TECHNICAL FIELD

The invention relates to a method and a device for measuring of thermal transport properties of a material (e.g. materials or layered materials and substances).

BACKGROUND ART

In US 5,044,767 is described a measuring device which comprises a thin element or layer of an electrically conductive material, e.g. metal, to be used for measuring thermal transport properties of a sample. The measuring device is brought in heat conductive contact with the sample to be measured. An electric current is passed through the electrically conductive material so as to heat the contact surfaces of the sample in order to cause an increase of the temperature of the sample. The increase, or variation, of the temperature on the contact surface is measured by measuring the voltage variation of the element or layer of the electrically conductive material. The increase of temperature with time depends on the thermal transport properties of the sample.

Another method for measuring of thermal transport properties is described in WO 00/70333. This method discloses the use of a similar sensor and heating device as in US 5,044,767 for measuring thermal transport properties of an anisotropic sample, i.e. a sample having the same thermal transport properties in the x-y directions (i.e. the plane which is parallel to the surface plane onto which the heat is applied and measured) but a thermal transport property in the z direction (i.e. the direction perpendicular to the surface plane) differing from the transport property in the x-y plane. This method thus allows calculating and distinguishing between thermal transport properties such as heat conductivity and diffusivity in the x-y-plane and in the perpendicular z-direction. This method has been used as a basis for the standard ISO 22007-2 for measurement of thermal transport properties of plastics and is therein thoroughly described.

DISCLOSURE OF INVENTION The invention relates to a method for measuring of thermal transport properties of a substance. According to the invention is heat applied to the surface of a subject to be measured by means of an appropriate energy source while measuring of the temperature of the surface onto which the heat energy is applied is performed a desired number of times.

So far, this method is similar to the procedure described in the patents cited above. However, as will be discussed more in detail below, this method is in particular intended to be used for measuring the thermal transport properties of inhomogeneous or layered material having different thermal transport properties as a function of the distance from the surface to which the heat is applied, i.e. different thermal transport properties in the z-direction. Hence, this method provides an estimation of thermal transport properties at different distances from the surface of the subject to which a heat flow is applied. The thermal transport properties are estimated by the use of mathematical calculations and the measured temperature values. According to the method is a first estimation of thermal transport properties made by using a first set of measured temperature values. These values are measured at certain time points which are associated with the measured temperature values. The measured temperature values are treated mathematically, based on a physical model, and thermal transport properties may be estimated. The estimated thermal transport properties may thus be associated with a time derived from the time points for the temperature values used.

There is also at least a second estimation of thermal transport properties made by using a second set of measured temperature values which also are measured at certain time points and associated with the measured temperature values of the second set. The second set of measured temperature values differs from the first set of values in that it comprises at least one measured temperature value associated with a time point differing from the time points comprised in the first set of temperatures for the first estimation of a thermal transport property. As described for the first set of measured temperature values, also the second set of measured temperature values are treated mathematically, based on a physical model, such that thermal transport properties may be estimated. The estimated thermal transport properties may thus be associated with a time derived from the time points for the second set of temperature values. By using the time points for the temperature values of the first and second set, it is possible to associate the estimated thermal transport properties of each set to distances from the surface on which the temperature is measured. Hence, the first and second estimation of the desired thermal transport property corresponds to distances from the surface on which the temperature is measured and those distances are related to the time points used for said estimations.

In order to achieve the above object of getting a value of a thermal property as a function of the distance to the surface (or depth depending value), it is assumed by the theoretical model that there is a 1 -dimensional heat flow into the material which is the subject of the measurements. This assumption may be made during a relatively short time when heating of the surface, which is the subject of the temperature measurements, starts. The possible time to approximate the heat flow as 1 -dimensional is depending on the conductivity of the material which is measured on, i.e. materials having high thermal conductivity (e.g. metals) will imply a shorter maximum time available for making temperature measurements relevant to be used in the calculations than materials having low thermal conductivity. Another factor influencing the maximum time for relevant temperature measurement is the area onto which the heat is supplied. If heat is supplied to a large area, the heat flux may be approximated as a 1 -dimensional flow for a longer time. In particular, it would be possible to reduce the influence from edge effects by applying heat to a rather large area while performing the measurements in the central part of the heated surface area. In general, the model used in this method allows to make this assumption for a depth, or distance to the surface, in the same range as a radius of circular surface area which is heated.

The present method thus provides a model for measuring temperature on the surface of a material and getting information of the thermal transport properties in the surface layer and being able to estimate the thermal transport properties. This method thus provides a non-invasive method for estimating thermal transport properties as a function of the distance from the surface. Providing such a non-invasive method for achieving these kinds of properties has a wide range of different uses as will be exemplified below. In many applications it may not be the actual value of the thermal transport property which is of interest but the thermal transport properties may be used as an indication of the status of the surface of an object. One such use could for example be the coating or painting process for a vehicle wherein a steel plate is covered by spray painting. If there is a desire to check the thickness of the coating, and make sure the thickness is the same or sufficiently thick all over the plate, it may be possible to use the present method to compare, for example, lambda values (thermal conductivity) at different spots on the coated surface. By indicating at which depth (distance from the surface) there is a considerable change in the lambda values, it is possible to estimate the thickness of the coating layer. In this case is it of course stipulated there is a difference in the heat conductivity between the coating layer and the underlying metal plate.

Still another example of use of the method may for example be detecting properties of the skin, e.g. the measurement of thermal transport properties as a function of the depth may indicate anomalies such as cancer or other irregularities beneath the surface of the skin. It has been verified that different symptoms, or different modifications of the normal skin, implies a change of the thermal transport properties of the skin.

It may thus also be possible to evaluate or indicate a penetration depth of a substance changing the thermal transport properties of the skin, e.g a skin lotion or cream, and performing a number of measurement sequences over the time in order to estimate for how long the cream will stay in the skin surface layer and at which depth. Hence, the present method provides a tool for making an estimation of the thermal transport properties of the surface of an subject as function of the distance to the surface and may thus, by adding a number of different estimations representing different distances from the surface, create a profile or curve of the thermal transport properties as a function of distance (depth). This has not been possible before and previous methods have only been able to make measurements of homogenous samples or, more correct, the models previously used treat the sample as homogenous with respect to the thermal transport properties in the z-direction. Hence, these models will only provide an average value of the thermal transport properties of the measured subject. No relevant, distance depending information could thus be achieved for an inhomogeneous sample but only a mean value. No technique has hitherto been developed in order to determine the spatial variation of the thermal transport properties of an inhomogeneous sample from a single set of measurements, placing a sensor probe at a single location in contact with the sample.

Examples of thermal properties, or thermal transport properties, which may be of interest to estimate in the described method are for example thermal conductivity (λ), thermal diffusivity (a) and thermal effusivity (E=A(a) ^{'0 5} ). In the examples comprised herein, the thermal conductivity and thermal diffusivity are used in the physical model upon which the mathematical calculations are made and those are thus the thermal transport properties which are estimated in these examples. In general, these estimated values may be used for deriving other thermal transport properties by using known relationships and using known data of the samples. The properties described above may in different contexts be referred to as thermal properties, thermal transport properties or thermo-physical properties.

There may be used a variety of different equipment in order to apply a heat flow to the surface of the subject to be measured and different measuring devices may be used to perform the temperature measurements. Suitable equipment may be the probe described in US 5,044,767 and WO 00/70333, i.e a probe comprising an electrically conductive material such that the surface of the object to be measured is heated by ohmic heating. However, the probe described in these documents is intended to be sandwiched between two identical pieces of material and supply heat to both these surfaces. In many cases is it desired to be able to apply heat to only one surface. This may for example be the case when there is a difficulty to provide two identical samples or when the surface is part of a rather large subject to be measured, e.g. the skin of a person or a painted sheet metal panel of a car body. For this purpose a special probe has been designed wherein one side of the probe has been provided with an insulating backing material and the probe may thus be used for measurements on one single surface. The thermal insulating properties of the backing material of the probe shall preferably be considerably higher than the thermal insulating property of the sample which is the subject of the measurements such that it may be approximated the complete heat flow from the probe is penetrating into the surface of the sample. It may of course be possible to include the heat flow to the backing material and compensating for this flow in the model but this will in general be difficult to estimate, in particular if the backing material has a relatively low insulating ability and allows a large flow of heat to the back side. The advantage of using an ohmic heater as described in WO 00/70333, with or without the heat insulating backing material, is that it provides a well defined amount of heat flow to the surface while also being able to perform very exact measurements of the temperature such that accurate input data for the estimation of thermal transport properties of the measured object may be provided.

Even though the above described equipment is suitable for the present method, it is obvious that other means for performing the method also may be used, e.g.. heating of the surface by microwaves and temperature reading by IR sensors. It shall also be noted that the heat does not have to be continuously supplied but it may also be possible to use heat applied at intervals, e.g. by regulating the power supply of an ohmic heater to be turned on and off in short intervals or irradiate by microwaves at time intervals. However, in general, the heat is applied by using a device for continuously delivering a well defined heat flow to the surface while measurements are made at uniform time intervals.

Even though there is no specific limitation of the size of the area to be the subject of measurements and heating, an appropriate size of the area for the probe is generally considered to be less than 10 square centimetres and preferably less than 5 square centimetres. While a larger area of the probe in general provides an improved accuracy of the subject matter to be measured, a smaller area of the probe implies a smaller probe which is easier to handle and make it possible to distinctly point out a small spot for the measurements. For many applications, the active area of the probe is less than 1 square centimetre. In certain application it may be desired to use a very small probe, e.g. for microelectronics, semi conductor devices or for internal investigations of the human body such that the probing area may be down to a few square millimetres or less. The probing area, or heated area, is also the main parameter for deciding the probing depth, i.e. the length or distance below the surface down to which relevant estimations of the thermal properties may be made, and for many applications of the present method is this distance thought to be well within 1 centimeter, e.g. for measurements made on the skin or on a painted car body panel. Even for subjects having a rather large volume it has often turned out that the part of certain interest is often the surface layer and a probing depth down to 1 centimetre is in most cases sufficient. The specific interest of the surface layer may be because the surface has been treated such that the surface properties differs from the internal, bulk structure which are well known or that the surface has been changed due to wear or abrasion. However, by increasing the surface area subjected to heating and, optionally, measurement, it may easily be possible to achieve thermal transport property values at a profounder depth, i.e. further away from the heated surface.

The mathematical model, or the mathematical calculations, may be made according to the model described below. In short, this model represents the temperature changes of the surface as a function of the thermal transport properties in the surface layer assuming a one-dimensional heat flow from the surface into the subject to be measured. In order to be able to make this approximation, the temperature measurements must be made during a relatively short time period while the heat flow may be approximated to be linear in a direction perpendicular to the heated surface and into the subject to be measured . Hence, the formula below thus describes a way of making the estimations of the thermal conductivity and the thermal diffusivity. The formula is as follows:

Δ T(ti) = A _z + Po * ( _π ^{(3 2)} * r * λ _ζ ) ^"1 * f ( _Tzi ), ¾ = t _z> ..... t _z + t _subset wherein ti is time point nr. i; Δ T(ti) is the temperature increase measured by the sensor at time point t,; A _z is a free variable, representing a thermal contact resistance between sensor and the surface of the measured object;

P ₀ is the heating power applied to the sensor;

r is a characteristic length scale of the transient plane source sensor (typically a radius for a disk-shaped sensor, or a strip length for a strip- shaped sensor);

λ _ζ is a free variable representing a best-fit thermal conductivity associated with d _z or t _z ;

Tz, is a dimensionless time, τ _ζ , = (ti-t _z , _C orr)° ⁵ Θ _Ζ ^" ° ⁵ ;

tz.corr is a free variable representing a time correction;

θ _ζ is a free variable representing a characteristic time, 0 _z =r ² /a _z for a disk- shaped sensor;

a _z is the best-fit thermal diffusivity associated with d _z or t _z;

t _SU bset is the length of the time interval incorporating the set of data points used for the estimation of thermal transport properties associated with d _z or t _z ;

Oaverage IS 3 Characteristic time, and

f (τ) is a dimensionless time-function, depending on the particular geometry of the sensor and evolution of heat flow. For short times, corresponding to essentially 1 D heat flow, f (τ)=τ for any plane sensor geometry (disc-shaped, square, strip-shaped etc.

Guidance for selecting parameters and functions to be used, e.g. for t _z , _CO rr or f (τ), may for example be found in ISO 22007-2.

In the equation above, the calculated thermal transport properties are associated with time points. In order to be able to correlate the time points with a distance from the surface to which heat is applied and on which the temperatures are measured, some kind of physical model should be used. One model to correlate the relation between the distance of the estimated values of the properties (heat conductivity and diffusivity in this case) to the surface of the measured object and the time points at which the measurements are made is approximated by the equation:

d _z = COnSt * (a _aV erage * t _z )°' ⁵ wherein d _z is the thermal depth of probing (or "probing depth");

const is a dimensionless model constant within the interval [1 ,3] ;

a _aV erage is average thermal diffusivity within the measured object;

t _z is the time representing the time interval selection of time measurement pOintS [t _z , tz+t _su bset]

This relation has turned out to give a reasonably well approximated value of the depth (or distance from the surface) of the values of the thermal transport properties. In order to improve this model it could be correlated, e.g. by changing the value of the constant, to some reference for a certain material or group of materials having similar thermal transport properties. In many cases it may not be important to exactly verify the depth at which the value of the thermal property is present but it may rather be of interest to perform comparative measurements where it is of interest to know the relative positions of a boundary layer, e.g. to compare relative penetration depth of a liquid or cream applied to a surface when compared to a second liquid or cream.

The temperature measurements of the surface is preferably performed at evenly distributed intervals and could be made at least one time every second, more preferably at least 5 times every second and most preferably at least 20 times every second. The sampling rate needed is dependent on the thermal transport properties of the subject for the measurements and the size of the heated surface area. For a small area on the surface of a highly conductive material (metal, e.g. copper), there is a need to make the samplings rather quick while measurements made on a rather large area for a less conductive material (e.g. skin), the samplings may be made with longer time intervals. The time point of the temperature measurements need not to be made at the same sampling frequency but for the sake of simplicity are they usually made this way. In case there is not a need for the use of all measured values, the undesired values are simply not used for the calculations.

It is mentioned that at least two sets of measured values shall be used in the model. It is not critical the exact number of measurements values that are contained within each set. However, a reasonable amount of measured values should be needed in order to get a reliable result and at least 5 measured values are considered to be necessary, preferably at least 10 measured values and most preferably at least 50 measured values. The desired number of values to be used is also dependent on the sampling rate possible and the heat conductivity of the material to be measured; High heat conductivity of the material and slow sampling rate indicates that rather few measurements should be used for each set since there will be rather few measurement points in the complete set of measurements. However, too few measurement points may not be desired since there may be noise in the measurements which will not be compensated for if too few measurements are used. In addition, when making a "best fit"-approximation using least square method or the like mathematical treatment, too few measurement points may result in an unreliable result. In the case of making measurements of skin, having a heat conductivity of approximately 1 - 2 λ (W / mK) and using a probe having a circular surface area of approximately 30 square millimetres, a suitable number of measured values for each set may be within the range of 20 - 100 if the sampling interval is around 50 every second. Too many values may not be desired since the calculations may be slow and there will be less sharp depth dependence of the measured values. Even though the present method could work with only two sets of measurement points used for estimating the thermal transport properties, it is thought that a minimum of least 5 different sets of measured temperature values are used, more preferably at least 10 different sets and most preferably 20 different sets indicating thermal transport properties corresponding to different depths in the surface layer. Each set is thus used for estimating the thermal transport properties of the subject at different distances from the surface which is measured on. As already mentioned, this method is considered to be suitable for estimating thermal transport properties of the skin of a human being or animal. Studies has shown that skin of different regions of the body usually have different thermal transport properties. However, almost surprisingly, studies has shown that the thermal transport properties of the skin of a certain region of the body is almost the same for different individuals provided that the skin has not been subject to any damage recently or have been permanently changed due to illness or accidents. Hence, the method may be used for detecting changes or irregularities of the structure of the skin in order to make a diagnosis of the status of the skin, using known reference values. Since there has not been any extensive research in this field yet there are yet not reliable data for making any detailed diagnosis based on this method. It is however evident that changes of the skin due to some illness usually also implies a change in the thermal transport properties of the skin. This method may thus be used to measure and estimate the thermal transport properties of the skin below the visible surface such that a non-visible, structural change of the skin may be detected. These changes may, with further research and experimental data, be used for diagnosing of particular symptoms or diseases affecting the skin. The method may further be used for evaluating a wide variety of surface treatment of essentially any kind of surfaces of subjects to be measured on. By making a comparative analysis of an untreated surface and a treated surface, wherein the treatment affects the thermal transport properties of the surface, it will be possible to evaluate the extent of the treatment. It may for example be possible to evaluate the penetration depth of the treatment due to a depth depending change of thermal transport properties. Such a treatment of a surface may for example be to apply some kind of skin care lotion, or a purely cosmetic substance, to the skin and by measuring the thermal transport properties estimating the penetration depth of the substance. It may also be able, by performing several measurements during a longer time, to evaluate the ability of a lotion to stay within the skin layer and thus estimate for how long and how deep the substance will remain in the skin. This would also be possible for other surfaces such as a wooden surface which has been treated with oil. Further examples for which the method may be useful is in the heat treatment of metal, in which the penetration depth of the treatment may be evaluated, coating or painting of sheet metal, surface properties of food products as an indication of the freshness of the product or invisible, below the surface, crack formations on structural elements subjected to forces without no evident sign of crack formations. Concerning the use of the method on humans, it has only been exemplified to use it for measurements of thermal properties of the skin. However, the method could also be used for other organs such as for example the liver, heart, arteries or pleura. The probe could be introduced into the body in known manner and perform in vivo measurements of thermal properties of such organs.

A field of specific interest for the present invention is the use as a quality assurance tool for detecting irregularities of surface treated subjects. In these cases are measurements made on surfaces intended to have been treated in the same way such that the same thermal transport properties should be present all over a certain surface. The subject for these measurements may for example be a subject which surface has been treated in order to increase the thermal insulation properties. By the use of the present method, and having a reference value or a reference curve which indicates a limit or two values or curves indicating an interval, it will be possible to compare and indicate differences of thermal transport properties below the visible surface as an indication of irregularities in the surface layer. To be able to use a noninvasive method for these purposes is thought to be of great importance since it will make it possible to evaluate an end product without ruining the surface layer when performing the tests of the product. Hence, the present method provides a tool for making an estimation of the thermal transport properties of the surface of an subject as function of the distance to the surface and may thus, by adding a number of different estimation at different distances from the surface, create a profile or curve of the thermal transport properties as a function of distance (depth). This has not been possible before and previous methods have only been able to make measurements of homogenous samples or, more correct, the models used treat the sample to be tested as homogenous such that no relevant value may be achieved for an inhomogeneous sample. No technique has hitherto been developed in order to determine the spatial variation of the thermal transport properties of an inhomogeneous sample from a single measurement, placing a sensor probe at a single location in contact with the sample.

BRIEF DESCRIPTION OF DRAWINGS Fig. 1 . Impacts on skin vs. depth caused by two different skin creams. Fig. 2. Basic structure of human skin. Fig. 3. Single-sided sensor.

Fig. 4. Temperature vs. time plot, and example of model. EMBODIMENT(S) OF THE INVENTION

The method described herein has been developed in order to overcome certain deficiencies of the previous methods. In many practical situations there is a need for non-destructive testing of thermal transport properties from one accessible surface only, and where the thermal transport properties varies spatially as a function of depth beneath the surface. Generally, thermal transport properties depend strongly on the particular structure of a sample. Therefore minor structural changes may have a measurable impact on the thermal conductivity. For instance, heat treatment of a metal alloy or an adjustment of fat content in a substance will normally result in changes in thermal conductivity, recordable with the above-mentioned techniques. The results and correlations for homogeneous isotropic or anisotropic materials have been documented in the literature and are for example described in the documents cited in the background art section.

For samples having a spatial variation of the structure vs. depth beneath the surface, it is expected that the thermal transport properties varies as a function of depth. Also, application of a penetrating substance onto sample surface may result in diffusion of the substance and a consequent structural change within the sample. One such example is the application of cream on human skin. The spatial variation of thermal conductivity of skin - without application of the skin cream - is found to differ from the spatial variation of thermal conductivity of skin onto which cream has been applied. The comparisons of thermal conductivity vs. depth profiles, which can easily be detected by the present invention, provide hitherto unavailable information on the particular action of a certain skin cream and its action at different depths as depicted in Fig. 1 . Such a graphical view may in an easy way describe the differences in penetration depth and saturation at different depths as a comparative analysis. The graph of fig. 1 shows the thermal conductivity λ (vertical axis) in units W / mK as a function of probing depth z (horizontal axis, in mm). Measurement time for each individual experiment (with corresponding curve) is 20 seconds, heating power 0.08 W, sensor diameter 6.7 mm. It may thus be easily seen that the lowest, continuous line represents no cream added to the skin and the heat conductivity is less in this experiment than in the two other curves representing cream added to the skin. The dashed line represents skin treated with "Cream 1 " while the dotted line represents skin treated with "Cream 2". As obvious from these curves, the impact on the heat conductivity when using "Cream 2" on the skin is larger than when using "Cream 1 " for the uppermost 0,5 mm of the skin layer or, to be even more accurate, for the part of the skin at a depth of 0,3 to 0,5 mm from the surface of the skin. In this aspect the graph also illustrates the problem of being able to measure the heat conductivity very close to the surface. The heat will flow into the subject very rapidly during the first seconds such that there will usually not be time enough to be able to perform sufficient measurements to estimate the surface layer closest to the probe. For skin is this distance around 0,2 - 0,3 mm as shown in the curves. In order to get a relevant estimation of the relationship between the heat conductivity value and the distance to the surface onto which heat is applied, the heat conductivity of this part of the skin need to be measured or estimated.

The change of the heat conductivity of the skin is due to the existence of cream in the skin. The presence of a substance in otherwise porous structures will thus increase the heat conductivity and the results from these curves shall be interpreted as there is a better penetration into or saturation of the skin when using "Cream 2" than when using "Cream 1 ". If there is a desire to quantify these comparative results there is a need to produce one or several reference samples in which specific saturation levels, absolute amounts of applied creams or other references which make it possible to relate the heat conductivity to a saturation degree or amount of applied and absorbed cream.

Figure 2 depicts the basic structure of human skin. The thickness of the epidermis 201 , i.e the outermost layer, varies between around 0.05-1 mm depending on the location of the skin. Similarly, dermis 202 normally varies between 1 -10 mm. The dermis 202 is located above the subcutis 203. When studying Fig. 1 , it can be noted a characteristic bend for all three curves at a depth slightly below 0.4 mm. This bend is most likely corresponding to the position of the structural change at the epidermal-dermal junction.

In addition to use the method for detecting effects of the skin by treatment of the same or addition of a substance, the identification of widespread or local anomalies in a biological material or substance beneath the surface, e.g. skin basal cell cancer or lymphatic metastases, can be detected and analyzed with the present invention in a non-destructive, non-invasive manner.

Even though the skin is the main object for the experiments described herein, there are several other examples on other application with inhomogeneous structures such as quality-control measurement of compound metal structures, ceramic heat-resistance coatings and inhomogeneous microelectronic structures.

The invention is based on the assumption that the heat flow from a source may be applied to a surface and under certain circumstances may the heat flow be approximated by a 1 -dimensional flow into the subject to be measured on. Results from current research confirms that measurements of spatial-variation of thermal transport properties is possible by adjustments (as compared to the documents US 5,044,767, WO 00/70333 and international standard ISO 22007-2) in selection of measurement time, frequency of data point acquisition and the procedure for numerical treatment of the physical model for estimating the thermal transport properties. Hence, if using the method described in ISO 22007-2 as a starting point, the key modifications in order to perform measurement of spatially varying thermal transport properties of an inhomogeneous sample are related to the measurement time, i.e. the time interval during temperature measurements are made, data logging frequency, i.e. the sampling interval or the time between the temperature measurements and the analysis of data. To be noted, and as explained in the general part of the description, the sampling frequency and the total time interval is dependent on for example such parameters as the thermal heat properties of the subject to be measured and the size of the area onto which a heat flow is applied. It may thus be possible that the same sampling frequency and total measurement time could be the same when for example performing an analysis of a highly conductive material, using a rather small probing area for the method as described in ISO 22007-2 as when performing an analysis of a subject having low thermal conductivity and using a rather large surface area to be heated and measured in the method as described herein. However, measuring on subjects having essentially the same heat conductivity properties, and using the same size of sensor - heating area, the present method demands a higher sampling frequency (i.e. more temperature measurements per time unit) and the temperature measurements relevant for the calculations should be measured during a shorter total time interval than what is needed and desired for the method of ISO 22007-2.

When performing a measurement according to the present method, a sensor design as described in ISO 22007-2 may be used and for detailed information of the sensor is it thus referred to ISO 22007-2. The sensor may thus be applied in a double-sided configuration. However, in general, it is preferred to use a single-sided measurement configuration due to convenience and ability to be used for a larger number of subjects to be measured. As previously mentioned, a single-sided measurement configuration, i.e. a "stethoscope-type measurement", should preferably be provided with a backing material as shown in fig 3. The sensor 301 comprises an electrically conductive material used as a heating source as well as a temperature measurement probe. A backing material 302 is provided on the backside of the sensor. The backing material is suitably selected as having a high thermal insulation (e.g. low thermal conductivity) in comparison to the sample being tested.

An electronic circuit, as described in ISO 22007-2, is used in order to supply a constant electric power to the sensor. The electric power is irreversibly converted into ohmic heat, which in turn dissipates through the surface into the sample. The average temperature increase of the sensor - typically in the shape of a double-spiral pattern - is recorded as a function of time, i.e. a transient recording of the temperature increase vs. measurement time is conducted. The sensor is therefore utilized both as a heat source and as a resistance thermometer simultaneously. A comparatively high electrical current passing the sensor of the order a 200-400 mA enables a precise, high-sensitivity measurement of average temperature increase of the double- spiral pattern of the sensor. The temperature measurement is typically with a sensitivity of or better than 100 micro-K. There is no exact critical size for the sensor area. For instance, for identifying structural changes of human skin, the dimension of the sensor can favourably be selected with a sensor diameter of 6-7 mm, making it possible to probe into the first 2-3 mm layers with a decent accuracy for estimation of the thermal transport properties. In general, the accuracy of the measurements, as well as the possibility to measure thermal transport properties deeper into the subject, is achieved if a larger surface contact area of the sensor pattern is selected. Hence, in this perspective, more favourable experimental conditions are obtained if the surface contact area of the sensor pattern is selected as large as possible. However, there are often a sample-side limitation which limits the dimension of the sensor. In addition, some times there is a desire to concentrate the measurements to a certain, small area and in those cases it may be desired to use a smaller probe. However, it may be possible, if the sample to be measured allows it, to apply heat to a rather large area while performing the measurements at a local point in the midst of that area such that a large area is uniformly heated while the measurements represent a smaller area. For the present probe such an arrangement may be achieved by providing a heating device, forming an outer circle surrounding the probe area and applying the same heat flow per area unit as the probe itself, such that the temperature measurements are only made in the central part (comprising the probe) while a larger surface area is heated. In such a way, the measurement may provide relevant values further below the surface without increasing the area on which measurements are made.

The measurement time to be used when making the estimation of the thermal transport properties according to the method herein described is t _max - 0,1 x Oaverage where Oaverage = r ² / a _aV erage wherein t _ma x is the measurement time, i.e. the time interval during which temperature measurements are made r is the radius of the sensor (or another corresponding characteristic length if the sensor geometry is not circular), and 0 _aV erage is the average thermal diffusivity of the sample. This measurement time enables an approximately 1 - dimensional heat flow oriented from the sensor into the sample, corresponding to a total probing from the surface down to a depth of around d =0,6 x r. Hence a smaller radius will limit the measurement to a smaller area in the sensor plane, as well as a shallower depth into the sample.

The present invention requires, or at least desires, a faster data logging frequency as for example described in ISO 22007-2. In short, a maximum amount of temperature data recordings should be obtained within the measurement time of t _ma x - 0, 1 x 0 _ave rage- There is an inverse correlation between noise in temperature data logging and the amount of samples obtained. It is recommended to adjust sampling rate to obtain a good balance regarding final resolution in depth profile versus acceptable noise in thermal conductivity estimations. Some trial-and-error testing of obtaining a balanced sampling rate and noise rejection may be required. The transient recording results in a set of discrete points of temperature as a function of time AT(t), which is used for further data analysis.

In the analysis of data, the measurement data are mathematically treated so as to obtain an estimation of the spatially varying thermal conductivity λ(ζ) and thermal diffusivity a(z) of the sample as a function of depth z below the surface. The mathematical treatment involves division of the total measurement time t _max ~ 0,1 x 0 _ave rage into data sets corresponding to temperature vs. time for limited time windows of length approximately 0,04 x t _max and indexed at a certain time t _z from the start of the transient recording. For each such time interval, the limited number of temperature data points as a function of real time (from the start of the transient recording) is subject to a best-fit procedure against a theoretical model described in ISO 22007-2. A curve made out of these best fit values is shown in fig. 4 using the physical model represented by the formula for Δ T(t). The free variables in the iteration scheme are λ _ζ , A _z , θ _ζ and t _cor r,z- Iteration of best-fit model results in λ _ζ (ί _ζ ) and a _z (t _z ). Since one may select t _z in the time interval [0, t _max ] and relate d _z (t _z ) = const * (a _aV erage * t _z ) ^0,5 , it is possible to plot λ _ζ (ί _ζ ) and a _z (t _z ) as function of the depth. This best fit procedure renders a local estimate of the thermal conductivity and a local estimate of the thermal diffusivity at an approximate depth position d _z = const * (a _aV erage * t _z ) ^0,5 where the constant before the square root numerically is within the range [1 , 3] and most often chosen to 2. Adjusting the subset of data points will render approximate thermal transport property results at a new depth position z. Repeating the adjustment of subset of data points will eventually result in estimation of thermal transport properties λ(ζ) and a(z) as a function of depth position z. Since the heat flow is nearly 1 -dimensional (at least for shorter times t _z ) it may become necessary to stabilize the estimation of the thermal transport properties λ(ζ) and a(z), suitably by assuming the specific heat c _p times the density p of the material is assumed to be constant throughout the inhomogeneous layer, which is for a wide range of inhomogeneous samples a very good approximation. This assumption has proved to be efficient in order to stabilize the estimation of the thermal transport properties.

The above described mathematical models may be substituted for similar ones while still using the basic idea of the invention, i.e. to perform temperature measurements on a surface of a subject which is heated and performing these measurements during a rather short period while the heat flow may be approximated to be a one-dimensional flow into the subject to be measured.