J. Jpn. Soc. Soil Phys.
No. +*+, p. / +* ,**/

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*ῌ**ῌ***Estimating Thermal Di#usivity of Soil Packed in a Cylinder Using
an Analytical Solution
Kosuke NOBORIO*, Ieyasu TOKUMOTO** and Yoshiaki MUKAIDA****, *** Faculty of Agriculture, Iwate University, Morioka *,*ῌ2//*, Japan** United Graduate School, Iwate University, Morioka *,*ῌ2//*, Japan* Present address : School of Agriculture, Meiji University, Kawasaki ,+.ῌ2/1+, Japan
Abstract
Soil thermal properties are critical to many processes.

For example, germination, crop growth,and nitriﬁcation depend on soil temperature, which is determined by thermal properties.

Ther-mal properties are usually measured in situ using specially designed probes that enclose a heatsource.

Here we propose and validate an alternative method for estimating soil thermal

di#usivity, based on changes in temperature at the center of a soil core subjected to changing
thermal boundary conditions. This method formerly required numerical analysis because no
analytical solution was known ; here we present an analytical solution. Estimates of thermaldi#usivity of an Andisol at various moisture levels, obtained using the new method, comparedfavorably to results derived with the conventional probe method, showing that the new method
constitutes a viable alternative.
Key words : Andisol, thermal properties, cylinder method, probe method, analytical solution^+    _Bristow et al., +33.` f*<fp*# qr s _,**-` ,[\]^ (TWX tuvwx+*# =>  _,**/`  e!"# $% &'()*+,-./01

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R{W a <=>?@0s RmW »Fig. + Measuring changes in soil temperature using
a cylinder packed soil method where T is
the soil temperature ({), To the temperatureof a water bath ({), and a the radius of acylinder (m).

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,(Tῌ( T  + (T῎tk
῍ (r , r (r ῏(t῍sW r <=>?@&~$LB RmW t %& RsW

 RCarslaw and Jaeger, +3/3W  T <=>?@C4# TtTo R{W \ ῍ 0  #(D RCarslaw and Jaeger, +3/3, p. +33W
Trt;

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TTikt῎ J*RrbnῌaW
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῕ῌ+Carslaw and Jaeger +3/3 'a ,. tVuvwxW?XY Tr 5 ktῌa , '_`y! k z{` m,ῌs t|}f~ s a OPQR m!"#yTable +Relationships, read from Fig. ,.
of Carslaw and Jaeger (+3/3), between relative temperature, Tr,and kt/a, where k is the thermal
di#usivity (m,/s), t the elapsed
time (s), and a the radius of acylinder (m).

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temperature and t/a, values measured in a cylinder. The slope of a regression line with a zero intercept value is k, thermal di#usivity.

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\!T'' *tuvw!
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1 ln ;t< l ῍ p ln ;t*< ῎/ k 16\11.ῌ ῍ ῐ ῏ ῎῎- ]1^&J* +_,῍ WXPQ k 61  1 W`

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452N¹6N ºFig. -Errors, from a pseudo-true value, associated with the number of data used forcalculating thermal di#usivity. The pseudo-true value was assumed to be thethermal conductivity calculated with an eight data set as shown in Table +.

rs : klmn8!tu&%vwefghiTxy!z?(^{:ῐῌ.

6789:!;<=>?@A%6789BCDEBCFGHI.JK LMN>?OP ῌ QR=NST4& T-TiU* VLMWXY ln Zt*[ ZP ῍[ \]@A^KFig. .

Temporal changes in probe temperature measured. A line indicates the regression
line of measured data to Eq. -, and ln(t*) indicates a value in Eq. ..

ῐῌ/Fig. /9_`abc q !d(^efghi k >?OK jNklmn8:!;opN6789:!;oqS%OT4(KThermal di#usivity, k, measured against volumetric water content, q. Symbols ῌ and῍ indicate measured data using a cylinder method and a probe method, respectively.

       !"#$%&'()'% *+,-./01234!5#$%&'()῎ ῒ ῑ ῏Bristow, K.L., White, R.D. and Kluitenberg, G. J. (+33.) :Comparison of single and dual probes for meas- ¦ +*+ § ,**/

10uring soil thermal properties with transient

/01234 567 12-ῌVII--. :heating. Aust. J. Soil Res., -, : ..1ῌ.0.

--ῌ-2.

Carslaw, H.S. and Jaeger, J.C. (+3/3) : Conduction ofNoborio, K. and McInnes, K. J. (+33-) : Thermal con-heat in solids. ,nd ed. Oxford University Press,

ductivity of salt-a#ected soils. Soil Sci. Soc. Am.

New York.

J., /1 : -,3ῌ--..

Fontana, A. J., Wacker, B., Campbell, C.S. and Camp-Ren, T., Noborio, K. and Horton, R. (+333) : Measuringbell, G.S. (,**+) : Simultaneous thermal conduc-soil water content, electrical conductivity andtivity, thermal resistivity, and thermal di#usi-thermal properties with a thermo-time domainvity measurement of selected foods and soils.

reﬂectometry probe. Soil Sci. Soc. Am. J., 0- : ./*ῌASAE meeting Paper No. *+ῌ0+*+. St. Joseph, MI.

./1.

Kasubuchi, T. (+311) : Twin transient-state cylindrical-Riha, S. J., McInnes, K. J., Childs, S.W. and Campbell,probe method for the determination of the ther-G.S. (+32*) : A ﬁnite element calculation for de-mal conductivity of soil. Soil Sci., +,. : ,//ῌ,/2termining thermal conductivity. Soil Sci. Soc.

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Am. J., .. : +-,-ῌ+-,/.
Shiozawa, S. and Campbell, G.S. (+33*) : Soil thermal !" ,**/ : #$% TDR &'$()*+,-.

῍conductivity. Remote Sens. Rev., / : -*+ῌ-+*.

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