to apply a pressure onto the vertical stack to maintain the vertical stack in a locked configuration during the measurement.

27. The system of claim 26, wherein a force sensor is attached above the first heatsink to measure the pressure applied onto the vertical stack.

28. The system of any one of claims 13 to 27, wherein the heat source provides a constant heat flux to the sample material over the measurement period.

29. The system of any one of claims 17 to 20, wherein the second heatsink is further configured to pull away the heat from the block material.

30. The system of any one of claims 13 to 29, wherein at least one of the first and the second heatsinks comprises a passive heat sink.31 . The system of any one of claims 13 to 30, wherein at least one of the first and the second heatsinks comprises a liquid-cooled heatsink.

32. The system of any one of claims 13 to 31 , wherein a temperature of each of the first and second heatsinks is set by an electronic temperature control system for measurements above 100 °C.

33. The system of any one of claims 13 to 32, further comprising a passive guard that wraps around the sample material.

34. The system of claim 33, wherein the passive guard is actively heated by an electronic temperature control system for measurements above room temperature.

35. The system of any one of claims 13 to 34, wherein the height of the system is measured electronically.

36. The system of any one of claims 13 to 35, wherein a levelling system is attached above the first heatsink to facilitate system alignment and parallelism.

37. The system of any one of claims 13 to 36, further comprising a computer device comprising: a network interface for receiving temperature sensor data from the acquisition device; a processor; and a non-transitory computer-readable memory storing computerexecutable instructions which, when executed by the processor, configure the system to perform the method of any one of claims 1 to 12 based on the temperature sensor data.

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