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Development of a guard-heated thermistor probe for the accurate measurement of surface temperature
International Journal of Heat and Mass Transfer 108 (2017) 2283–2292
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Development of a guard-heated thermistor probe for the accurate measurement of surface temperature Takahiro Okabe a,⇑, Junnosuke Okajima b, Atsuki Komiya b, Shigenao Maruyama b a b
Graduate School of Science and Engineering, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 980-8577, Japan Institute of Fluid Science, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan
a r t i c l e
i n f o
Article history: Received 21 September 2016 Received in revised form 10 January 2017 Accepted 19 January 2017
Keywords: Temperature measurement Surface temperature Thermistor Heat loss Guard heater
a b s t r a c t It is difficult to accurately measure the absolute value of the surface temperature of a material through ordinary methods such as with a thermocouple or a thermistor. This is due to heat loss along the electrical lead wires of the component, which causes conduction error and can ultimately influence the results. In this paper, we propose a thermistor probe that utilizes a guard heater. The goal of this design is to obtain an accurate measurement of the surface temperature of a material at a higher temperature than the ambient temperature. The probe consists of two thermistors, each with a diameter of 0.43 mm. One thermistor was utilized for the temperature sensor, while the other was used with the guard heater to minimize heat loss, and inserted into a fluorinated ethylene propylene (FEP) tube. The guard heater was placed above a half-exposed thermistor, and operated as both a sensor and a heater in order to minimize the temperature difference between the two thermistors. To evaluate the minimization of heat loss along the thermistor’s lead wires in a surface temperature measurement, experiments were conducted with the surface of an aluminum block heated to 35.00 °C in two scenarios. Measurements were taken using a guard-heated thermistor probe with and without guard heating. The experimental results showed that the surface temperature was measured as 34.98 °C in the scenario where guard heating was utilized, and 34.79 °C in the scenario where it was not utilized. Therefore, the results experimentally demonstrated that the guard heater allowed the thermistor probe to provide a more accurate measurement of the surface temperature, regardless of the contact method. In addition, a two-dimensional axisymmetric heat conduction analysis was also conducted. The purpose was to quantitatively evaluate the amount of heat that passes through the lead wires of a thermistor while it is measuring the surface temperature of a heated material. The calculation results confirmed that a guard heater successfully minimized heat loss through the lead wires. The minimized heat loss was 0.016 mW, which was one-sixth of the loss measured in the scenario without guard heating. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Medical treatment that utilizes heat transfer phenomena has attracted a lot of attention among researchers and has been studied actively because it has the advantage of providing less invasive treatment options. This kind of treatment can be classified into two types. One type is a method that utilizes heating, such as the hyperthermia therapy [1], laser therapy [2], and thermal therapy [3,4]. The other type is a method that utilizes cooling, such as the hypothermia therapy [5] and cryosurgery [6,7]. In these treatments, failures related to temperature control cause unnecessary damage in a patient’s healthy tissues due to overheating/cooling.
⇑ Corresponding author. E-mail address: [email protected] (T. Okabe). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.072 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
Thus, monitoring the tissue temperature during treatment plays an important role in preventing the treatment from failing due to overheating/cooling. Skin surface temperature is a reflection of the physiological state of the human body. In fact, it has been determined that the surface temperature of human skin is regulated by the individual’s local metabolism, blood perfusion underneath the skin, and heat exchange between the body and ambient condition [8,9]. A change in any one of these parameters can induce a variation in the skin surface temperature. Therefore, many researchers have attempted to accurately measure skin surface temperature [10–12] and apply that information to medical techniques responsible for diagnosing a variety of diseases such as diabetes, fever, breast cancer, and skin cancer [13–18]. Most studies of medical diagnoses involving skin surface temperature have used a non-contact method, such as
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Nomenclature A c k KP q_ Q r t T Tc TD Tg TI Tlead Ts DT V
sectional area, m2 specific heat, J/(kgK) thermal conductivity, W/(mK) proportional gain heat generation rate, W/m3 amount of heat, W radius, m time, s temperature, °C temperature of thermistor chip, °C derivative time, s temperature of guard heater integral time, s temperature of lead wire temperature of sensor temperature difference, °C voltage, V
infrared (IR) thermography, to measure radiation emitted from the surface of the skin. This method has great advantages, such as a non-invasive modality, and a large amount of data, meaning a temperature distribution over the entire visible surface is attainable. This is why IR thermography is widely used in the clinical applications mentioned above. However, it should be noted that the topical application of substances such as ultrasound gel to the skin in clinical situations, might influence the skin surface temperature by causing emissivity changes. According to Bernard et al., the changes in emissivity due to substances applied to the skin resulted in temperature errors of over 1 °C [19]. This means that if a skin temperature abnormality caused by an inflammationinduced high metabolic rate or blood perfusion in a lesion is of the order of 0.1 K or less, IR thermography may be inappropriate as a diagnostic tool to measure even a relative value. In addition, it is difficult for IR thermography to exactly measure the absolute value of skin surface temperature because of the following uncertainty factors: (1) the emissivity of skin is unknown and may vary in different conditions; (2) the emission may be directional; (3) there may be an incident component from the environment; (4) there may be light attenuation between the emission source and the detection element, depending on room humidity, air composition, etc. Thus, if one needs to accurately measure the skin surface temperature with an uncertainty of the order of 0.1 °C or less, another measuring technique may be preferable. The contact method, for instance, is a more convenient technique for temperature measurement, and utilizes a thermocouple or a thermistor. It is well known that the contact method can achieve much higher accuracy than a non-contact method. However, when the surface temperature of a material is measured at a higher temperature than ambient temperature, heat losses along the sensor lead wires and adhesive tape due to the temperature difference can cause significant errors in temperature readings (please note that adhesive tape is used to secure sensor contact). This problem has been discussed in previous studies, and the majority of them have focused on the effect of lead wires on the reading using a thermocouple. J. C. Chato conducted a simplified analysis to estimate the error caused by heat loss along T-type (copper – constantan) thermocouple’s wires running perpendicular to the biological tissue surface [20]. According to their analysis [20], to keep the error within 10%, the diameter of the lead wires needed to be less than 5.72 lm, which is not a realistic value for manufacturing and practical use. Boelter and Lockhart experimentally investigated the effects of thermocouple type, thermocouple size, wire size, and
Vc z
volume of thermistor chip, m3 depth, m
Greek symbols q density, kg/m3 Subscripts c thermistor chip D derivative g guard heater I integral lead lead wire loss heat loss mean mean P proportional s sensor
electrical insulation on the surface measurement of a stainlesssteel plate (0.94 mm thick) exposed to hot air at about 540 °C on one side and to cool air at about 38 °C on the other side of the plate [21]. They used two types of thermocouple (J type and K type) with different wire sizes (0.11–3.3 mm). Moreover, they studied the effect of thermocouple attachment methods (horizontal and vertical) on the temperature readings. Their experiment indicated that J-type (iron – constantan) thermocouple gives higher conduction error in the reading than K-type (chromel – alumel) thermocouple. Tarnopolsky and Seginer carried out experimental work to determine conduction error as a function of thermocouple type (T type and K type), wire diameter (0.075–0.50 mm), electrical insulation and length of contact between wire and sample during surface temperature measurement on plastic plate and vegetable leaves [22]. According to their experimental results, a K-type thermocouple needs only about 40% contact length of a T-type thermocouple for the same conduction error. In addition, the required contact length of an uninsulated thermocouple wire is only about half of that of an insulated wire. Kidd estimated the surface error caused by heat loss along the thermocouple wires by running twodimensional numerical simulations under various conditions, including different sized thermocouples, material types, and several skin thicknesses [23]. The numerical result shows that thermocouple wire with diameters less than 0.076 mm cause smaller temperature error, and that E-type (chromel – constantan) thermocouple gives a lower conduction error than that in other types of thermocouple. Shaukatullah and Claassen conducted experiments using a T-type thermocouple on the surface temperature measurement of electric packages in order to investigate the effects of the wire sizes (0.08–0.51 mm) and the attachment methods (polyimide tape, aluminum tape, and silver plus insulating epoxy) [24]. The experiments indicated that smaller thermocouples with lower thermal conductivity wires can minimize heat loss through the wires. Moreover, they advised that use of tapes and non-thermally conductive epoxy to attach thermocouples results in larger errors. Al Waaly et al. conducted an experiment to investigate the effects of the lead wires of K-type thermocouple on the surface temperature of a heated or cooled Peltier module at 4– 35 °C [25]. Their experimental results showed that the maximum temperature decrease due to heat loss was equal to 2 °C and 4 °C for 80 lm and 200 lm, respectively, when the surface temperature of the Peltier module was 35 °C. As described above, most previous studies of the surface temperature measurement are evaluations of the effects of the heat loss along the lead wires. In summary, the conduction error in
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the surface temperature measurement can be reduced by (1) using smaller diameter of the lead wires, (2) improving contact between the wires and the material to be measured, and (3) using sensor with lower thermal conductivity. However, it appears that it is still difficult for an ordinary contact method to accurately measure the absolute value of the surface temperature, unless the ambient temperature is the same as that of the material to be measured. In this study, we focused on the minimization of heat loss along the lead wires. If heat loss along the lead wires was successfully minimized, it would be theoretically possible to measure the absolute value of the surface temperature, even using a contact method. Additionally, to achieve the measurement with an uncertainty of the order of 0.1 °C or less, the thermistor was used as a measuring sensor instead of a thermocouple because it has a much higher temperature-measuring accuracy than that of thermocouple. The objective of this study is to develop an accurate measuring device using a thermistor that can minimize heat loss along the lead wires in the surface temperature measurement. In this study, we introduce a guard heater for minimizing the temperature difference between the sensor and the lead wires to the probe design. The minimized temperature difference only causes the minimized heat loss along the lead wires, and the probe to be developed in this study allows an accurate measurement of the absolute surface temperature regardless of a contact method. To evaluate the minimization of heat loss along the thermistor’s lead wires in a surface temperature measurement, experiments are conducted with the surface of a heated aluminum block. Moreover, a numerical simulation is also conducted to quantitatively evaluate the amount of heat that passes through the lead wires. 2. Development of a guard-heated thermistor probe 2.1. Thermistor A thermistor is a device that changes its electrical resistance with temperature. It is the most accurate sensor that can be mass-produced at low cost and fabricated into many different shapes, depending on the application. Therefore, a thermistor is widely utilized in a variety of applications, such as for automatic control, as a measuring tool in engineering fields, and even in household appliances. Generally, thermistors used for temperature measurement have a negative temperature coefficient of resistance and are called ‘‘negative temperature coefficient” thermistors (NTC thermistor). This indicates that its electrical resistance will decrease when its temperature is increased. Furthermore, it can be used as not only a temperature sensor, but also as a point heating source. Since the 1960s, many researchers have taken advantage of this feature and have utilized thermistors for the measurement of thermophysical properties such as thermal conductivity and thermal diffusivity [26–29]. In this study, a glass-coated thermistor with a diameter of 0.43 mm (produced by Shibaura Electronics Co., LTD, PSB-S9 type, 10.74 kX at 25 °C) was utilized to develop a device for accurately measuring the surface temperature of a material at higher temperature than the ambient. This glass-coated thermistor was chosen in order to take advantage of several of its unique features, such as good stability, glass electrical insulation, small size, and faster response time (thermal time constant: 0.6 s in air), for the practical use.
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should be clarified. In this study, a calibration experiment was conducted using a quartz thermometer (DMT-610B, Tokyo Denpa Co., Ltd.) with a resolution of ±0.001 °C and a calibration uncertainty of ±0.05 °C as a standard. The thermistor and the quartz thermometer probe were inserted into the center of a copper block, whose dimensions included a diameter of 30 mm and height of 65 mm. The block was preheated (or precooled) enough, and surrounded by the insulation material (a polystyrene foam). The variations in the electrical resistance of the thermistor and the temperature measured by the quartz thermometer were measured until the temperature reached room temperature. This temperature calibration should be conducted for each thermistor, because of the individual differences that can be created in each component during manufacturing. This calibration experiment conducts a highprecision and high-reliability temperature measurement so that a calibrated thermistor shows a resolution of ±0.005 °C and an uncertainty of ±0.051 °C, including the uncertainty of the quartz thermometer. 2.3. Guard-heated thermistor probe As explained above, the thermistor enables the precise measurement of temperature; however, it still has the problem of conduction error along its lead wires when the surface temperature is higher temperature than ambient. In this study, we have developed a thermistor probe that utilizes a guard heater for measuring the absolute surface temperature of a heated material. The guard heater method is well-used in the measurement of effective thermal conductivity of insulation material [30,31]. It has been introduced to the probe design for the minimization of heat loss along the lead wires. Fig. 1 shows a diagram and a picture of a guard-heated thermistor probe. This probe consisted of two 0.43 mm diameter thermistors. One was used as a temperature sensor and the other was used for the guard heater. They were inserted into the fluorinated ethylene propylene (FEP) tube of 20 mm in length. By inserting the thermistors into a FEP tube, sufficient strength for contact with any material was achieved. The positions of the two thermistors were fixed by an adhesive. Fig. 2 shows the schematic of the entire measuring system for the guard-heated thermistor probe. A thermistor for temperature measurement at the tip of probe was connected to a digital multi-meter (DMM) to measure the electrical resistance. The thermistor for the guard heater was connected to both the DMM and the DC power supply to measure the voltage and current, because it was also used as a point heat source for guard heating by controlling the applied voltage. The DMMs and DC power supply were connected to a PC to record the measured data and to control the applied voltage and current for the guard heating using LabVIEW (National Instrument). In the measurement, a half-exposed thermistor in the tip of FEP tube made contact with the material surface (it was used for sensing temperature). When a material reaches a temperature higher than ambient, heat loss should be minimized for the absolute measurement of surface temperature, as discussed. Therefore, the heat generation of the thermistor for the guard heater is always controlled to minimize the temperature difference between thermistors by a PID algorithm. In other words, the guard heater can minimize heat loss along the lead wires and a tube, and can locally create adiabatic conditions at the contact surface. Therefore, the absolute measurement of surface temperature at a higher temperature than ambient can be achieved through the contact method. The PID algorithm can be expressed as follows [32];
2.2. Temperature calibration
Z 1 t dDTðtÞ ; V g ðtÞ ¼ K P DTðtÞ þ DTðsÞds þ T D TI 0 dt
ð1Þ
Before the temperature is measured, the relationship between the electrical resistance and temperature of the thermistor used
DT ¼ T s T g ;
ð2Þ
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Lead wires
Tg Ts
Guard heating
(Ts – Tg
FEP tube (20 mm) Guard heater
0)
1 mm
Temp. sensor
0.43
Sample
[
1 mm
(a)
(b)
Fig. 1. A guard-heated thermistor probe: (a) diagram and (b) picture.
For temp.sensor
DMM For guard heater PC DMM Thermistor probe
20 mm
Power supply Fig. 2. Schematic of the entire measuring system for the guard-heated thermistor probe.
where t is time, Vg is the applied voltage to the thermistor for guard heating. Vg is a manipulated variable in PID algorithm, and. DT is the temperature difference between the thermistors. The proportional gain K P , integral time T I , and derivative time T D , are the tuning parameters. 3. Experimental study 3.1. Experimental setup To experimentally evaluate the guard-heated thermistor probe, it was necessary to define the experimental condition which utilized a material that did not produce a spatial and temporal temperature distribution. An experimental setup using a Peltier module that produces constant temperature in a material was created and is shown in Fig. 3. This device is composed of an aluminum block with a diameter of 120 mm and a height of 75 mm, and a Peltier module (60 mm 60 mm) surrounded by an insulation material. The surface of the aluminum block was covered with insulation material with a thickness of 10 mm. The aluminum block was heated by a Peltier module to the preset temperature of 35.00 °C, which is similar to the human skin temperature (generally 32–35 °C) [33,34]. A Peltier module was controlled by a PID algorithm to minimize the temperature difference between the preset temperature (35.00 °C) and the temperature measured by a thermistor embedded 1 mm into the surface. The embedded thermistor was also calibrated by the same system as mentioned above, and had an uncertainty of ±0.051 °C. Fig. 4 shows how the temperature of the embedded thermistor varied with time: (a) whole variation and (b) captured data at the steady state (400– 600 min). As shown in Fig. 4, a stable temperature of 35.00 °C
was observed at the steady state. The temperature variation was within only ±0.0008 °C, which was caused by the uncertainty due to the resolution of DMM. Here, it can be assumed that there is no spatial and temporal temperature distribution near the surface, due to the high heat capacity and thermal conductivity of the aluminum when surrounded by insulation material. Thus, the appropriate condition for the surface temperature measurement of a heated material was obtained. This experimental condition enables a reliable surface temperature measurement. By using the above mentioned system, the surface temperature measurements of the heated aluminum block were conducted five times to experimentally evaluate the guard-heated thermistor probe. The experiment was conducted in a room maintained at 26 °C. The following experimental procedure was used for the tests. First, a probe tip made contact with a heated material surface at 35.00 °C through a hole so that only the exposed junction of the probe was in point contact. After contact with the material, the temperature of sensor (Ts) increases with time. This temperature increase causes heat loss along the lead wires due to a temperature difference from the temperature of the wires (Tlead). Then, the guard heater (Tg) traces the temperature variation of Ts by controlling the heat generation of the guard heater using a PID algorithm. By minimizing the temperature difference between two thermistors (DT), the lead wires of temperature sensor contacting with the guard heater is also heated to be equal to Ts. Consequently, unwanted conduction through the lead wires is indeed minimized. Before the experiment, thermal grease was applied to the surface between the probe tip and the aluminum to reduce the thermal contact resistance. During the experiment, the temperatures of the thermistors were recorded at 0.067 s intervals. The temperature responses of the thermistors were observed for 70 s which depends on the digital multimeter. This interval was properly chosen from the aspect of the balance between the temperature accuracy and the sampling speed. The temperature response in the scenario with guard heating was compared to the case without guard heating. 3.2. Experimental results and discussions Fig. 5 shows an example of the measured temperature responses in the scenarios with and without guard heating while Fig. 6 shows the temperature difference from the preset temperature of 35.00 °C. These figures plot both temperatures for the sensor and the guard heater in the scenarios with and without guard heating. In the scenario without guard heating, the temperatures could not be reached at 35.00 °C because of heat loss along the lead wires and the tube, which were caused by the temperature difference between the sensor and the specimen. At the steady state, the measured temperature indicated 34.65 °C. Then, the temperature difference from 35.00 °C was 0.35 °C. The temperature drop in this
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Thermistor probe (Ts, Tg)
Tamb
Aluminum ( 120 mm) 10 mm
DMM Thermistor, Tobj 75 mm
Ts > Tamb Peltier module (60 mm
Power supply
60 mm)
Insulation material Fig. 3. Experimental setup utilizing a Peltier module for a surface temperature measurement.
(a)
(b)
Fig. 4. Temperature variations of an embedded thermistor (1 mm depth) with time: (a) whole variation and (b) captured data at the steady state.
Fig. 5. Example of measured temperature responses on the heated aluminum block in cases with and without guard heating.
case seems to be relatively small compared to previous studies where a thermocouple was utilized [25]. This is because of the smaller sensor size and the lower thermal conductivity of the glass covering the thermistor. This means that a glass-coated thermistor is preferable for surface temperature measurement. However, it should be noted that the error caused by heat loss cannot be neglected when the measurement accuracy on the order of 100–101 mK is required.
Fig. 6. Temperature difference from a preset temperature of 35.00 °C in cases with and without guard heating.
For the scenario with guard heating, the guard heater temperature could trace the sensor temperature immediately after contact with the heated material. Then, the sensor temperature indicated 34.97 °C at the steady state. The measurement resolution was approximately ±0.005 °C, which was much more precise than that of the other sensors. The offset error from 35.00 °C was only 0.03 °C, which was 10 times smaller than in the case without guard heating. It is important that the offset error was within the
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calibration uncertainty of the thermistors was ±0.05 °C. Note that, to easily and smoothly make a contact between the probe tip and the material surface, the hole of 2 mm in diameter was created in the insulation material before the experiment. Thus, it is also possible that it was caused by a temperature decrease due to heat losses by the heat conduction, radiation, and natural convection on the surface in contact. Additionally, the time needed to reach a steady state was shorter than in the case without guard heating. Therefore, the results show that the guard heater effectively minimized heat loss in the measurements, and enables not only absolute temperature measurement of a heated material, but also faster measurement. Fig. 7 shows the temperature difference between the thermistor used for the sensor and the guard heater, and the applied power to the guard heater during the measurement with guard heating. As seen in the experimental results, the guard heater could rapidly trace the temperature variation of the thermistor for the sensor, and minimize the temperature difference from the sensor temperature by changing the applied power. This shows that the temperature difference was mostly minimized after approximately 5 s, and was within only ±0.01 °C, which was caused by the uncertainty of thermistors at the steady state. The maximum power, which was approximately 1.5 mW, was observed at the moment just after the contact. After that, it gradually decreased to keep the temperature difference minimized between the thermistors. All of the experimental data regarding surface temperature at the steady state is summarized in Table 1. As shown in Table 1, the averaged surface temperatures of the five measurements were 34.97 ± 0.027 °C in the case with guard heating and 34.64 ± 0.051 °C in the case without it. Here, the standard deviation may include the temperature decrease of the material surface due to natural convection. The differences between thermistors in cases with and without a guard heating showed 0.00–0.05 °C and 0.18–0.24 °C, respectively. The guard heater temperatures mostly did not indicate a significant difference from the sensor temperature in the case with guard heating, although there was an obvious difference of approximately 0.2 °C in each measurement in the case without guard heating. Consequently, the results showed the possibility that the guard-heated thermistor probe enabled
the measurement of the absolute surface temperature of the material at higher temperature than ambient, despite the contact-based method. 4. Numerical simulation for performance evaluation 4.1. Calculation model To conduct the performance evaluation of the guard heater by numerical simulation, it is necessary to create the appropriate numerical model. However, the thermistor used in this study has a complicated shape because it is glass-coated and contains two lead wires, which makes modeling difficult. To easily model the complex shape, Ould-Lahoucine et al. transformed an actual 3D shape into a simple axial symmetrical 2D form [35]. In their model, the lead wires, the thermistor chip, and the glass covering the chip were assumed to be a simple shape - a cylinder with a single wire coated by glass. They proposed an estimation method for thermal conductivity by comparing the measured and calculated temperature responses using a proposed two dimensional (2D) axisymmetric model. The estimated thermal conductivities of the standard materials agreed well with the reference values. It was revealed that a transformed model of the thermistor can represent the actual heat transfer phenomena by conducting an experiment to determine the shape parameters. In this study, the complicated actual shape of a thermistor chip was transformed to a simpler 2D axisymmetric form to simulate the temperature response in the measurement. Fig. 8 shows (a) the actual shape of a thermistor, (b) the transformed shape for a simulation and (c) detailed dimensions of transformed thermistor. The actual shape and the dimensions of a thermistor chip are rectangular parallelepiped and approximately 0.24 mm 0.24 mm 0.12 mm. This was measured by a microscope. The actual glass covering the chip has a spheroid shape and the maximum diameter and length measured are approximately 0.43 mm and 0.58 mm, respectively. The lead wires are comprised of a dumet alloy with
Glass
Lead wires Glass
Chip
Chip
(a) Actual thermistor shape.
Lead wire
(b) Transformed shape.
0.095
0.05
0.15
0.1 0.24 0.58
(c) Detailed dimensions of transformed thermistor. Fig. 7. Temperature difference between thermistors for the sensor and the guard heater and applied power to guard heater in the case with guard heating.
Fig. 8. (a) Actual thermistor shape, (b) transformed shape and (c) detailed dimensions.
Table 1 Experimental results of mean surface temperature in cases with and without guard heating. No.
1
2
3
4
5
Tave ± SD
w/guard heating
Ts,mean [°C] Tg,mean [°C]
34.94 34.94
35.01 35.06
34.96 34.97
34.98 35.00
34.97 34.97
34.97 ± 0.027 34.99 ± 0.047
w/o guard heating
Ts,mean [°C] Tg,mean [°C]
34.65 34.46
34.63 34.42
34.67 34.48
34.56 34.32
34.69 34.51
34.64 ± 0.051 34.44 ± 0.077
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a diameter of 0.07 mm. In the model, the thermistor chip was assumed to be a cylinder, while the glass was assumed to be a rounded rectangle. The detailed shape and dimensions of the thermistor used in the calculation are shown in Fig. 8(c). The 2D axisymmetric model could not simulate the presence of the two wires, so only a single wire with an appropriate diameter (0.1 mm) was considered to represent the actual heat loss along the wires. The radius of the modeled wire was determined to be the same thermal conductance as the actual two wires. To represent heat loss in the connected area between the lead wires and the thermistor chip in reality, the lead wire in the model was assumed to be inserted with an area equal to the estimated one by a microscope (see Fig. 8(c)). These approximations of the shape of the thermistor mentioned above may influence the calculation results. Thus, a determination of the shape parameters in the numerical model must be conducted to compare to the experimental temperature response, using a standard material. In this study, the radius and thermal diffusivity of the thermistor chip, which has a significant influence on temperature response, were selected as the shape parameters. The lengths of the thermistor chip and the glass bead were fixed at 0.24 mm and 0.58 mm, respectively, which are the values measured by the microscope. The temperature response when the two parameters were varied was compared to the experimental one. Fig. 9(a) shows the 2D axisymmetric model for a determination of the shape parameters, which means that a modeled thermistor with a single lead wire was inserted into standard material. In this experiment, the agar-gelled water (1 wt%) was used as the standard material. The calculation domain was 10.0 mm 20.0 mm, which is larger enough for the calculated temperature responses of the thermistors. Although the length of the lead wire above the insulation material is not included in the calculation model, it has been confirmed that it has no impact on the temperature response of the sensor thermistor. The number Adiabatic condition
of grids was 400 400. All of the boundary conditions were adiabatic. The initial temperatures at each material were given as 26 °C. The thermal contact resistances between components were neglected. The thermophysical properties of each material used in this simulation were shown in Table 2 [36]. The 2D axisymmetric heat conduction equation is expressed as follows:
qc
@T 1 @ @T @ @T _ þ þ q; ¼ kr k @t r @r @r @z @z
ð3Þ
where q [kg/m3] is the density, c[J/(kgK)] is the specific heat, k [W/ (mK)] is the thermal conductivity and q_ [W/m3] is the heat generation rate of thermistor chip. An implicit implementation of the finite volume method was chosen as the numerical method to solve the partial differential equation in this formulation [37]. Based on the algorithm, a FORTRAN90 code was written and run on a personal computer. To determine the shape of the thermistor, the temperature response was calculated during and after a constant power (3 mW) was applied to a thermistor chip for 3 s, in order to compare with the experimental results. This was for the determination of shape parameters. This temperature response included not only the temperature increase during heating, but also the temperature decay after heating, so that a more reliable parameters can be determined. Here, the temperature of the thermistors was evaluated as the volume-averaged temperature of the thermistor chip expressed as:
R Vc
Ts
or T g ¼
0
T c dV ; Vc
ð4Þ
where Ts, Tg, Tc, and Vc denote the volume averaged temperature for the sensor and guard heater, the temperature of the thermistor chip, and the volume of thermistor chip, respectively. The temperature measurement with agar-gelled water (1 wt%) was conducted to determine the shape parameters in the model. Adiabatic condition
Specimen
Insulation material
FEP tube Air Lead wire
Lead wire
Glass
Aluminum
Adiabatic condition
Isothermal condition (T = 35 oC)
10 mm
10 mm
(a)
(b)
20 mm
Thermistor Chip Air
Adiabatic condition
Adhesive
20 mm
Thermistor Chip
Adiabatic condition
Glass
Fig. 9. Calculation models used in this study: (a) model for determination of shape parameters and (b) model for temperature and thermal conductivity measurement.
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Table 2 Thermophysical properties of each material used in simulations [36]. Material
Thermal conductivity, W/(mK)
Specific heat, J/(kgK)
Density, kg/m3
Agar-gelled water Glass Lead wire (dumet) Air FEP tube Adhesive Insulation material Aluminum
0.60 0.70 150 0.026 0.25 0.50 0.03 238
4180 4300 400 1006 2145 2000 1900 917
997 900 8500 1.17 1200 1200 15.9 2700
A thermistor was connected to the DMM and DC power supply and used as a sensor and a point heat source. In the measurement, the thermistor was inserted into the agar-gelled water at a room temperature of 26 °C, and was heated by a constant power of 3 mW at the steady state. Then, the temperature response was measured during and after heating, and compared to the calculated response using the model mentioned above. By comparison, the radius and thermal diffusivity of the thermistor in the simulation was varied until the temperature difference between the experimental and calculated results was minimized enough at each time. Finally, the determined values were used as shape parameters in a simulation for the surface temperature measurement. Fig. 10 shows a comparison between the experimental and calculated temperature responses for the determination of the shape parameters. As shown in figure, the experimental and calculated temperature responses were in good agreement each other. The temperature difference at each time was mostly within ±0.02 °C, meaning that the transformed thermistor successfully represented the actual temperature response both during and after the heating, despite the approximated dimensions of the 2D axisymmetric model. The determined values of each parameter are shown in Table 3. In this study, the determined values for the radius and thermal diffusivity were used for the calculation model for the performance evaluation of the guard-heated thermistor probe. 4.2. Simulation results and discussions Next, a numerical simulation of the surface temperature measurement of the heated aluminum block was conducted to
Fig. 10. Comparison between experimental and calculated results for determination of shape parameters.
Table 3 Determined shape parameters: radius and thermal diffusivity of thermistor chip. Material
Radius, mm
Thermal diffusivity, m2/s
Thermistor chip
0.095
5.5 107
theoretically evaluate heat loss along the lead wires using the guard-heated thermistor probe. Fig. 9(b) shows the 2D axisymmetric model with the shape parameters, including the thermistor for the guard heater, the FEP tube covering the thermistors, and the adhesive to demonstrate the guard-heated thermistor probe. This model represents the guard-heated thermistor probe contacting the heated aluminum block at 35.00 °C. The probe was surrounded by an insulation material. This model included a PID control to minimize the temperature difference between the two thermistors using Eq. (1). The length between thermistors was assumed to be 0.1 mm. The calculation code is basically the same as the one used in the determination of the shape parameters, except only the calculation conditions were different. The thermophysical properties of each component are shown in Table 2. In this calculation, all of the boundary conditions were given as adiabatic, except at the bottom of domain, which represented isothermal conditions at 35.00 °C. At the initial conditions, the temperatures of the probe and the insulation material were at 26.00 °C, while the temperature of the aluminum was at 35.00 °C. The thermal contact resistance at the contact surface, and the effects of the natural convection and radiation were neglected. Fig. 11 shows the calculated temperature responses of the thermistors for (a) sensor and (b) guard heater in the cases with and without guard heating after the contact. In order to validate the calculation results, the experimental results are also plotted. For the case without guard heating, the temperatures for the sensor and guard heater ultimately indicated 34.56 °C and 33.84 °C at 60 s, but they still did not reach the steady state. This implies that heat loss significantly influenced the thermistor temperature. In addition, the temperature increase after contact was relatively slow due to heat loss through the lead wire. In comparison with the experimental results, the sensor temperature showed a good agreement, but the guard heater temperature did not quantitatively agree due to the difference from the real structure of a guard-heated thermistor probe such as the contact with other materials and lead wire length of guard heater. For the case with guard heating, on the other hand, the temperatures for the sensor and guard heater rapidly increased and showed 34.99 °C, indicating a small offset error of 0.01 °C, which might be caused by heat loss to the insulation material and a FEP tube at 26 °C. However, the guard heater worked very well to trace the temperature for the sensor, and accurately minimized the temperature difference in comparison to the case without guard heating. The temperature was reached at a steady state after approximately 15 s, indicating that this simulation exhibits the same behavior as the experimental results. As a consequence, it was revealed that, the calculation model can show a reliable result, and can be used for the evaluation of the amount of heat that passes through the lead wire of the sensor thermistor during a measurement. In addition, the calculation results indicated that the guard-heated thermistor probe allows for an accurate measurement of the absolute surface temperature based on the minimization of heat loss by guard heater. Fig. 12 shows the calculated results of heat loss along the lead wire for the thermistor for the sensor in cases with and without guard heating. Heat loss along the lead wire was calculated by Fourier’s law, using a temperature gradient on the middle point between two thermistors at each time, expressed as:
Q loss ðtÞ ¼ Alead klead
dT lead ; dz
ð5Þ
where Qloss, Alead, klead, and Tlead denote the amount of heat, the cross-sectional area, the thermal conductivity of lead wire and the temperature of lead wire, respectively. For the case without guard heating, heat loss from the sensor thermistor to the guard heater increased to approximately
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(a) Sensor
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(b) Guard heater
Fig. 11. Calculation results of temperature responses in cases with and without guard heating: (a) sensor and (b) guard heater.
heated at 35.00 °C in the cases with and without guard heating. Moreover, a two-dimensional axisymmetric heat conduction analysis was conducted to quantitatively evaluate the amount of heat that passes through the lead wires. Based on the results, the following conclusions were obtained.
Fig. 12. Calculation results of heat loss through lead wire of thermistor for sensor in cases with and without guard heating.
0.5 mW just after contact, and gradually decreased to 0.1 mW. However, temperature did not reach the steady state at 60 s, because the guard heater did not work. Then, heat loss caused the temperature to decrease to 0.44 °C in the thermistor for the sensor. Thus, heat loss along the lead wires cannot be neglected in the case without guard heater, so, it is necessary to minimize heat loss along the lead wire for the accurate measurement of surface temperature in a heated material. For the case with guard heating, on the other hand, heat loss showed a negative value just after contact, and gradually approached a minimum value that was 0.016 mW. Note that the negative value represented the amount of heat from a guard heater to a sensor thermistor. The amount of heat always showed a much smaller value than that in the case without guard heating. The estimated heat loss of 0.016 mW caused only a 0.01 °C temperature drop from the preset temperature of 35.00 °C. It was revealed that a guard heater could effectively minimize heat loss along the lead wire, and enabled the ability to accurately measure the surface temperature in a heated material at a higher temperature than the ambient.
5. Conclusions In this study, a guard-heated thermistor probe that used a guard heater for the minimization of heat loss along the lead wires was developed for the purpose of accurately measuring the absolute surface temperature of a material at a higher temperature than the ambient temperature. To evaluate heat loss along the thermistor’s lead wires in a surface temperature measurement, experiments were conducted with the surface of an aluminum block
– The experimental results showed that the guard-heated thermistor probe achieved the minimization of heat loss along the lead wires, and allowed for a more accurate measurement of the absolute surface temperature of a heated material, regardless of contact method. – The 2D axisymmetric heat conduction analysis demonstrated that the guard heater successfully minimized heat loss along the lead wire to 0.016 mW which was a much smaller value than that in the case without guard heating (0.1 mW). The estimated heat loss of 0.016 mW caused only a 0.01 °C temperature drop from the preset temperature of 35.00 °C. This showed a good agreement with the experimental results. – The guard-heated thermistor probe is an appropriate option for the accurate measurement of the absolute skin surface temperature in the future. In addition, the present probe makes it possible to observe a skin temperature fluctuation caused by the blood perfusion underneath the human skin. A preliminary study has already been performed.
Acknowledgement This study was supported by Grant-in-Aid for JSPS Fellows 13J08342.
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[6] J. Okajima, A. Komiya, S. Maruyama, 24-gauge ultrafine cryoprobe with diameter of 550 lm and its cooling performance, Cryobiology 69 (2014) 411– 418. [7] H. Takeda, S. Maruyama, J. Okajima, S. Aiba, A. Komiya, Development and estimation of a novel cryoprobe utilizing the Peltier effect for precise and safe cryosurgery, Cryobiology 59 (2009) 275–284. [8] A. Shitzer, R.C. Eberhart (Eds.), Heat Transfer in Medicine and Biology, Plenum Press, New York, 1985. [9] Z. Deng, J. Liu, Blood perfusion-based model for characterizing the temperature fluctuation in living tissues, Phys. A 300 (2001) 521–530. [10] J.D. Hardy, The radiation of heat from the human body: 1. An instrument for measuring the radiation and surface temperature of the skin, J. Clini. Investig. 13 (1934) 593–604. [11] C.J. Tyler, The effect of skin thermistor fixation method on weighted mean skin temperature, Physiol. Meas. 32 (2011) 1541–1547. [12] C.A. James, A.J. Richardson, P.W. Watt, N.S. Maxwell, Reliability and validity of skin temperature measurement by telemetry thermistors and a thermal camera during exercise in the heat, J. Therm. Biol 45 (2014) 141–149. [13] F. Ring, Foot technology, Part 1 of 2: thermal imaging today and its relevance to diabetes, J. Diabetes Sci. Technol. 4 (4) (2010) 857–862. [14] H. Peregrina-Barreto, L.A. Morales-Hernandez, J.J. Rangel-Magdaleno, P.D. Vazquez-Rodriguez, Thermal image processing for quantitative determination of temperature variations in plantar angiosomes, in: IEEE International Instrumentation and Measurement Technology Conference (12MTC), IEEE, 2013, pp. 816–820. [15] M.U. Selent, N.M. Molinari, A. Baxter, A.V. Nguyen, H. Siegelson, C.M. Brown, A. Plummer, A. Higgins, S. Podolsky, P. Spandorfer, N.J. Cohen, D.B. Fishbein, Mass screening for fever in children: a comparison of 3 infrared thermal detection systems, Pediatr. Emerg. Care 29 (3) (2013) 305–313. [16] K. Das, S.C. Mishra, Non-invasive estimation of size and location of a tumor in a human breast using a curve fitting technique, Int. Commun. Heat Mass Transf. 56 (2014) 63–70. [17] M.P. Çetingül, C. Herman, Quantification of the thermal signature of a melanoma lesion, Int. J. Therm. Sci. 50 (2011) 421–431. [18] A. Bhowmik, R. Repaka, S.C. Mishra, Thermographic evaluation of early melanoma within the vascularized skin using combined non-Newtonian blood flow and bioheat models, Comput. Biol. Med. 53 (2014) 206–219. [19] V. Bernard, E. Staffa, V. Mornstein, A. Bourek, Infrared camera assessment of skin surface temperature - effect of emissivity, Physica Med. 29 (2013) 583– 591. [20] J.C. Chato, Measurement of thermal properties of biological materials, in: A. Shitzer, R.C. Eberhart (Eds.), Heat Transfer in Medicine and Biology, Plenum Press, New York, 1985, pp. 167–192. [21] L.M.K. Boelter, R.W. Lockhart, NACA Technical Note 2427, An Investigation of Aircraft Heaters: Xxxv-Thermocouple Conduction Error Observed in Measuring Surface Temperatures, University of California, Washington, 1951.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Development of a guard-heated thermistor probe for the accurate measurement of surface temperature Takahiro Okabe a,⇑, Junnosuke Okajima b, Atsuki Komiya b, Shigenao Maruyama b a b
Graduate School of Science and Engineering, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 980-8577, Japan Institute of Fluid Science, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan
a r t i c l e
i n f o
Article history: Received 21 September 2016 Received in revised form 10 January 2017 Accepted 19 January 2017
Keywords: Temperature measurement Surface temperature Thermistor Heat loss Guard heater
a b s t r a c t It is difficult to accurately measure the absolute value of the surface temperature of a material through ordinary methods such as with a thermocouple or a thermistor. This is due to heat loss along the electrical lead wires of the component, which causes conduction error and can ultimately influence the results. In this paper, we propose a thermistor probe that utilizes a guard heater. The goal of this design is to obtain an accurate measurement of the surface temperature of a material at a higher temperature than the ambient temperature. The probe consists of two thermistors, each with a diameter of 0.43 mm. One thermistor was utilized for the temperature sensor, while the other was used with the guard heater to minimize heat loss, and inserted into a fluorinated ethylene propylene (FEP) tube. The guard heater was placed above a half-exposed thermistor, and operated as both a sensor and a heater in order to minimize the temperature difference between the two thermistors. To evaluate the minimization of heat loss along the thermistor’s lead wires in a surface temperature measurement, experiments were conducted with the surface of an aluminum block heated to 35.00 °C in two scenarios. Measurements were taken using a guard-heated thermistor probe with and without guard heating. The experimental results showed that the surface temperature was measured as 34.98 °C in the scenario where guard heating was utilized, and 34.79 °C in the scenario where it was not utilized. Therefore, the results experimentally demonstrated that the guard heater allowed the thermistor probe to provide a more accurate measurement of the surface temperature, regardless of the contact method. In addition, a two-dimensional axisymmetric heat conduction analysis was also conducted. The purpose was to quantitatively evaluate the amount of heat that passes through the lead wires of a thermistor while it is measuring the surface temperature of a heated material. The calculation results confirmed that a guard heater successfully minimized heat loss through the lead wires. The minimized heat loss was 0.016 mW, which was one-sixth of the loss measured in the scenario without guard heating. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Medical treatment that utilizes heat transfer phenomena has attracted a lot of attention among researchers and has been studied actively because it has the advantage of providing less invasive treatment options. This kind of treatment can be classified into two types. One type is a method that utilizes heating, such as the hyperthermia therapy [1], laser therapy [2], and thermal therapy [3,4]. The other type is a method that utilizes cooling, such as the hypothermia therapy [5] and cryosurgery [6,7]. In these treatments, failures related to temperature control cause unnecessary damage in a patient’s healthy tissues due to overheating/cooling.
⇑ Corresponding author. E-mail address: [email protected] (T. Okabe). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.072 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
Thus, monitoring the tissue temperature during treatment plays an important role in preventing the treatment from failing due to overheating/cooling. Skin surface temperature is a reflection of the physiological state of the human body. In fact, it has been determined that the surface temperature of human skin is regulated by the individual’s local metabolism, blood perfusion underneath the skin, and heat exchange between the body and ambient condition [8,9]. A change in any one of these parameters can induce a variation in the skin surface temperature. Therefore, many researchers have attempted to accurately measure skin surface temperature [10–12] and apply that information to medical techniques responsible for diagnosing a variety of diseases such as diabetes, fever, breast cancer, and skin cancer [13–18]. Most studies of medical diagnoses involving skin surface temperature have used a non-contact method, such as
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Nomenclature A c k KP q_ Q r t T Tc TD Tg TI Tlead Ts DT V
sectional area, m2 specific heat, J/(kgK) thermal conductivity, W/(mK) proportional gain heat generation rate, W/m3 amount of heat, W radius, m time, s temperature, °C temperature of thermistor chip, °C derivative time, s temperature of guard heater integral time, s temperature of lead wire temperature of sensor temperature difference, °C voltage, V
infrared (IR) thermography, to measure radiation emitted from the surface of the skin. This method has great advantages, such as a non-invasive modality, and a large amount of data, meaning a temperature distribution over the entire visible surface is attainable. This is why IR thermography is widely used in the clinical applications mentioned above. However, it should be noted that the topical application of substances such as ultrasound gel to the skin in clinical situations, might influence the skin surface temperature by causing emissivity changes. According to Bernard et al., the changes in emissivity due to substances applied to the skin resulted in temperature errors of over 1 °C [19]. This means that if a skin temperature abnormality caused by an inflammationinduced high metabolic rate or blood perfusion in a lesion is of the order of 0.1 K or less, IR thermography may be inappropriate as a diagnostic tool to measure even a relative value. In addition, it is difficult for IR thermography to exactly measure the absolute value of skin surface temperature because of the following uncertainty factors: (1) the emissivity of skin is unknown and may vary in different conditions; (2) the emission may be directional; (3) there may be an incident component from the environment; (4) there may be light attenuation between the emission source and the detection element, depending on room humidity, air composition, etc. Thus, if one needs to accurately measure the skin surface temperature with an uncertainty of the order of 0.1 °C or less, another measuring technique may be preferable. The contact method, for instance, is a more convenient technique for temperature measurement, and utilizes a thermocouple or a thermistor. It is well known that the contact method can achieve much higher accuracy than a non-contact method. However, when the surface temperature of a material is measured at a higher temperature than ambient temperature, heat losses along the sensor lead wires and adhesive tape due to the temperature difference can cause significant errors in temperature readings (please note that adhesive tape is used to secure sensor contact). This problem has been discussed in previous studies, and the majority of them have focused on the effect of lead wires on the reading using a thermocouple. J. C. Chato conducted a simplified analysis to estimate the error caused by heat loss along T-type (copper – constantan) thermocouple’s wires running perpendicular to the biological tissue surface [20]. According to their analysis [20], to keep the error within 10%, the diameter of the lead wires needed to be less than 5.72 lm, which is not a realistic value for manufacturing and practical use. Boelter and Lockhart experimentally investigated the effects of thermocouple type, thermocouple size, wire size, and
Vc z
volume of thermistor chip, m3 depth, m
Greek symbols q density, kg/m3 Subscripts c thermistor chip D derivative g guard heater I integral lead lead wire loss heat loss mean mean P proportional s sensor
electrical insulation on the surface measurement of a stainlesssteel plate (0.94 mm thick) exposed to hot air at about 540 °C on one side and to cool air at about 38 °C on the other side of the plate [21]. They used two types of thermocouple (J type and K type) with different wire sizes (0.11–3.3 mm). Moreover, they studied the effect of thermocouple attachment methods (horizontal and vertical) on the temperature readings. Their experiment indicated that J-type (iron – constantan) thermocouple gives higher conduction error in the reading than K-type (chromel – alumel) thermocouple. Tarnopolsky and Seginer carried out experimental work to determine conduction error as a function of thermocouple type (T type and K type), wire diameter (0.075–0.50 mm), electrical insulation and length of contact between wire and sample during surface temperature measurement on plastic plate and vegetable leaves [22]. According to their experimental results, a K-type thermocouple needs only about 40% contact length of a T-type thermocouple for the same conduction error. In addition, the required contact length of an uninsulated thermocouple wire is only about half of that of an insulated wire. Kidd estimated the surface error caused by heat loss along the thermocouple wires by running twodimensional numerical simulations under various conditions, including different sized thermocouples, material types, and several skin thicknesses [23]. The numerical result shows that thermocouple wire with diameters less than 0.076 mm cause smaller temperature error, and that E-type (chromel – constantan) thermocouple gives a lower conduction error than that in other types of thermocouple. Shaukatullah and Claassen conducted experiments using a T-type thermocouple on the surface temperature measurement of electric packages in order to investigate the effects of the wire sizes (0.08–0.51 mm) and the attachment methods (polyimide tape, aluminum tape, and silver plus insulating epoxy) [24]. The experiments indicated that smaller thermocouples with lower thermal conductivity wires can minimize heat loss through the wires. Moreover, they advised that use of tapes and non-thermally conductive epoxy to attach thermocouples results in larger errors. Al Waaly et al. conducted an experiment to investigate the effects of the lead wires of K-type thermocouple on the surface temperature of a heated or cooled Peltier module at 4– 35 °C [25]. Their experimental results showed that the maximum temperature decrease due to heat loss was equal to 2 °C and 4 °C for 80 lm and 200 lm, respectively, when the surface temperature of the Peltier module was 35 °C. As described above, most previous studies of the surface temperature measurement are evaluations of the effects of the heat loss along the lead wires. In summary, the conduction error in
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the surface temperature measurement can be reduced by (1) using smaller diameter of the lead wires, (2) improving contact between the wires and the material to be measured, and (3) using sensor with lower thermal conductivity. However, it appears that it is still difficult for an ordinary contact method to accurately measure the absolute value of the surface temperature, unless the ambient temperature is the same as that of the material to be measured. In this study, we focused on the minimization of heat loss along the lead wires. If heat loss along the lead wires was successfully minimized, it would be theoretically possible to measure the absolute value of the surface temperature, even using a contact method. Additionally, to achieve the measurement with an uncertainty of the order of 0.1 °C or less, the thermistor was used as a measuring sensor instead of a thermocouple because it has a much higher temperature-measuring accuracy than that of thermocouple. The objective of this study is to develop an accurate measuring device using a thermistor that can minimize heat loss along the lead wires in the surface temperature measurement. In this study, we introduce a guard heater for minimizing the temperature difference between the sensor and the lead wires to the probe design. The minimized temperature difference only causes the minimized heat loss along the lead wires, and the probe to be developed in this study allows an accurate measurement of the absolute surface temperature regardless of a contact method. To evaluate the minimization of heat loss along the thermistor’s lead wires in a surface temperature measurement, experiments are conducted with the surface of a heated aluminum block. Moreover, a numerical simulation is also conducted to quantitatively evaluate the amount of heat that passes through the lead wires. 2. Development of a guard-heated thermistor probe 2.1. Thermistor A thermistor is a device that changes its electrical resistance with temperature. It is the most accurate sensor that can be mass-produced at low cost and fabricated into many different shapes, depending on the application. Therefore, a thermistor is widely utilized in a variety of applications, such as for automatic control, as a measuring tool in engineering fields, and even in household appliances. Generally, thermistors used for temperature measurement have a negative temperature coefficient of resistance and are called ‘‘negative temperature coefficient” thermistors (NTC thermistor). This indicates that its electrical resistance will decrease when its temperature is increased. Furthermore, it can be used as not only a temperature sensor, but also as a point heating source. Since the 1960s, many researchers have taken advantage of this feature and have utilized thermistors for the measurement of thermophysical properties such as thermal conductivity and thermal diffusivity [26–29]. In this study, a glass-coated thermistor with a diameter of 0.43 mm (produced by Shibaura Electronics Co., LTD, PSB-S9 type, 10.74 kX at 25 °C) was utilized to develop a device for accurately measuring the surface temperature of a material at higher temperature than the ambient. This glass-coated thermistor was chosen in order to take advantage of several of its unique features, such as good stability, glass electrical insulation, small size, and faster response time (thermal time constant: 0.6 s in air), for the practical use.
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should be clarified. In this study, a calibration experiment was conducted using a quartz thermometer (DMT-610B, Tokyo Denpa Co., Ltd.) with a resolution of ±0.001 °C and a calibration uncertainty of ±0.05 °C as a standard. The thermistor and the quartz thermometer probe were inserted into the center of a copper block, whose dimensions included a diameter of 30 mm and height of 65 mm. The block was preheated (or precooled) enough, and surrounded by the insulation material (a polystyrene foam). The variations in the electrical resistance of the thermistor and the temperature measured by the quartz thermometer were measured until the temperature reached room temperature. This temperature calibration should be conducted for each thermistor, because of the individual differences that can be created in each component during manufacturing. This calibration experiment conducts a highprecision and high-reliability temperature measurement so that a calibrated thermistor shows a resolution of ±0.005 °C and an uncertainty of ±0.051 °C, including the uncertainty of the quartz thermometer. 2.3. Guard-heated thermistor probe As explained above, the thermistor enables the precise measurement of temperature; however, it still has the problem of conduction error along its lead wires when the surface temperature is higher temperature than ambient. In this study, we have developed a thermistor probe that utilizes a guard heater for measuring the absolute surface temperature of a heated material. The guard heater method is well-used in the measurement of effective thermal conductivity of insulation material [30,31]. It has been introduced to the probe design for the minimization of heat loss along the lead wires. Fig. 1 shows a diagram and a picture of a guard-heated thermistor probe. This probe consisted of two 0.43 mm diameter thermistors. One was used as a temperature sensor and the other was used for the guard heater. They were inserted into the fluorinated ethylene propylene (FEP) tube of 20 mm in length. By inserting the thermistors into a FEP tube, sufficient strength for contact with any material was achieved. The positions of the two thermistors were fixed by an adhesive. Fig. 2 shows the schematic of the entire measuring system for the guard-heated thermistor probe. A thermistor for temperature measurement at the tip of probe was connected to a digital multi-meter (DMM) to measure the electrical resistance. The thermistor for the guard heater was connected to both the DMM and the DC power supply to measure the voltage and current, because it was also used as a point heat source for guard heating by controlling the applied voltage. The DMMs and DC power supply were connected to a PC to record the measured data and to control the applied voltage and current for the guard heating using LabVIEW (National Instrument). In the measurement, a half-exposed thermistor in the tip of FEP tube made contact with the material surface (it was used for sensing temperature). When a material reaches a temperature higher than ambient, heat loss should be minimized for the absolute measurement of surface temperature, as discussed. Therefore, the heat generation of the thermistor for the guard heater is always controlled to minimize the temperature difference between thermistors by a PID algorithm. In other words, the guard heater can minimize heat loss along the lead wires and a tube, and can locally create adiabatic conditions at the contact surface. Therefore, the absolute measurement of surface temperature at a higher temperature than ambient can be achieved through the contact method. The PID algorithm can be expressed as follows [32];
2.2. Temperature calibration
Z 1 t dDTðtÞ ; V g ðtÞ ¼ K P DTðtÞ þ DTðsÞds þ T D TI 0 dt
ð1Þ
Before the temperature is measured, the relationship between the electrical resistance and temperature of the thermistor used
DT ¼ T s T g ;
ð2Þ
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Lead wires
Tg Ts
Guard heating
(Ts – Tg
FEP tube (20 mm) Guard heater
0)
1 mm
Temp. sensor
0.43
Sample
[
1 mm
(a)
(b)
Fig. 1. A guard-heated thermistor probe: (a) diagram and (b) picture.
For temp.sensor
DMM For guard heater PC DMM Thermistor probe
20 mm
Power supply Fig. 2. Schematic of the entire measuring system for the guard-heated thermistor probe.
where t is time, Vg is the applied voltage to the thermistor for guard heating. Vg is a manipulated variable in PID algorithm, and. DT is the temperature difference between the thermistors. The proportional gain K P , integral time T I , and derivative time T D , are the tuning parameters. 3. Experimental study 3.1. Experimental setup To experimentally evaluate the guard-heated thermistor probe, it was necessary to define the experimental condition which utilized a material that did not produce a spatial and temporal temperature distribution. An experimental setup using a Peltier module that produces constant temperature in a material was created and is shown in Fig. 3. This device is composed of an aluminum block with a diameter of 120 mm and a height of 75 mm, and a Peltier module (60 mm 60 mm) surrounded by an insulation material. The surface of the aluminum block was covered with insulation material with a thickness of 10 mm. The aluminum block was heated by a Peltier module to the preset temperature of 35.00 °C, which is similar to the human skin temperature (generally 32–35 °C) [33,34]. A Peltier module was controlled by a PID algorithm to minimize the temperature difference between the preset temperature (35.00 °C) and the temperature measured by a thermistor embedded 1 mm into the surface. The embedded thermistor was also calibrated by the same system as mentioned above, and had an uncertainty of ±0.051 °C. Fig. 4 shows how the temperature of the embedded thermistor varied with time: (a) whole variation and (b) captured data at the steady state (400– 600 min). As shown in Fig. 4, a stable temperature of 35.00 °C
was observed at the steady state. The temperature variation was within only ±0.0008 °C, which was caused by the uncertainty due to the resolution of DMM. Here, it can be assumed that there is no spatial and temporal temperature distribution near the surface, due to the high heat capacity and thermal conductivity of the aluminum when surrounded by insulation material. Thus, the appropriate condition for the surface temperature measurement of a heated material was obtained. This experimental condition enables a reliable surface temperature measurement. By using the above mentioned system, the surface temperature measurements of the heated aluminum block were conducted five times to experimentally evaluate the guard-heated thermistor probe. The experiment was conducted in a room maintained at 26 °C. The following experimental procedure was used for the tests. First, a probe tip made contact with a heated material surface at 35.00 °C through a hole so that only the exposed junction of the probe was in point contact. After contact with the material, the temperature of sensor (Ts) increases with time. This temperature increase causes heat loss along the lead wires due to a temperature difference from the temperature of the wires (Tlead). Then, the guard heater (Tg) traces the temperature variation of Ts by controlling the heat generation of the guard heater using a PID algorithm. By minimizing the temperature difference between two thermistors (DT), the lead wires of temperature sensor contacting with the guard heater is also heated to be equal to Ts. Consequently, unwanted conduction through the lead wires is indeed minimized. Before the experiment, thermal grease was applied to the surface between the probe tip and the aluminum to reduce the thermal contact resistance. During the experiment, the temperatures of the thermistors were recorded at 0.067 s intervals. The temperature responses of the thermistors were observed for 70 s which depends on the digital multimeter. This interval was properly chosen from the aspect of the balance between the temperature accuracy and the sampling speed. The temperature response in the scenario with guard heating was compared to the case without guard heating. 3.2. Experimental results and discussions Fig. 5 shows an example of the measured temperature responses in the scenarios with and without guard heating while Fig. 6 shows the temperature difference from the preset temperature of 35.00 °C. These figures plot both temperatures for the sensor and the guard heater in the scenarios with and without guard heating. In the scenario without guard heating, the temperatures could not be reached at 35.00 °C because of heat loss along the lead wires and the tube, which were caused by the temperature difference between the sensor and the specimen. At the steady state, the measured temperature indicated 34.65 °C. Then, the temperature difference from 35.00 °C was 0.35 °C. The temperature drop in this
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Thermistor probe (Ts, Tg)
Tamb
Aluminum ( 120 mm) 10 mm
DMM Thermistor, Tobj 75 mm
Ts > Tamb Peltier module (60 mm
Power supply
60 mm)
Insulation material Fig. 3. Experimental setup utilizing a Peltier module for a surface temperature measurement.
(a)
(b)
Fig. 4. Temperature variations of an embedded thermistor (1 mm depth) with time: (a) whole variation and (b) captured data at the steady state.
Fig. 5. Example of measured temperature responses on the heated aluminum block in cases with and without guard heating.
case seems to be relatively small compared to previous studies where a thermocouple was utilized [25]. This is because of the smaller sensor size and the lower thermal conductivity of the glass covering the thermistor. This means that a glass-coated thermistor is preferable for surface temperature measurement. However, it should be noted that the error caused by heat loss cannot be neglected when the measurement accuracy on the order of 100–101 mK is required.
Fig. 6. Temperature difference from a preset temperature of 35.00 °C in cases with and without guard heating.
For the scenario with guard heating, the guard heater temperature could trace the sensor temperature immediately after contact with the heated material. Then, the sensor temperature indicated 34.97 °C at the steady state. The measurement resolution was approximately ±0.005 °C, which was much more precise than that of the other sensors. The offset error from 35.00 °C was only 0.03 °C, which was 10 times smaller than in the case without guard heating. It is important that the offset error was within the
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calibration uncertainty of the thermistors was ±0.05 °C. Note that, to easily and smoothly make a contact between the probe tip and the material surface, the hole of 2 mm in diameter was created in the insulation material before the experiment. Thus, it is also possible that it was caused by a temperature decrease due to heat losses by the heat conduction, radiation, and natural convection on the surface in contact. Additionally, the time needed to reach a steady state was shorter than in the case without guard heating. Therefore, the results show that the guard heater effectively minimized heat loss in the measurements, and enables not only absolute temperature measurement of a heated material, but also faster measurement. Fig. 7 shows the temperature difference between the thermistor used for the sensor and the guard heater, and the applied power to the guard heater during the measurement with guard heating. As seen in the experimental results, the guard heater could rapidly trace the temperature variation of the thermistor for the sensor, and minimize the temperature difference from the sensor temperature by changing the applied power. This shows that the temperature difference was mostly minimized after approximately 5 s, and was within only ±0.01 °C, which was caused by the uncertainty of thermistors at the steady state. The maximum power, which was approximately 1.5 mW, was observed at the moment just after the contact. After that, it gradually decreased to keep the temperature difference minimized between the thermistors. All of the experimental data regarding surface temperature at the steady state is summarized in Table 1. As shown in Table 1, the averaged surface temperatures of the five measurements were 34.97 ± 0.027 °C in the case with guard heating and 34.64 ± 0.051 °C in the case without it. Here, the standard deviation may include the temperature decrease of the material surface due to natural convection. The differences between thermistors in cases with and without a guard heating showed 0.00–0.05 °C and 0.18–0.24 °C, respectively. The guard heater temperatures mostly did not indicate a significant difference from the sensor temperature in the case with guard heating, although there was an obvious difference of approximately 0.2 °C in each measurement in the case without guard heating. Consequently, the results showed the possibility that the guard-heated thermistor probe enabled
the measurement of the absolute surface temperature of the material at higher temperature than ambient, despite the contact-based method. 4. Numerical simulation for performance evaluation 4.1. Calculation model To conduct the performance evaluation of the guard heater by numerical simulation, it is necessary to create the appropriate numerical model. However, the thermistor used in this study has a complicated shape because it is glass-coated and contains two lead wires, which makes modeling difficult. To easily model the complex shape, Ould-Lahoucine et al. transformed an actual 3D shape into a simple axial symmetrical 2D form [35]. In their model, the lead wires, the thermistor chip, and the glass covering the chip were assumed to be a simple shape - a cylinder with a single wire coated by glass. They proposed an estimation method for thermal conductivity by comparing the measured and calculated temperature responses using a proposed two dimensional (2D) axisymmetric model. The estimated thermal conductivities of the standard materials agreed well with the reference values. It was revealed that a transformed model of the thermistor can represent the actual heat transfer phenomena by conducting an experiment to determine the shape parameters. In this study, the complicated actual shape of a thermistor chip was transformed to a simpler 2D axisymmetric form to simulate the temperature response in the measurement. Fig. 8 shows (a) the actual shape of a thermistor, (b) the transformed shape for a simulation and (c) detailed dimensions of transformed thermistor. The actual shape and the dimensions of a thermistor chip are rectangular parallelepiped and approximately 0.24 mm 0.24 mm 0.12 mm. This was measured by a microscope. The actual glass covering the chip has a spheroid shape and the maximum diameter and length measured are approximately 0.43 mm and 0.58 mm, respectively. The lead wires are comprised of a dumet alloy with
Glass
Lead wires Glass
Chip
Chip
(a) Actual thermistor shape.
Lead wire
(b) Transformed shape.
0.095
0.05
0.15
0.1 0.24 0.58
(c) Detailed dimensions of transformed thermistor. Fig. 7. Temperature difference between thermistors for the sensor and the guard heater and applied power to guard heater in the case with guard heating.
Fig. 8. (a) Actual thermistor shape, (b) transformed shape and (c) detailed dimensions.
Table 1 Experimental results of mean surface temperature in cases with and without guard heating. No.
1
2
3
4
5
Tave ± SD
w/guard heating
Ts,mean [°C] Tg,mean [°C]
34.94 34.94
35.01 35.06
34.96 34.97
34.98 35.00
34.97 34.97
34.97 ± 0.027 34.99 ± 0.047
w/o guard heating
Ts,mean [°C] Tg,mean [°C]
34.65 34.46
34.63 34.42
34.67 34.48
34.56 34.32
34.69 34.51
34.64 ± 0.051 34.44 ± 0.077
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a diameter of 0.07 mm. In the model, the thermistor chip was assumed to be a cylinder, while the glass was assumed to be a rounded rectangle. The detailed shape and dimensions of the thermistor used in the calculation are shown in Fig. 8(c). The 2D axisymmetric model could not simulate the presence of the two wires, so only a single wire with an appropriate diameter (0.1 mm) was considered to represent the actual heat loss along the wires. The radius of the modeled wire was determined to be the same thermal conductance as the actual two wires. To represent heat loss in the connected area between the lead wires and the thermistor chip in reality, the lead wire in the model was assumed to be inserted with an area equal to the estimated one by a microscope (see Fig. 8(c)). These approximations of the shape of the thermistor mentioned above may influence the calculation results. Thus, a determination of the shape parameters in the numerical model must be conducted to compare to the experimental temperature response, using a standard material. In this study, the radius and thermal diffusivity of the thermistor chip, which has a significant influence on temperature response, were selected as the shape parameters. The lengths of the thermistor chip and the glass bead were fixed at 0.24 mm and 0.58 mm, respectively, which are the values measured by the microscope. The temperature response when the two parameters were varied was compared to the experimental one. Fig. 9(a) shows the 2D axisymmetric model for a determination of the shape parameters, which means that a modeled thermistor with a single lead wire was inserted into standard material. In this experiment, the agar-gelled water (1 wt%) was used as the standard material. The calculation domain was 10.0 mm 20.0 mm, which is larger enough for the calculated temperature responses of the thermistors. Although the length of the lead wire above the insulation material is not included in the calculation model, it has been confirmed that it has no impact on the temperature response of the sensor thermistor. The number Adiabatic condition
of grids was 400 400. All of the boundary conditions were adiabatic. The initial temperatures at each material were given as 26 °C. The thermal contact resistances between components were neglected. The thermophysical properties of each material used in this simulation were shown in Table 2 [36]. The 2D axisymmetric heat conduction equation is expressed as follows:
qc
@T 1 @ @T @ @T _ þ þ q; ¼ kr k @t r @r @r @z @z
ð3Þ
where q [kg/m3] is the density, c[J/(kgK)] is the specific heat, k [W/ (mK)] is the thermal conductivity and q_ [W/m3] is the heat generation rate of thermistor chip. An implicit implementation of the finite volume method was chosen as the numerical method to solve the partial differential equation in this formulation [37]. Based on the algorithm, a FORTRAN90 code was written and run on a personal computer. To determine the shape of the thermistor, the temperature response was calculated during and after a constant power (3 mW) was applied to a thermistor chip for 3 s, in order to compare with the experimental results. This was for the determination of shape parameters. This temperature response included not only the temperature increase during heating, but also the temperature decay after heating, so that a more reliable parameters can be determined. Here, the temperature of the thermistors was evaluated as the volume-averaged temperature of the thermistor chip expressed as:
R Vc
Ts
or T g ¼
0
T c dV ; Vc
ð4Þ
where Ts, Tg, Tc, and Vc denote the volume averaged temperature for the sensor and guard heater, the temperature of the thermistor chip, and the volume of thermistor chip, respectively. The temperature measurement with agar-gelled water (1 wt%) was conducted to determine the shape parameters in the model. Adiabatic condition
Specimen
Insulation material
FEP tube Air Lead wire
Lead wire
Glass
Aluminum
Adiabatic condition
Isothermal condition (T = 35 oC)
10 mm
10 mm
(a)
(b)
20 mm
Thermistor Chip Air
Adiabatic condition
Adhesive
20 mm
Thermistor Chip
Adiabatic condition
Glass
Fig. 9. Calculation models used in this study: (a) model for determination of shape parameters and (b) model for temperature and thermal conductivity measurement.
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Table 2 Thermophysical properties of each material used in simulations [36]. Material
Thermal conductivity, W/(mK)
Specific heat, J/(kgK)
Density, kg/m3
Agar-gelled water Glass Lead wire (dumet) Air FEP tube Adhesive Insulation material Aluminum
0.60 0.70 150 0.026 0.25 0.50 0.03 238
4180 4300 400 1006 2145 2000 1900 917
997 900 8500 1.17 1200 1200 15.9 2700
A thermistor was connected to the DMM and DC power supply and used as a sensor and a point heat source. In the measurement, the thermistor was inserted into the agar-gelled water at a room temperature of 26 °C, and was heated by a constant power of 3 mW at the steady state. Then, the temperature response was measured during and after heating, and compared to the calculated response using the model mentioned above. By comparison, the radius and thermal diffusivity of the thermistor in the simulation was varied until the temperature difference between the experimental and calculated results was minimized enough at each time. Finally, the determined values were used as shape parameters in a simulation for the surface temperature measurement. Fig. 10 shows a comparison between the experimental and calculated temperature responses for the determination of the shape parameters. As shown in figure, the experimental and calculated temperature responses were in good agreement each other. The temperature difference at each time was mostly within ±0.02 °C, meaning that the transformed thermistor successfully represented the actual temperature response both during and after the heating, despite the approximated dimensions of the 2D axisymmetric model. The determined values of each parameter are shown in Table 3. In this study, the determined values for the radius and thermal diffusivity were used for the calculation model for the performance evaluation of the guard-heated thermistor probe. 4.2. Simulation results and discussions Next, a numerical simulation of the surface temperature measurement of the heated aluminum block was conducted to
Fig. 10. Comparison between experimental and calculated results for determination of shape parameters.
Table 3 Determined shape parameters: radius and thermal diffusivity of thermistor chip. Material
Radius, mm
Thermal diffusivity, m2/s
Thermistor chip
0.095
5.5 107
theoretically evaluate heat loss along the lead wires using the guard-heated thermistor probe. Fig. 9(b) shows the 2D axisymmetric model with the shape parameters, including the thermistor for the guard heater, the FEP tube covering the thermistors, and the adhesive to demonstrate the guard-heated thermistor probe. This model represents the guard-heated thermistor probe contacting the heated aluminum block at 35.00 °C. The probe was surrounded by an insulation material. This model included a PID control to minimize the temperature difference between the two thermistors using Eq. (1). The length between thermistors was assumed to be 0.1 mm. The calculation code is basically the same as the one used in the determination of the shape parameters, except only the calculation conditions were different. The thermophysical properties of each component are shown in Table 2. In this calculation, all of the boundary conditions were given as adiabatic, except at the bottom of domain, which represented isothermal conditions at 35.00 °C. At the initial conditions, the temperatures of the probe and the insulation material were at 26.00 °C, while the temperature of the aluminum was at 35.00 °C. The thermal contact resistance at the contact surface, and the effects of the natural convection and radiation were neglected. Fig. 11 shows the calculated temperature responses of the thermistors for (a) sensor and (b) guard heater in the cases with and without guard heating after the contact. In order to validate the calculation results, the experimental results are also plotted. For the case without guard heating, the temperatures for the sensor and guard heater ultimately indicated 34.56 °C and 33.84 °C at 60 s, but they still did not reach the steady state. This implies that heat loss significantly influenced the thermistor temperature. In addition, the temperature increase after contact was relatively slow due to heat loss through the lead wire. In comparison with the experimental results, the sensor temperature showed a good agreement, but the guard heater temperature did not quantitatively agree due to the difference from the real structure of a guard-heated thermistor probe such as the contact with other materials and lead wire length of guard heater. For the case with guard heating, on the other hand, the temperatures for the sensor and guard heater rapidly increased and showed 34.99 °C, indicating a small offset error of 0.01 °C, which might be caused by heat loss to the insulation material and a FEP tube at 26 °C. However, the guard heater worked very well to trace the temperature for the sensor, and accurately minimized the temperature difference in comparison to the case without guard heating. The temperature was reached at a steady state after approximately 15 s, indicating that this simulation exhibits the same behavior as the experimental results. As a consequence, it was revealed that, the calculation model can show a reliable result, and can be used for the evaluation of the amount of heat that passes through the lead wire of the sensor thermistor during a measurement. In addition, the calculation results indicated that the guard-heated thermistor probe allows for an accurate measurement of the absolute surface temperature based on the minimization of heat loss by guard heater. Fig. 12 shows the calculated results of heat loss along the lead wire for the thermistor for the sensor in cases with and without guard heating. Heat loss along the lead wire was calculated by Fourier’s law, using a temperature gradient on the middle point between two thermistors at each time, expressed as:
Q loss ðtÞ ¼ Alead klead
dT lead ; dz
ð5Þ
where Qloss, Alead, klead, and Tlead denote the amount of heat, the cross-sectional area, the thermal conductivity of lead wire and the temperature of lead wire, respectively. For the case without guard heating, heat loss from the sensor thermistor to the guard heater increased to approximately
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(a) Sensor
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(b) Guard heater
Fig. 11. Calculation results of temperature responses in cases with and without guard heating: (a) sensor and (b) guard heater.
heated at 35.00 °C in the cases with and without guard heating. Moreover, a two-dimensional axisymmetric heat conduction analysis was conducted to quantitatively evaluate the amount of heat that passes through the lead wires. Based on the results, the following conclusions were obtained.
Fig. 12. Calculation results of heat loss through lead wire of thermistor for sensor in cases with and without guard heating.
0.5 mW just after contact, and gradually decreased to 0.1 mW. However, temperature did not reach the steady state at 60 s, because the guard heater did not work. Then, heat loss caused the temperature to decrease to 0.44 °C in the thermistor for the sensor. Thus, heat loss along the lead wires cannot be neglected in the case without guard heater, so, it is necessary to minimize heat loss along the lead wire for the accurate measurement of surface temperature in a heated material. For the case with guard heating, on the other hand, heat loss showed a negative value just after contact, and gradually approached a minimum value that was 0.016 mW. Note that the negative value represented the amount of heat from a guard heater to a sensor thermistor. The amount of heat always showed a much smaller value than that in the case without guard heating. The estimated heat loss of 0.016 mW caused only a 0.01 °C temperature drop from the preset temperature of 35.00 °C. It was revealed that a guard heater could effectively minimize heat loss along the lead wire, and enabled the ability to accurately measure the surface temperature in a heated material at a higher temperature than the ambient.
5. Conclusions In this study, a guard-heated thermistor probe that used a guard heater for the minimization of heat loss along the lead wires was developed for the purpose of accurately measuring the absolute surface temperature of a material at a higher temperature than the ambient temperature. To evaluate heat loss along the thermistor’s lead wires in a surface temperature measurement, experiments were conducted with the surface of an aluminum block
– The experimental results showed that the guard-heated thermistor probe achieved the minimization of heat loss along the lead wires, and allowed for a more accurate measurement of the absolute surface temperature of a heated material, regardless of contact method. – The 2D axisymmetric heat conduction analysis demonstrated that the guard heater successfully minimized heat loss along the lead wire to 0.016 mW which was a much smaller value than that in the case without guard heating (0.1 mW). The estimated heat loss of 0.016 mW caused only a 0.01 °C temperature drop from the preset temperature of 35.00 °C. This showed a good agreement with the experimental results. – The guard-heated thermistor probe is an appropriate option for the accurate measurement of the absolute skin surface temperature in the future. In addition, the present probe makes it possible to observe a skin temperature fluctuation caused by the blood perfusion underneath the human skin. A preliminary study has already been performed.
Acknowledgement This study was supported by Grant-in-Aid for JSPS Fellows 13J08342.
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