J. agric. Engng Res. (2001) 80 (2), 209}216doi:10.1006/jaer.2001.0730, available online at http://www.idealibrary.com onSW*Soil and Water

Measurement of the Thermal Conductivity of Sandy Loam andClay Loam Soils using Single and Dual Probes

N. H. Abu-Hamdeh

Agricultural Engineering and Technology Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid, Jordan;e-mail: nidal@just.edu.jo

(Received 13 July 1999; accepted in revised form 27 March 2001, published online 17 May 2001)

The propagation of heat in soil is governed by its thermal characteristics. The ability to monitor soil thermalconductivity is an important tool in managing the soil temperature regime to a!ect seed germination and cropgrowth. The e!ect of bulk density and moisture content on the thermal conductivity of two sieved and repackedsoils was investigated through laboratory studies. These laboratory experiments used the single-probe anddual-probe methods to measure and compare thermal conductivities. The soils used were classi"ed as sandyloam and clay loam. Thermal conductivity increased with increasing soil density and moisture content. Thermalconductivity measured by the single-probe method ranged from 0)19 to 1)13 for sandy loam and from 0)35 to0)69 Wm~1K~1 for clay loam at densities from 1)25 to 1)49 g cm~3 and water contents from 7)2 to 18)2%.Thermal conductivity measured by the dual-probe method ranged from 0)21 to 1)15 for sandy loam and from0)37 to 0)70 Wm~1 K~1 for clay loam at same densities and water contents. Finally, it was found that the sandyloam had higher values of thermal conductivity than the clay loam for the soil conditions studied.

( 2001 Silsoe Research Institute

1. Introduction

Soil thermal properties are required in many areas ofengineering, agronomy, and soil science, and in recentyears considerable e!ort has gone into developing tech-niques to determine these properties. Thermal conductiv-ity is considered one of the most important thermalproperties of the plant environment. It is considered asthe property that controls heat #ow through materials ofdi!erent types.

The thermal conductivity of a soil depends on severalfactors. These factors can be arranged into two broadgroups, those which are inherent to the soil itself, andthose which can be managed or controlled, at least toa certain extent by human management. Those factors orproperties that are inherent to the soil itself include thetexture and mineralogical composition of the soil. Fac-tors in#uencing the thermal conductivity of a soil thatcan be managed externally include water content and soilbulk density. Water content plays a major role in thethermal conductivity of a soil, but is also the most di$-cult to manage. The way a soil is managed will play an

0021-8634/01/100209#08 $35.00/0 209

important part in determining its thermal conductivity.Any practice or process which tends to cause soil com-paction will increase bulk density and decrease porosityof a soil. This in turn will have a signi"cant e!ect onthermal conductivity. A certain soil will not necessarilyhave a given value of thermal conductivity unless all ofthe factors are approximately the same whenever themeasurements are taken.

Thermal properties can be determined indirectly bymeasuring the rise or fall of temperature in response toheat input to a line source at the point of interest (Jack-son & Taylor, 1965). De Vries (1952, 1963) developedmodels that allow estimation of thermal conductivity andvolumetric heat capacity of soils from the volume frac-tions of their constituents and the shape of the soilparticles. The dual-probe heat-pulse technique (Cam-pbell et al., 1991; Bristow et al., 1993; Kluitenberg et al.,1993; Bristow et al., 1994a) has also been used to makemeasurements of soil thermal properties. It consists oftwo parallel needle probes separated by a distance r. Oneprobe contains a heater and the other a temperaturesensor. With the dual-probe device inserted in the soil,

( 2001 Silsoe Research Institute

210 N. H. ABU-HAMDEH

a heat pulse is applied to the heater and the temperatureat the sensor probe is recorded as a function of time. Soilthermal conductivity can be determined from these data.

The purpose of this study was to determine thermalconductivity of some soil types as a!ected by bulk den-sity and moisture content using the single and dual-probetechniques. The results obtained using the single-probemethod are compared with the results obtained for thesame soil type but using the dual-probe method. Further-more, thermal conductivity of other soil types evaluatedusing both methods is compared.

2. Theory

The single and dual-probe methods were used tomeasure the thermal conductivity of the soils in thisstudy. In the single-probe method, an electrical wire isimplanted in the experimental soil sample. A steady cur-rent is supplied to the electrical wire and the temperaturerise and fall of the heating wire is measured by a ther-mocouple and recorded during a short heating andcooling.

Due to the linear heat source and cylindrical geometryof the single probe dissipation sensors, sensor temper-ature ¹ during heating is related to time t according tothe theoretical solution for a line heat source (De Vries,1963; Campbell et al., 1991; Bristow et al., 1994b; Reece,1996):

¹!¹0"(q@/4nj) ln (t#t@ )#d (1)

where: ¹0

is the initial temperature in 3C; q@ is the energyinput per unit length of heater per unit time in W m~1,j is the thermal conductivity of the material surrounding

the line source in W m~1K~1; t@ is a time correction usedto account for the "nite dimensions of the heat sourceand the contact resistance between the heat source andthe medium outside the source; and d is a constant. Thecorresponding equation for the sensor temperature dur-ing cooling after t

hseconds of heating is given by:

¹!¹0"(q@/4nj) [ln(t#t@ )!ln(t#t@!t

h)]#d (2)

Non-linear least-squares regression is used to solve forj. An alternative approach is to assume t@@t so thatln(t#t@) approximately equals ln(t). With this assump-tion, linear regression can be used to calculate j fromheating data with Eqn (1) and ln(t) as the independentvariable or from cooling data with Eqn (2) andln[t/(t!t

h)] as the independent variable. Furthermore, if

the relation between ¹ and ln(t) is linear, then j can besimply estimated from the change in sensor temperaturebetween two times, t

1and t

2, by

j"(q@/4n) [ln(t2)!ln(t

1)]/[¹t

2!¹t

1] (3)

For cooling, the analogous equation to Eqn (3) is:

j"(q@/4n) ln [(t2/t

1) (t

1!t

h)/(t

2!t

h)]/[¹t

2!¹t

1] (4)

Equations (3) and (4) can be approximated by substitu-ting I2 R for q@ as:

j"0)0796I2R/S (5)

where: j is the thermal conductivity in W m~1K~1; I isthe current in the line source in A; R is the speci"cresistance of the wire in ) m~1; and S is the slope of thestraight-line portion of the temperature rise or fall as

Notation

d constantI current in the source, Aq@ energy input per unit length of the heater per

unit time, W m~1

R speci"c resistance of the wire, ) m~1

r the distance between electrodes, mSc

slope of the straight-line portion of the tem-perature fall as a function of time

Sh

slope of the straight-line portion of the tem-perature rise as a function of time

¹ sensor temperature at any time, 3C¹

0initial temperature, 3C

D¹m

the maximum temperature change at a dis-tance from the heater, K

t time, sth

time of heating, stm

time at which maximum temperaturechange is recorded, s

t0

heat pulse duration, st1

time of the "rst measurement, st2

time of the second measurement, st@ time correction used to account for the"nite dimensions of the heat source, s

j thermal conductivity, Wm~1 K~1

oc

volumetric heat capacity, J m~3K~1

i thermal di!usivity, m2 s~1

THERMAL CONDUCTIVITY OF SOILS 211

a function of time t. This slope during heating process isdesignated as S

h(i.e. S

h"D¹/Dln(t)) and during the

cooling process as Sc(i.e. S"D¹/D ln[t/(t!t

h)]).

The dual-probe methodology is based on a solution ofthe radial heat conduction equation for an in"nite-lineheat source in a homogenous and isotropic medium ata uniform initial temperature. Volumetric heat capacityocin Jm~3K~1 may be determined with a dual-probe

heat-pulse method (Bristow et al., 1994a) as:

oc"(q@/4niD¹

m) [Ei(!r2/4i (t

m!t

0)!Ei(!r2/4it

m)]

(6)

i"(r2/4) M[1/(tm!t

0)!1/t

m]/[ln(t

m/(t

m!t

0))]N (7)

where: i is the thermal di!usivity in m2 s~1; r is thedistance between electrodes in m; D¹

mis the maximum

temperature change at a distance r from the heater in K;tm

is the time at which D¹m

is recorded in s; t0

is a heatpulse duration in s; and !Ei(!x) is the exponentialintegral of the function x. The exponential integral can beevaluated using procedures developed by Abramowitzand Stegun (1972) for 0)x)1 and for 1)x)R. Theapparent thermal conductivity of soil j in W m~1K~1 isobtained by the de"nition (Bristow et al., 1994a):

j"ioc

(8)

Substituting Eqns (6) and (7) into Eqn (8) yields:

j"(q@/4nD¹m)MEi[!ln(t

m/(t

m!t

0))/(t

0/tm)]

!Ei[!ln(tm/(t

m!t

0))/(t

0/(t

m!t

0))]N (9)

in which r is eliminated.

3. Materials and methods

The dual-probe heat-pulse device used for makingmeasurements in this study consisted of parallel heaterand sensor needle probes made from thin stainless steeltubing 100 mm long and 2 mm in diameter. The needleswere "xed on an acrylic plate by epoxy glue. The heaterto sensor probe spacing was 7)5 mm. The diameter,length, and spacing of the needles were such that theassumptions of a probe of in"nite length would producenegligible errors in the calculated thermal conductivity(Kluitenberg et al., 1995). The line heater was made fromenameled Evanohm wire (Wilbur B. Driver Co., Newark,NJ), which was pulled into the heater needle. The heaterresistance R was 300 ) m~1. The temperature sensorconsisted of copper}constantan thermocouple junction,which was pulled into and centred in the sensor needle.

The needles were "lled with high thermal conductivityepoxy glue to minimize radial temperature gradientsthrough the probe and to provide a water-resistant, elec-trically insulated probe. Heat was generated by applyingvoltage from a 9 V DC power supply to the heater fora "xed period of time. Lower power inputs were used tominimize the e!ects of heating on soil water movementand, hence, thermal conductivity. Actual current throughthe heater element was calculated with Ohm's law bymeasuring the voltage drop across a 10 ) reference resis-tor in series with the heater wire. Heating power input toa sensor was calculated by multiplying the resistance perunit length of heating wire (300 ) m~1) by the squareof the applied current. Heating power inputs of11}12 Wm~1 was used in this study. During applicationof power to the heater, temperature of the thermocoupleand the applied voltage were recorded with a datalogger(Model CR7X, Campbell Scienti"c Inc., Logan, UT). Thesingle probe con"guration consisted of a heater anda temperature sensor mounted together in a thin needle-like probe. With the heater and thermocouple pulled intothe same needle, it was "lled with thermal conducti-vity epoxy glue to provide a water-resistant, electricallyinsulated probe.

In these experiments, rectangular steel boxes of dimen-sions 40 cm in length, 20 cm in width and 25 cm heightwere constructed in which the soil was packed. Afterpacking the soil in the box to the desired bulk density, thesingle and dual probes were vertically inserted from thetop of the box into the soil at the same time with about25 cm between them. The electrical wire for both probeswas then connected to the power supply unit. For single-probe measurements, temperature was measured andrecorded every 5 s for the "rst minute and then every 10 still the end of the heating period (200 s). The powersupply unit was then disconnected and cooling periodwas started immediately. The thermocouple continued torecord the temperature after the battery was discon-nected. The temperature was recorded every 5 s for the"rst 30 s and then every 10 s until the end of the coolingperiod. Temperature was plotted versus the logarithm oftime. Slopes of the linear portions of these curves weredetermined, and these values were used to calculate ther-mal conductivity. Figure 1 shows an example of theseplots. Thermal conductivity of the soil was calculatedfrom the temperature}time record and power input ac-cording to Eqn (5). For dual-probe measurements, powerwas applied to the heater for 8 s (time of heating t

0).

During application and after termination of power to theheater, temperature changes of the thermocouple wererecorded. The peak value for t

mand *¹

mwere deter-

mined by inspection of the measured temperatures bytime data. These data, together with the values of t

0, q@

and r were then used to determine the soil thermal

Fig. 1. Wire temperature as a function of time t during heating for sandy loam at a moisture content of 7)2% and diwerent soil densities(single probe method): , 1)25 g cm!3; , 1)36 g cm!3; , 1)43 g cm!3

212 N. H. ABU-HAMDEH

conductivity by using Eqn (9). The same procedure wasrepeated for di!erent soil bulk densities at various levelsof moisture content for each soil type.

Measurements of thermal conductivity were made ontwo types of soils: sandy loam soil (76% sand, 9% silt,and 15% clay) and clay loam soil (20% sand, 38% silt,and 42% clay). Soil samples were air dried and screenedthrough a 0)2 cm sieve. The soil sample was brought tothe desired water content by adding a known amount ofdistilled water and then mixing thoroughly. Then the soilof known weight at the given moisture content waspacked to di!erent known volumes marked on the box tobring the soil sample to the desired bulk density. Variouslevels of bulk density and moisture content were used.

4. Results and discussion

4.1. Single-probe method

A paired t-test was used to test the null hypothesis thatj obtained from heating data was not di!erent thanj obtained from cooling data using the single-probemethod. The value of the probability P was 0)16, indicat-ing that both the heating method and cooling methodyield identical thermal conductivity values. The averageof heating and cooling estimates of j was used in thisstudy.

Thermal conductivity measured using single-probemethod of two sieved and repacked soils as a function ofbulk density and water content is shown in Figs 2 and 3.

The sandy loam soil had higher thermal conductivityvalues than the clay loam soil at all bulk densities. Ther-mal conductivity increased with increasing bulk densityfor the two soils as a result of particle contact enhance-ment as porosity is decreased. For the clay loam soil,thermal conductivity did not continue to increase rapidlywith increasing bulk density at various water contents(Fig. 3). There was a rapid increase in the thermal con-ductivity of the clay loam soil with the "rst increment inbulk density. However, further increase in bulk densitycaused only a slight increase in thermal conductivity.Such a phenomenon was absent in the sandy loam soil. Itappears that increase in bulk density of sandy loam soilbeyond 1)37 g cm~3 did improve contact between therelatively larger sand particles than the silt and clay. Ata given bulk density, thermal conductivity increased withincreasing soil water content. It is observed that beyonda certain bulk density, higher values of moisture contentincreased thermal conductivity less rapidly in the case ofclay loam soil, and more rapidly in the case of sandyloam soil. Increasing water content perhaps completedwater "lms around relatively larger sand particles thansilt and clay, and thus increased the contact area betweensand particles that caused the thermal conductivity toincrease rapidly.

4.2. Dual-probe method

Figure 4 is an example of plots of measured temper-ature as a function of time at a sensor probe located

Fig. 2. Thermal conductivity as a function of soil density for sandy loam at four moisture contents: , 7)2%; , 9)7%; , 12)6%;, 17)1%

THERMAL CONDUCTIVITY OF SOILS 213

7)5 mm from the heater obtained using an 8 s heat pulse.These data show a rapid increase in the temperature atthe sensor probe to a maximum, and then a slow decreaseback toward the original temperature value.

Thermal conductivity measured using dual-probemethod of the same two sieved and repacked soils asa function of bulk density and water content is shown inFigs 5 and 6. Again, the sandy loam soil had higherthermal conductivity values than the clay loam soil at all

Fig. 3. Thermal conductivity as a function of soil density for clay, 18

bulk densities. As for thermal conductivity measured forthe clay loam soil using the single-probe method, thermalconductivity measured using the dual-probe method didnot continue to increase rapidly with increasing bulkdensity at various water contents (Fig. 6 ). There wasa rapid increase in the thermal conductivity of the clayloam soil with the "rst increment in bulk density. How-ever, further increase in bulk density caused only a slightincrease in thermal conductivity. At a given bulk density,

loam at three diwerent moisture contents: , 10)1%; , 14)7%;)2%

Fig. 4. Measured temperature as a function of time at a sensor probe located 7)5-mm from the heater for sandy loam soil at a moisturecontent 7)2% and soil density of 1)25 g cm!3 (dual probe method); *Tm, the maximum temperature change at a distance from the heater

in K; tm, time at which maximum temperature change occurs in s

214 N. H. ABU-HAMDEH

thermal conductivity increased with increasing soil watercontent. Similar to the phenomena noticed in the resultsobtained using the single probe method, it is observedthat beyond a certain bulk density, higher values ofmoisture content increased thermal conductivity less rap-idly in the case of clay loam soil, and more rapidly in thecase of sandy loam soil.

Statistical analysis was performed on the data for eachsoil type using the statistical analysis software MINITAB(1994). The analysis was performed at a 5% level of

Fig. 5. Thermal conductivity as a function of soil density for sa, 7)2%; , 9)7%;

signi"cance where the null hypothesis was that the con-ductivity values at certain moisture content and bulkdensity for each soil type have the same mean. Compari-sons of the average conductivity values obtained usingthe single and dual-probe methods at di!erent moisturecontents and bulk densities are shown in Table 1 forsandy loam and in Table 2 for clay loam. As shown inboth tables, there is a signi"cant di!erence between someof the average values obtained using the single probe andthose obtained using the dual probe for the two soil

ndy loam using the dual probe method at four moisture contents:, 12)6%; , 17)1%

Fig. 6. Thermal conductivity as a function of soil density forclay loam using the dual probe method at three moisture contents:

, 10)1%; , 14)7%; , 18)2%

Table 2Statistical comparison of thermal conductivity values obtained bysingle and dual probe methods for clay loam soil at di4erent soildensities q and moisture contents; means represent three measure-

ments in each determination method

Moisturecontent,

Soildensity,

Thermal conductivity, W m!1 K!1

% g cm!3 Single probe Dual probe

10)1 1)33 0)35! 0)37!

1)39 0)55! 0)58"

1)49 0)62! 0)62!

14)7 1)33 0)40! 0)42!

1)39 0)59! 0)59!

1)49 0)65! 0)69"

18)2 1)33 0)51! 0)51!

1)39 0)61! 0)61!

1)49 0)69! 0)70!

Note. Means in columns, within the same bulk density andmoisture content, followed by the same letter were not signi"-cantly di!erent at a 5% level.

THERMAL CONDUCTIVITY OF SOILS 215

types. In general, the thermal conductivities determinedusing the single-probe method were slightly lower thanthose determined using the dual-probe method for bothsoils. One possible reason is that the density of the soilnear the probe was not as uniform as intended. Thesesmall scale variations in soil density near the probes mayyield di!erences in thermal conductivity for the two

Table 1Statistical comparison of thermal conductivity values obtained bysingle and dual probe methods for sandy loam soil at di4erent soildensities q and moisture contents; means represent three

measurements in each determination method

Moisturecontent,

Soildensity,

Thermal conductivity, W m!1 K!1

% g cm!3 Single probe Dual probe

7)2 1)25 0)19! 0)21!

1)36 0)51! 0)54"

1)43 0)79! 0)84"

9)7 1)25 0)20! 0)20!

1)36 0)55! 0)57!

1)43 0)89! 0)94"

12)6 1)25 0)22! 0)23!

1)36 0)69! 0)70!

1)43 0)98! 0)99!

17)1 1)25 0)30! 0)33"

1)36 0)81! 0)83!

1)43 1)13! 1)15!

Note: Means in columns, within the same bulk density andmoisture content, followed by the same letter were not signi"-cantly di!erent at a 5% level.

probes. Another possible error in determination of ther-mal conductivity may arise from poor contact betweenthe probe and surrounding soil. Poor probe/soil contact,possibly due to wobbling during probe insertion, mayresult in an air gap around the probe. This air gapdecreases the conductance of the soil adjacent to theprobe which produces errors in temperature readingsand leads to errors in the determination of j, so care isneeded when inserting the probe into the soil. Also, thecomplicating factors arising from water movement inresponse to temperature gradients caused by heating isanother source of error in the determination of j. Lowpower inputs were used since lower power inputs arepreferable to minimize the e!ects of heating on soil watermovement and hence thermal conductivity.

Clay loam soil had a lower thermal conductivity mea-sured using both methods than sandy loam soil at allwater contents and bulk densities studied. Thermal con-ductivity values reported here lie well within the range of0)16}0)71 Wm~1K~1 for clay loam soil as given byGhuman and Lal (1985). Some values obtained for ther-mal conductivity are higher than the 0)59 Wm~1K~1

obtained by Ghuman and Lal (1985) at a 10% moisturecontent and the 0)64 W m~1K~1 obtained by Van Wijk(1963) for sandy loam soil. The di!erences in mineralogyand sand, silt, and clay fractions in their sandy loam soilmay account for this variation. In the present study,higher values of thermal conductivity were obtained forthe sandy loam soil than for the clay loam soil. Thedecrease of e!ective thermal conductivity with decreasein grain size may be explained by the fact that as the grainsize decreases, more particles are necessary for the same

216 N. H. ABU-HAMDEH

porosity, which means more thermal resistance betweenparticles (Tavman, 1996). This suggests that clay loamsoils with low thermal conductivities would exhibit largersurface temperature changes, compared with sandy loamunder equal heat #ux densities. This could in#uence thesuccessful raising of temperature-sensitive crops on theclayey soils in the "eld.

5. Conclusions

Thermal conductivities for sandy loam and clay loamsoils at di!erent bulk densities and moisture contentswere measured and compared using single-probe anddual-probe methods. The results show that thermal con-ductivity varies with soil texture, water content, and bulkdensity. For the two soils studied, an increase in bulkdensity at a given moisture content increased thermalconductivity, and increasing moisture content at a givenbulk density increased thermal conductivity. Clay loamsoils exhibit a slight increase in thermal conductivitybeyond a certain bulk density. Clay loam soil generallyhad lower thermal conductivity than sandy loam soil. Ingeneral, the dual-probe method yielded thermal conduc-tivities that were slightly higher than those obtainedusing the single-probe method. Since other soil thermalproperties can be obtained from a single heat-pulsemeasurement, additional studies are needed to testthe dual-probe method for a range of soils at di!erentconditions.

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