Thermal conductivity and diffusivity measurements by the transient two linear and parallel probe method

513

Z’hermochinica Acta, 148 (1989) 513-520 Elsevier Science Publishers B.V., Amsterdam-Printed

in The Netherlands

AND DIFFUSIVIJY

THERMAL CONOUCJIVIJY

MEASUREMENTSBY

THE TRANSIENT JWO LINEAR AND PARALLEL PROBE METHOD

P. MORABITO ENEL - Centro

Ricerca

Idraulica

e Strutturale

20162 MILANO (ITALY)

ABSTRACT

A

new

transient

diffusivity probes

measurements

to be

linear

method

inserted

heating

recording

in

while

of the

temperature

and

particularly materials, The

suitable

like concrete, reliability

of

experimental

results

measurements

performed

are

determined

in

conductivity linear

One

a

by Carslaw

applications

probe

second

in few

parallel

is used

temperature

sensor.

probe

and Jaeger

These

and

and

as a By

and applying

(19591, thermal

minutes

with

properties

very

low

make the method

nonhomogeneous,

damp

and porous

rock and soil. the

method

obtained on

as

of this

to the sample.

two

test.

one

rise

developed

applied for

under

other

temperature

diffusivity

gradients

the

thermal

It employs

the material

the line heat source theory, conductivity

simultaneous

is described.

source

the rate

for

the

has

in same

been

verified

some

reference

samples

by other

by

comparing

the

with

the

materials known

and standardized

methods. Some

applications

thermal

properties

thermal

conductivity:

Thermal

Analysis

concern

of concrete

Highlights,

the

effects

of

and correlations

experimental

results

9th ICTA, Jerusalem,

the

moisture

between

are presented

Israel, 21-25 August

dry

content

on

the

sand density

and

and discussed.

1988.

514 INTRODUCTION

Thermal

conductivity rock

concrete, ranging

from

structural

For

example

the

of

the

to

materials

engineering

techniques

like

applications

for

forecasting

structures.

main of

gradient

thermal

damp and

properties

porous

solids,

by conventional

solution

this

extensively

aim

thermal

with

the moisture

so

methods

in the

studied

the

sensors

is

content

the

damp

and

such

changes

arising

The ways

as

to prevent

the run time of the test

sample.

with

during

The

a very

second

solution

high sensitivity

can

so that

adopted.

last years

as in

in

to the material.

to

usually

be overcome

conductivity

as much as possible

applied

is more

that must

the

in reducing

gradient

problems

is applied

the use of temperature

the first To

scheme

thermal

is associated

a thermal

involve

in many

are heterogeneous,

of their

determination

this effect consist and

and soil

one

materials

as

of large

structural

to large errors.

experimental porous

of

are of importance

displacements rock

diffusivity

conservation

the measurement

subjected

far

and soil energy

Concrete, that

and

transient

comparison

with

measurement

steady

state

methods

have

techniques

they

been are

less time-consuming.

THE TRANSIENT

The

THERMAL

most

conductivity

PROBE METHOD

widely

used

is the thermal

transient

Briefly,

from the heating

source

T(r,t)

= - ti

that

measuring

the

thermal

the

by Carslaw

buried

and Jaeger

in an infinite

temperature

rise

T at

(1959) referred

homogeneous a radial

medium. distance

r

is given by

q 4n?. where

developed

linear heat source it states

for

probe method.

It is based on the theory to an infinite

method

Ei is an exponential

r2 Ei (- -_)

(1)

4Dt integral,

q is the power input for unit length of

515 the

heat

source,

diffusivity,

?.

and

D

are

By expanding

the exponential

thermal

expression

in a power

series,

it is possible (1) becomes

-

resistivity

- C

(2)

constant.

shows

of the time

THE THERMAL

integral

r2

C is the Euler's

thermal

and

4D In t + In

4z1

logarithm

conductivity

of r and long time t equation

9 T(t) = -

This

thermal

respectively.

to show that for small values

where

the

that

the

is a straight

of the material

temperature line whose

rise slope

against

the

natural

is proportional

to the

to be tested.

PROBE

Figure

1 shows

the details

of the thermal

probe

that we have

used

as a

can have a diameter

of 1

linear heat source. It is

made

UP

stainless

of

steel sheath which

mm and a length of 70 mm or a diameter it there

of 300 mm. Inside

are a karma resistive wire as heating element arranged for the whole

length

of

middle

height.

the

probe

The electrical alumina

of 4 mm and a length

and

wires

a NTC

thermistor

inside

the

tube. An epoxy resin

as temperature

probe

sensor

are insulated

is used to fill the voids

placed

electrically

inside

by

the tube

at

an

and to

seal its ends. After thermal to

that

the

equilibrium

evaluate

switched

on

and corrected In order a silicon

probe with

a possible

is it,

to have

grease

rise

drift

a good

Fig. 2 shows a typical with

of

thermal

sample

readings the

readings

to the thermal

is used at their

the time in comparison

in the

temperature

thermal

and temperature according

buried

drift

contact

and

for 400

sample.

against

the

coefficient between

allowed

to

come

set are performed

Then

the

time

are carried

previously

probe

to

power

q is out

obtained.

and solid samples,

interface.

graph of the temperature the ideal

rise of the probe

line heat source

response.

against

516

Fig.

1 - Getails

of a

thermal

and material

method,

are ev ident

dimensions

properties

In order to overcome

based on the same theory,

THE TWO LINEAR AND PARALLEL

dT

-

This function Taking

into

show

interval

exp

(1) with

is plotted

in fig. 3.

the maximum

that

evaluated

by the following

probe

to be tested.

of time where

equation

the following

(2) must

more reliable

METHOD

respect

to time we obtain:

(- -_) 4ot

to

between

has been developed.

4n3.t

possible

They depend

r2

-

account

interface

(al and

response.

times.

of the material

this limitation

9 (r,tl =

dt

(b) line heat source

PROBE MEASUREMENT

equation

the ideal

at short and long heating

can mask the right

Differentiating

between

of the probe, on the thermal

and on the thermal

These effects be applied.

real

probe.

Some differences on the finite

2 - Comparison

Fig.

the

value

thermal

expressions:

(31

m and the

conductivity

related and

time tm,

diffusivity

it is can

be

517

Fig. 3 - Plot of dT/dt

Fig.

versus

4 - Example

of a test performed

in a dry sand sample.

time t.

r2 A=

D=-_

q m

4ne

The

experimental

probe,

In

plot

as temperature

well known distance 4

fig.

tm

4 tm

of

equation

sensor,

(3)

inserted

r from the heating

a typical

(4)

test

is

by

into the material

probe

result

obtained

and parallel

carried

out

using

a

second

to be tested

at a

to it.

on a dry

sand

sample

is

capacity

in

presented. The finite

dimensions

of the probe introduce

series with the interface test.

Their

effects

properly

evaluated

approach

reported

give

resistance

arise

to a thermal

and taken

measurement

diffusivity

- low thermal In

order

tested.

The

gradient to

plate method

probe

transient

during

each

and material

to whose test

under

duration

is

by a particular

of thermal

are:

conductivity

(from 400

and diffusivity;

set to 1000

set in dependence

on the

of the sample); applied

verify

relative

with the results

account

of this new method

- short run time of the test thermal

into

between

thermal

in [2].

The main advantages - simultaneous

thermal

a finite

its thermal

obtained

for thermal

to the sample. reliability, conductivity

on the same samples conductivity

some

solid

measurements

materials have

by the standardized

measurements.

have

been

been

compared

hot-guarded

518 The results thermal

reported

conductivity

in fig.

5,

measurements

and the corresponding

measurements

show a quite

good agreement

performed

by the

performed

with the method

hot-guarded

between plate

the

method

proposed

in this

probe method

and the

work.

0

1

2 W

hoc1

3

1

THEiiMAL CONDUCTIVITY HEASUAEHENT BY THE THO-LIhEAR-PARALLEL-PROBE METHOO

Fig. 5 - Comparison

between

hot-guarded

Finally,

a

laboratory shown

and

that

reproducible

kept

of at

tests

performed

a constant

thermal

within

and parallel

plate method.

lot

the

the two linear

on

concrete

temperature

conductivity

and

and

samples, moisture

diffusivity

prepared content,

in have

measurements

are

+ 2-32 i4/.

APPLICATIONS

The main applications the evaluation

of the thermal

and their dependence As an example, performed

of the two linear properties

on some other

of concrete,

parameters

fig. 6 shows the thermal

in different

concretes

against

and parallel

probe method

concern

rock and soil samples

of the materials. conductivity

their moisture

measurements content.

results

519

3.0

0.5 0

12

6

MOISTURE Fig. 6 - Thermal

conductivity

They put in evidence

that

linear way with the moisture have

shown

moisture

the

of concrete.

dependence As

that

the

thermal

conductivity

density

are

content

ranges

applications

with

seems

of concrete.

increases

in a quite

The same experimental to

be

from 0.005 cm*/sec

independent

tests of the

to 0.009 cm*/sec

in

/3/. carried

measurements the

content

conductivity

of concrete.

diffusivity

ts value

reported:

the moisture

thermal

on the type of concrete

regards

conductivity

the

thermal

(% in vol.)

CONTENT

against

24

18

of

results

the sand density.

two

out

in

dry

different

exhibit

the

sand, sands

increase

in fig. against of

the

7 the the

dry

thermal

520

0.20

0.22

0.24 TbiERMAL

Fig. 7 - Thermal

0.29

0.26 COFiGUCTIVITY

conductivity

against

0.30 [W/

h’C1

0.32

0.34

I

the dry bulk density

of sand.

CONCLUSIONS

A

new

diffusivity

transient

method

measurements

for

simultaneous

thermal

conductivity

It is based on the linear

is proposed.

and

heat source

theory. Some applications conductivity

applied

have in

the influence

of the sand and put in evidence

on the thermal They

have shown

properties also

damp

steady-state

shown

and

methods

of the density

the effects

on the thermal

of the water

content

of concrete. that

the

method

solids

porous

is

where

particularly

water

suitable

migration

can

to

be

arise

if

are used.

REFERENCES 1. H.S.

Carslaw

University 2. A.Lanciani 3. P.Morabito. 4. P.Morabito

and

Press,

J.C.

Conduction

of

heat

in

solids.

1959.

and P.Morabito. Proc.

Jaeger.

Internal

report

no 3580,

ENEL OSR-CRIS.

11th ETPC.

and A.Donati,

ENEL - Rassegna

Tecnica

no 6, 1983.

Oxford