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Krishpersad Manohar, I David W. Yarbrough,2 and James R. Booth3 Measurement of Apparent Thermal Conductivity by the Thermal Probe Method Authorized Reprint from Journal of Testing and Evaluation, Sept. 2000 @Copyright 2000 American Society for Testing and Materials, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959 REFERENCE: Manohar, K., Yarbrough, D. W., and Booth, J. R., "Measurement of Apparent Thermal Conductivity by the Thermal Probe Method," Journal of Testing and Evaluation, HEV A, Vol. 28, No.5, September 2000, pp. 345-351. ABSTRACT: Three thermal probes were constructed in accor- dance with ASTM D 5334 and calibrated using heat-flow metre data. The temperature-time response of the thermal probes for de- termining apparent thermal conductivity Aunder transient state con- ditions was logged at 1 s intervals. The instrumentation used re- duced the determinate error associated with voltage and current measurements to a negligibly small value that made the uncertainty in A dependent on the uncertainty of the slope dTldlnt. A test method was run in 1000 s, in which a criterion of 2.5% spread among three consecutive slope values was used to determine the ex- tent of the linear segment of the T-In t curve. The probes demonstrated repeatability within :!::3.5% but had definite individual bias indicating a need for individual calibration. Using individual probe calibration factors, the experimentally de- termined ASfor all-purpose sand, sifted sand, and soil were deter- mined to be 0.520, 0.445, and 2.11 W1m'K, respectively. KEYWORDS: thermal probe, thermal conductivity, line source method Nomenclature n Number of data points in chosen time interval Q Power emitted by probe per unit length, Wlm R Electrical resistance, n r Radial distance from probe, mm T Temperature, °C To Initial temperature, °C t Time, s V Voltage, V K Thermal diffusivity, m2/s iI. Apparent thermal conductivity, W/m.K The use of small-diameter heated probes to approximate a line- source in a semi-infinite medium has been in the literature for many years [1-4]. The probe normally consists of an electrical heater and a temperature sensor, typically a thermocouple. The probe is in- serted into an isothermal material and powered. The time-tempera- Manuscript received 09/22/99; accepted for publication 6107100. ] Lecturer, Mechanical Engineering Department, The University of the West Indies, St. Augustine, Trinidad, West Indies. 2 Professor and chairman, Chemical Engineering Department, Tennessee Technological University, Cookeville, TN. 3 Adjunct professor, Chemical Engineering Department, Tennessee Techno- logical University, Cookeville, TN. @2000 by the American Society for Testing and Materials ture data from the probe are analyzed to obtain the mean apparent thermal conductivity iI.for the material over the temperature range introduced in the experiment. Apparent thermal conductivities are obtained from the data using Eq 1, which is an approximation of the solution for the boundary value problem describing the physical situation [4]. (Q/47T) iI. = (dT/dlnt) (1) Equation 1 indicates an attractive method for thermal conductivity measurement with the advantages of low cost and short test time. Hence, this method would be ideal for conducting many tests per day and testing material with moisture. However, in the past the re- liability of the results was poor [1-4] and hence the method was seldom used. This study concentrated on improving the reliability of the test method by reducing the associated equipment error and monitoring the time-temperature response of the thermal probe at I s intervals. This paper focuses on probe calibration, data acquisition, and ap- parent thermal conductivity data obtained for four materials. Thermal Probe The thermal probes in this work were constructed from seamless thin-walled stainless steel tubes, 100 mm long and 3 mm outer di- ameter. The main probe components are a manganin heater wire and a thermocouple as shown in Fig. 1. The probe assembly is sim- ilar to that described in ASTM D 5334 [5]. Insulated manganin heater wire, 0.358 mm in diameter, was looped and inserted into the full length of the tube to form the heat- ing element; a 30 gage T-type thermocouple (wires supplied by Cole-Parmer) was inserted midway along the length of the tube. Both ends of the heating element and the thermocouple wires pro- truded from the same end of the tube and were passed through a ny- lon cap. Following the procedure described in ASTM D 5334 [5], the tube was filled with a clear plastic epoxy resin and a metal tip was placed on the open end of the tube. The epoxy was allowed 24 h setting time, and the extended heater wire ends were cut close to the thermal probe and power supply leads were soldered to them. Electrical Circuit The thermal probe was powered by a regulated doc power sup- ply. The electrical circuit used is shown schematically in Fig. 2. The system employed a Hewlett Packard 6114A precision power supply capable of varying the voltage in steps of 0.001 V from 0 to 30 V and holding steady at the set value. The voltage across the thermal probe was monitored continuously with a 7081 Schlum- berger precision voltmeter [6]. The voltmeter was calibrated by the manufacturer and checked with the Hewlett Packard precision 345
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Page 1: ASTM Therm Probe

Krishpersad Manohar, I David W. Yarbrough,2 and James R. Booth3

Measurement of Apparent Thermal Conductivityby the Thermal Probe MethodAuthorized Reprint from Journal of Testing and Evaluation, Sept. 2000 @Copyright 2000American Society for Testing and Materials, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959

REFERENCE: Manohar, K., Yarbrough, D. W., and Booth, J. R.,"Measurement of Apparent Thermal Conductivity by theThermal Probe Method," Journal of Testing and Evaluation,HEV A, Vol. 28, No.5, September 2000, pp. 345-351.

ABSTRACT: Three thermal probes were constructed in accor-dance with ASTM D 5334 and calibrated using heat-flow metredata. The temperature-time response of the thermal probes for de-termining apparent thermal conductivity Aunder transient state con-ditions was logged at 1 s intervals. The instrumentation used re-duced the determinate error associated with voltage and currentmeasurements to a negligibly small value that made the uncertaintyin A dependent on the uncertainty of the slope dTldlnt. A testmethod was run in 1000 s, in which a criterion of 2.5% spreadamong three consecutive slope values was used to determine the ex-tent of the linear segment of the T-In t curve.

The probes demonstrated repeatability within :!::3.5% but haddefinite individual bias indicating a need for individual calibration.Using individual probe calibration factors, the experimentally de-termined ASfor all-purpose sand, sifted sand, and soil were deter-mined to be 0.520, 0.445, and 2.11 W1m'K, respectively.

KEYWORDS: thermal probe, thermal conductivity, line sourcemethod

Nomenclature

n Number of data points in chosen time intervalQ Power emitted by probe per unit length, WlmR Electrical resistance, nr Radial distance from probe, mmT Temperature, °C

To Initial temperature, °Ct Time, s

V Voltage, VK Thermal diffusivity, m2/siI. Apparent thermal conductivity, W/m.K

The use of small-diameter heated probes to approximate a line-source in a semi-infinite medium has been in the literature for manyyears [1-4]. The probe normally consists of an electrical heater anda temperature sensor, typically a thermocouple. The probe is in-serted into an isothermal material and powered. The time-tempera-

Manuscript received 09/22/99; accepted for publication 6107100.] Lecturer, Mechanical Engineering Department, The University of the West

Indies, St. Augustine, Trinidad, West Indies.2 Professor and chairman, Chemical Engineering Department, Tennessee

Technological University, Cookeville, TN.3 Adjunct professor, Chemical Engineering Department, Tennessee Techno-

logical University, Cookeville, TN.

@2000 by the American Society for Testing and Materials

ture data from the probe are analyzed to obtain the mean apparentthermal conductivity iI.for the material over the temperature rangeintroduced in the experiment. Apparent thermal conductivities areobtained from the data using Eq 1, which is an approximation of thesolution for the boundary value problem describing the physicalsituation [4].

(Q/47T)iI. = (dT/dlnt)

(1)

Equation 1 indicates an attractive method for thermal conductivitymeasurement with the advantages of low cost and short test time.Hence, this method would be ideal for conducting many tests perday and testing material with moisture. However, in the past the re-liability of the results was poor [1-4] and hence the method wasseldom used.

This study concentrated on improving the reliability of the testmethod by reducing the associated equipment error and monitoringthe time-temperature response of the thermal probe at I s intervals.This paper focuses on probe calibration, data acquisition, and ap-parent thermal conductivity data obtained for four materials.

Thermal Probe

The thermal probes in this work were constructed from seamlessthin-walled stainless steel tubes, 100 mm long and 3 mm outer di-ameter. The main probe components are a manganin heater wireand a thermocouple as shown in Fig. 1. The probe assembly is sim-ilar to that described in ASTM D 5334 [5].

Insulated manganin heater wire, 0.358 mm in diameter, waslooped and inserted into the full length of the tube to form the heat-ing element; a 30 gage T-type thermocouple (wires supplied byCole-Parmer) was inserted midway along the length of the tube.Both ends of the heating element and the thermocouple wires pro-truded from the same end of the tube and were passed through a ny-lon cap. Following the procedure described in ASTM D 5334 [5],the tube was filled with a clear plastic epoxy resin and a metal tipwas placed on the open end of the tube. The epoxy was allowed 24h setting time, and the extended heater wire ends were cut close tothe thermal probe and power supply leads were soldered to them.

Electrical Circuit

The thermal probe was powered by a regulated doc power sup-ply. The electrical circuit used is shown schematically in Fig. 2.The system employed a Hewlett Packard 6114A precision powersupply capable of varying the voltage in steps of 0.001 V from 0 to30 V and holding steady at the set value. The voltage across thethermal probe was monitored continuously with a 7081 Schlum-berger precision voltmeter [6]. The voltmeter was calibrated by themanufacturer and checked with the Hewlett Packard precision

345

Page 2: ASTM Therm Probe

346 JOURNAL OF TESTING AND EVALUATION

Thennocouple wire

Nyloncap

Steelprobe

Thermocouple

Epoxy

Heaterwire

FIG. I-Schematic of thermal probe used.

Thermocouplewires

Thenna1 probe

Test specimen

FIG. 2-Schematic of electrical circuit and data acquisition systemused.

power supply. This unit displayed voltage values to 10-6 V with anuncertainty of :!::1.3 X 10-5 V within the 0 to 10 V range [6]. Thecurrent in the circuit was obtained by monitoring the voltage dropacross a standard 1.0 0 resistor. Data acquisition was done with anIBM-compatible PC via an Advantech Enhanced Multi-Lab card-PCL812PG with Advantech PCL789D amplifier and multiplexerboard. The computer was programmed by the timer function inQuickBasic V4.5 to monitor the voltage drop ten times each sec-ond, calculate the current, and display the mean current value eachsecond.

Data Acquisition

The temperature-time variation of the thermocouple in the ther-mal probe was monitored and recorded by the computer throughthe I/O board. Electronic compensation was provided for the ther-mocouple. The computer was programmed to sense ten tempera-ture signals per second, compute the average and display it eachsecond, store and display readings of current, time, and tempera-ture for a total of 1000 entries, and at the end prompt for input ofthe voltage across the thermal probe.

Theory

The general solution for the temperature variation with time of acylinder of a perfect conductor with small radius transferring heatat a constant rate to the surrounding isothermal infinite mediumwith constant properties indicates that in all cases a plot of temper-ature against In t has a linear asymptote of slope (Q/47TA) [4].Therefore, if the value of Q is known, the apparent thermal con-ductivity Ais determined by Eq I.

Steady state

g'"2~'"0.E'"f-

I,~

Linear

Non-linear

10 100 1000 10000

Time (s)

FIG. 3-Typical experimental test results (idealized curve) [2,5].

In practical situations, however, the finite radius ofthe probe hasthe effect of a time delay before the theoretical rate of radial heatflow through the surface of the probe is equal to the heat dissipatedby the heater filament [2]. Therefore, for practical situations, thegeneral shape of the T-In t plot includes an initial nonlinear regionfollowed by a linear region. With the passage of time, the probetemperature will level off to a steady-state value because of anisothermal specimen boundary. The general shape of a typical T-Int plot is shown in Fig. 3 [2,5].

Experimental Procedure

The thermal probe can be used to test specimens in the labora-tory or materials in situ. The analysis characterized by Eq I re-quired that the specimen be isothermal, thus limiting in situ usage.The experimental procedure involved inserting the probe in the ma-terial to be tested after both were in thermal equilibrium with thesurroundings. Since the friction associated with inserting the probemay cause a measurable temperature increase, the probe tempera-ture was monitored to make certain that isothermal conditions were

attained before the heater was powered. This thermal equilibrationusually takes 10 to IS min.

The data acquisition system and heater power were turned on to-gether once thermal equilibrium had been achieved. The data ac-quisition system recorded probe current, temperature, and time forapproximately 1000 s. Since manganin wire has a negligiblechange in electrical resistance with temperature [7], the power tothe probe heater remained constant.

A properly configured test could be completed with about 1000s of data collection. Within this time limit, the T-In t variation ofthe probe showed three distinct segments, i.e., an initial nonlinearsegment, a linear segment, and a final steady state. The T-In t curveleveling off too soon «800 s) is an indication that the power sup-plied is too low. This resulted in the linear section of the plot beingtoo brief for analysis and the temperature increase too small for re-liable results. A rapid increase in probe temperature is an indicationthat the power supplied to the heater is too high. This can cause heatbuildup in the probe resulting in damage [2], and for materials withmoisture a large rapid temperature gradient could result in moisturemigration, causing a change in material properties [8]. The powercan be adjusted up or down to satisfy the test design time of1000 s.

Experimental Uncertainty

The experimentally determined A is calculated from Eq 1, inwhich A is proportional to the ratio of Q/(dT/dln f). The value of Q

Page 3: ASTM Therm Probe

depends on the product of the voltage and current readings. Thecurrent reading is computed from a voltage taken across a standardresistor. (dT/dln t) is the slope b of the T-In t curve. From the the-ory of uncertainty analysis [9], the square of the uncertainty in theexperimentally determined A.is given by Eq 2.

(~A.)2 - (~V

)2 + (~V)2 + (

~R

)2 + (M)2 (2)

A. - V Voltage V Current R b

h ~A. ~V ~R d M h . .. .were T' V' R' an bare t e uncertamtles m expenmen-tally determined A.,voltage, resistance, and slope, respectively [9].

The 7018 Schlumberger precision voltmeter displayed voltagereadings with a limiting uncertainty of ::I::1.3 X 10-5 V in the 0 to10 V range [6]. The standard 1 D resistor showed a resistance of1.00010 D, resulting in an uncertainty of 0.000 10 D. From Eq 2 thesquare of the uncertainty associated with the measured A.is:

( ~A.A.Y = (1.3 X 10-5)2

+ (1.3 X 10-5)2+ (0.0~01OY + ( ~: y

In comparison to the range of values associated with measured A.,the uncertainty of the sum of the voltage and current readings isnegligible. Hence, the uncertainty of A.is characterized by the un-certainty in the slope b of the straight line fit to the experimentaldata.

Test Design Criteria and Data Analysis

The theory associated with determining apparent thermal con-ductivity from the T-In t plot of the thermal probe (Eq 1) makes useof the slope associated with the linear segment of the heat-up curve.A least squares fit to a linear expression for T in terms of In twasused to describe this segment of the heat-up curve. The analysis in-volves determining the slope for candidate intervals of 0 to 1000 s,50 to 950 s, 100 to 900 s, etc. The linear segment was taken to besuch that three consecutive calculations of the slope differed fromeach other by no more than 2.5%. The slope, dT/dln t, of the best-fit line for the data points within the selected time intervals was cal-culated using Eq 4 [10].

~-dint -

n I (In t)(T) - (I In t)(I T)

n I (In t)2 - (I In tY

This equation gives the slope of the linear regression line throughthe selected data points. The experimentally determined value forA.is inversely proportional to dT/dln t, which is the result of ananalysis of the (T, In t) data. A standard statistical technique [10]was used to estimate the 95% confidence interval of this slope. Thisis an important step since the uncertainty in the slope (dT/dln t)contributes to the overall uncertainty in A..Equations 5 and 6 wereused for this purpose, where n is the number of data points withinthe chosen time interval for the analysis.

95% confidence limits of slope

= ::I::1.96s;

I (lnt)2 - ~ (I In ry

MANOHAR ET AL. ON THE THERMAL PROBE METHOD 347

where Sy

r n(n ~2) ]

('" ) ('"

)]2

rnI(ln t)(T) - LJ In t LJT

X In~>' - (LT)' - [nLOnt)'- (L Int)']

(6)

Calibration

(3)

Three thermal probes were constructed and calibrated usingcommercially available fine cryogenic perlite as the reference ma-terial. The A.of a 254 by 254 by 52 mm thick perlite specimen at adensity of 51 kg/m3 was determined in a heat-flow meter apparatusbuilt by LaserComp [11] at mean temperatures of9, 14, 19,24,29,34, 39, 44, and 46°e with a temperature difference of 22°e be-tween the hot and cold plates. This heat-flow meter was built andoperated in accordance with ASTM e 518 [12]. The heat-flow me-ter was designed to provide A.measurements with an accuracy of::I::1% with ::1::0.2% repeatability and ::1::0.5% reproducibility.

The experimental A.data for perlite were fit to a linear expressionin T using the method of least squares to obtain Eq 7.

A. = 0.037493 + (0.15727 X 1O-3)T (7)

The thermal probes built for this project were checked in a 51kg/m3 perlite specimen contained in a 305 by 305 by 305 mmwooden container. From the theory of the continuous line sourceheater [4], Eq 8 is the approximate solution for the temperaturevariation with time in an infinite solid, initially at temperature To,heated by a line source.

T - To = (Q/4'ITK)ln(4Kt/r2)- 0.5772(Q/4'ITK) (8)

(4)

Using a specific heat estimate of 1005 J/kg °e for 51 kg/m3 perliteat 31°e, the radial distance r at which (T - To) is zero after 1000 sis 43 mm. Therefore, for all practical purposes, the 305 mm cubedspecimen simulated an infinite medium with respect to the thermalprobes over the test time of 1000 s.

Eight calibration tests were conducted for each thermal probe.For each test the slope was determined using the procedure out-lined earlier. The linear region of the slope was selected in accor-dance with the 2.5% criterion. Test data that did not satisfy the con-ditions of the test design were discarded. The 95% confidenceinterval, the mean value for the slope, and A.for data that satisfiedthe test conditions were calculated. Table 1 shows the calibrationtest results for probe 1.

Of the eight calibration tests for probe 1, six satisfied the testdesign conditions (Table 1) and two were discarded. The resultsshow that the 95% confidence interval for the slope that satisfiedthe test conditions was ::I::1.55%. The A.indicated a spread from0.0410 to 0.0422 W/m'K and the mean A.was calculated to be0.0414 W/m.K at a mean temperature of 28.5°e. From Eq 7, thee 518 value of A.for perlite at 28.5°e is 0,0420 W/m'K. The dif-ference between A.c518and A.probe1 is 0.0006 W/m'K. To accountfor the difference in A.values, the assigned calibration factor cffor probe J is:

(5)

cfI = (A.cm)I(A.probe 1) = (0.0420)/(0.0414)= 1.01

Page 4: ASTM Therm Probe

348 JOURNALOF TESTING AND EVALUATION

TABLE I-Calibration Test 1 results-Probe 1.

Calibration Test 1 Results-Probe 1Voltage = 0.5609 V CUlTent= 0.4102 A Mean Test Temperature = 28.5°C

% Spread95% Confidence

Interval of SlopeMean Slope,

dTldln tA,

W/m.K

::':0.0222 (::':0.89%)

0.46% ::':0.0285 (::': 1.14%) 2.48 0.0410

::':0.0382 (::': 1.55%)

Calibration Test 2 Results-Probe 1Voltage = 0.5609 V Current = 0.4102 A Mean Test Temperature = 28.5°C

Time Period,s

Slope,dTldln t % Spread

95% Confidence

Interval of SlopeMean Slope,

dTldln tA,

W/m.K

0-1 000 2.2261

50-950 2.4943 ::':0.0128 (::':0.51%)

100-900

150-850

2.4876 1.42% ::':0.0168 (::':0.65%)

::':0.0197 (::':0.80%)

2.48 0.0410

200-800

250-750

2.4593

2.4324

2.4176

Calibration Test 3 Results-Probe IVoltage = 0.5606 V Current = 0.4102 A Mean Test Temperature = 28.5°C

% Spread95% Confidence

Interval of SlopeMean Slope,

dT/dln tA.

W/m.K

1.12%

::':0.0133 (::':0.53%)

::':0.0164 (::':0.65%) 2.52 0.0404

::':0.0198 (::':0.79%)

Calibration Test 4 Results-Probe 1Voltage = 0.4262 V Current = 0.3252 A Mean Test Temperature = 27°C

% Spread95% Confidence

Interval of SlopeMean Slope,

dTldln tA,

W/m.K

::':0.0094 (::':0.65%)

1.43% ::':0.0121 (::':0.83%) 1.45 0.0422

::':0.0152 (::':1.06%)

Time Period, Slope,s dTldln t

0-1000 2.2007

50-950 2.4813

100-900 2.4918

150-850 2.4699

200-800 2.4464

250-750 2.3768

Time Period, Slope,s dTldln t

0-1000 2.2368

50-950 2.5216

100-900 2.5323

150-850 2.5043

200-800 2.4888

250-750 2.4681

Time Period, Slope,s dTldln t

0-1000 1.2884

50-950 1.4569

100-900 1.4577

150-850 1.4372

200-800 1.4132

250-750 1.4086

Page 5: ASTM Therm Probe

MANOHAR ET AL. ON THE THERMAL PROBE METHOD 349

TABLE I-Continued

Calibration Test 5 Results-Probe IVoltage = 0.5714 V Current = 0.3950 A Mean Test Temperature = 28.4°C

% SpreadA,

W/m.K95% Confidence

Interval of SlopeMean Slope,

dT/dln t

1.65%

::':0.0112 (::':0.52%)

::':0.0141 (::':0.65%) 2.15 0.0421

::':0.0165 (::':0.78%)

Calibration Test 6 Results-Probe 1Voltage = 0.5172 V Current = 0.3926 A Mean Test Temperature = 28.4°C

% SpreadA,

W/m.K

1.11%

95% Confidence

Interval of SlopeMean Slope,

dTldln t

::':0.0149 (::':0.69%)

::':0.0194 (::':0.90%) 2.15 0.0417

::':0.0243 (::':1.14%)

The calibration test for probe 2 showed that the 95% confidenceinterval for the slope that satisfied the test conditions was::'::1.07%.The A indicated a spread from 0.0319 to 0.0340 W/m.K, and themean A was calculated to be 0.0327 W/m' K at a mean temperatureof 31°c. From Eq 7, the C 518 value of A for perlite at 31°C is0.0424 W/m' K. The difference between AC518 and Aprobe2 is0.00963 W/m' K. To account for the difference in A values, the as-signed calibration factor for probe 2 is:

cfz = (AC5I8)/(Aprobe2) = (0.0424)/(0.0327) = 1.30

The calibration test for probe 3 showed that the 95% confidenceinterval for the slope that satisfied the test conditions was::'::1.05%.The A indicated a spread from 0.0370 to 0.0385 W/m'K, and themean Awas calculated to be 0.0378 W/m' K at a mean temperatureof 31°c. From Eq 7, the C 518 value of A for perlite at 31°C is0.0424 W/m'K. The difference between AC518 and Aprobe3 is0.00459 W/m'K. To account for the difference in A values the as-signed calibration factor for probe 3 is:

cf3 = (AC5I8)/(Aprobe3) = (0.0424)/(0.0378)= 1.12

The apparent thermal conductivity of the three probes with their re-spective calibration factors are compared with the C 518 measure-ments in Table 2.

A Measurements

Using the three calibrated probes, A measurements were con-ducted on samples of general all-purpose sand, sifted sand, and

soil. The general all-purpose sand is commercially available in pre-packaged bags ("Quikrete" brand), and the material was allowed toattain equilibrium with laboratory conditions of 24°C and 50% rel-ative humidity for three days. The sifted sand was sized between106 and 500 /Lmusing the appropriate size sieves, and the materialwas allowed to attain equilibrium with laboratory conditions of24°C and 50% relative humidity for three days. The soil sampleused was 152 mm diameter, 200 mm long, and was obtained fromthe Cookeville, Tennessee area. The soil was of a brown, sandy-clay nature with a density of 1893 kg/m3 and moisture content of20.3% by weight.

The all-purpose and sifted sand specimens were prepared usingcommercially available 2000 mL plastic containers. The sizes ofthe specimens were 108 mm diameter, 200 mm high, and the den-sities were 1730 and 1654 kglm3, respectively. Using thermal dif-fusivity values of K = 0.46 mm2/s and K = 0.20 mm2/s for soil andsand, respectively [4], the radial distances at which there is zerotemperature change after 1000 s were calculated from Eq 8 to be32.1 and 21.2 mm, respectively.

Time Period, Slope,s dTldln t

0-1000 1.9114

50-950 2.1526

100-900 2.1587

150-850 1.1237

200-800 2.0964

250-750 2.0774

Time Period, Slope,s dTldln t

0-1000 1.9070

50-950 2.1562

100-900 2.1631

150-850 2.1396

200-800 2.0932

250-750 2.0501

TABLE 2-Afromprobes and C 518.

A, A X cf, AC5IS, Difference,W/m.K W/m.K W/m.K ACSIS- A X cf

Probe 1 (28.5°C) 0.0414 0.0418 0.0420 0.0002Probe 2 (31°C) 0.0327 0.0425 0.0424 -0.0001Probe 3 (31°C) 0.0378 0.0423 0.0424 0.0001

Page 6: ASTM Therm Probe

350 JOURNALOF TESTING AND EVALUATION

For each test material, four tests were conducted with eachprobe, and the voltage, current, and time-temperature data werelogged. For each test the time regression analysis on the slope de-scribed earlier was conducted for the T-ln tdata. For the results thatsatisfied the 2.5% criterion, the 95% confidence intervals were cal-culated, the mean slope determined, and the A evaluated using EqI. Table 3 shows the experimental test data for tests conducted withprobe 1 on all-purpose sand (1730 kg/m3). Figure 4 shows the T-Int curve for probe I experimental data for all-purpose sand. This isa typical curve of T-In t variation for the probes. A summary of theresults is shown in Table 4.

Discussion

The theory associated with A measurements using small diame-ter heated probes has been in existence for over four decades [1-4].However, the stringent conditions under which the theory holds aredifficult to meet in practical situations because of many compro-mising conditions. As such the reported ASdetermined by thismethod range in precision from 5 to 50% [3,5]. Another factor con-tributing to the poor precision of reported ASis the difficulty inmonitoring the temperature-time response of the probe on whichthe test method hinges (Eq 1) [1,2,5].

In this work, an electrical circuit and data acquisition system wasassembled to monitor precisely the temperature-time response. Thecircuit design and equipment brought the determinate error associ-ated with the voltage and current measurements to a negligibly

G~

G)

;:;cri::;0.EG)r-

35 -

30

:~-~25

20 ,-

0 6 82 4

In t (s)

FIG. 4--T-In t curve for thermal probe 1: Test I-All-Purpose Sand.

TABLE 3-Thermal probe 1: test 1: all-purpose sand (1730 kg/m3).

Test 1 Test 2 Test 3 Test 4

Test critena Valid Valid Valid Not-Valid

Voltage, V 1.5228 1.4001 1.4009 1.4010

Current, A 1.1572 1.063480 1.0635 1.0635

Mean test temperature, °C 31.5 30.0 30.0 30.0

Slope, time interval (0-1000) 1.6883 1.3087 1.2594 1.3279

(50-950) 1.6220 1.2526 1.2354 1.2357

(100-900) 1.5999 1.2276 1.2133 1.2039

(150-850) 1.5898 1.2122 1.1970 1.1685

(200-800) 1.5858 1.2207 1.1989 1.1260

(250-750) 1.5597 1.2186 1.2076 1.1027

Minimum % spread between 0.89% 1.27% 1.36 5.75%three consecutive slopes

95% Confidence (100-900) ::to.0I07 ::to.0094 ::'::0.0101

Interval of (150-850) ::to.0146 ::to.0I25 ::to.0141

Slope (200-800) ::to.0224 ::'::0.0190 ::to.0214

Mean Slope aTtaint 1.5918 1.2202 1.2031

>..,W/m.K 0.4894 0.5398 0.5475

(>..)(1.01) (W/m'K) 0.4943 0.5452 0.5530

Mean corrected >..,(W/m'K) 0.5308

TABLE 4--Experimentally determined >..by the thermal probes.

>"probe" >"probe2, >"probe3, Mean>..,W/m'K W/m'K W/m'K W/m'K

All-purpose sand, 0.5308 0.5168 0.5129 0.521730kg/m3 .

Sifted sand, 1654 kg/m3 0.4614 0.4432 0.4288 0.44Soil, 1893 kg/m3, 2.2412 1.9238 2.1595 2.11

20.3% moisture by wt.

Page 7: ASTM Therm Probe

small value. Therefore, from Eq I, the precision of A.becomes de-pendent on the precision of determining the slope of the linear seg-ment of the T-In t curve. In the past this was estimated from a phys-ical plot of the T-In t curve [1,2,5]. In this work, the availability ofa large database made it possible to use standard statistical methodsfor determining the slope.

Specific test design conditions were set for determining the lin-ear region of the T-In t curve as described in the text, and theprobes were checked against a C 518 measurement. The 95% con-fidence interval of the slope, and hence A.,for all the calibrationtests was within::!::1.55%. This indicates that the criteria set and the

statistical analysis are effective in providing a precise determina-tion of the slope. Probes I, 2, and 3 demonstrated repeatability of::!::2.27%,::!::3.22%,and::!::1.94%, respectively. However, a definitebias was observed between A.probeand A.C5IS,indicating the need forindividual calibration. Calibration factors of 1.01, 1.30, and 1.12were computed for the three probes in the project.

Tests were conducted on samples of all-purpose sand, siftedsand, and soil. Using the respective calibration factors, the mean A.values listed in Table 4 demonstrate that the calibration and re-

peatability for the individual probes are consistent. The large vari-ation in the measured soil samples (::!::8.7%)is indicative of thenonhomogeneity and moisture-associated complexity of soil sam-ples [8]. The measured A.Swere all within the range of publishedvalues [12-14]; however, these results were obtained with probesthat were calibrated with a material of much lower A..

Conclusions

I. A precision temperature-time data logging system for col-lecting probe data has been shown useful in automating the mea-surement of A.for particulates.

2. A statistical analysis and the 2.5% spread between three con-secutive slope values for determining the linear segment of theT-In t curve can give results for homogenous material with a 95%confidence of about::!::1.5%.

3. Probes need to be individually calibrated with a referencematerial of known A..The A.of the reference material should beclose to that of the materials to be tested.

4. The probe method is capable of providing reliable and repeat-able A.measurements within ::!::3.5%for homogeneous materials.

References

[1] Herzen, R. V. and Maxwell, A. E., "The Measurement ofThermal Conductivity of Deep-Sea Sediments by a Needle-

MANOHAR ET AL. ON THE THERMAL PROBE METHOD 351

Probe Method," Journal of Geophysical Research, Vol. 64,No. 10, 1959, pp. 1557-1563.

[2] Winterkorn, H. F., "Suggested Method of Test for ThermalResistivity of Soil by the Thermal Probe," Special Procedurefor Testing Soil and Rock for Engineering Purposes, ASTMSTP 479, ASTM, 1970, pp. 264-270.

[3] Tihen, S. S., Carpenter, H. C, and Sohns, H. W., "ThermalConductivity and Thermal Diffusivity of Green River OilShale," Thermal Conductivity, Proceedings of the SeventhConference, D. R. Flynn and B. A. Peavy, Jr., Eds., NationalBureau of Standards Special Publication 302, September1968, pp. 529-535.

[4] Carslaw, H. S. and Jaeger, J. C, Conduction of Heat inSolids, Oxford Press, 2nd ed., 1964, pp. 58-60, 344-345.

[5] ASTM D 5334 Standard Test Method for Determination ofThermal Conductivity of Soil and Soft Rock by Thermal Nee-dle Probe Procedure, 1995 Annual Book of ASTM Standards,Vol. 04.09, pp. 225-229.

[6] Solartron Instruments, Solartron Schlumberger 7081 Preci-sion Voltmeter, Instruction Manual, 2 Westchester Plaza,Elmsford, NY.

. [7] Weast, R. C, Ed., CRCHandbookof Chemistryand Physics,CRC Press Inc., 62nd ed., 1982, p. E-82.

[8] Kersten, M. S., "Thermal Properties of Soils," Bulletin of theUniversity of Minnesota Institute of Technology, EngineeringExperiment Station, Vol. LII, No. 28, 1949.

[9] Coleman, H. W. and Steller, W. G., Experimentation and Un-certainty Analysis for Engineers, 2nd ed., John Wiley andSons, New York, 1999, pp. 47-64.

[10] Natrella, M. G., Experimental Statistics, National Bureau ofStandards Handbook 91, 1963.

[11] LaserComp FOX 304, "Heat Flow Meter Thermal Conduc-tivity Instrument," Information Sheet, LaserComp, Wake-field, MA, USA.

[12] ASTM C 518 Standard Test Method for Steady-State HeatFlux Measurement and Thermal Transmission Properties byMeans of the Heat Flow Meter Apparatus, 1998 Annual Bookof ASTM Standards, Vol. 04.06, pp. 163-174.

[13] Rohsenow, W. M., Hartnett, J. P., and Cho, Y. I., Eds., Hand-book of Heat Transfer, 3rd ed., pp. 2.68-2.74.

[14] American Society of Heating, Refrigerating and Air-Condi-tioning Engineers, ASHRAE Handbook of Fundamentals,1993, pp. 22.13-22.22.

[15] Meinel, A. B. and Meinel, M. P., Applied Solar Energy, Ad-dison-Wesley Publishing Company, 1976, p. 619.