Thermal Conductivity Coefficient

8/12/2019 Thermal Conductivity Coefficient

1/23

1

PARTEA A II A PART II

Lucrarea nr. II.1 Work no. II.1

COEFICIENTUL DE

CONDUCTIVITATE TERMIC

1. Principiul lucr rii

Coeficientul de conductivitatetermic este o constant fizic a materi-alelor, care caracterizeaz proprietateaacestora de a conduce fluxul termic. Eldepinde de temperatura, natura, starea deagregare, forma sub care se gsetematerialul i se determin pe caleexperimental.

n ipoteza plcilor plane, cusuprafeele izoterme paralele i atransferului termic staionar, fluxul termicunitar transmis pe direcia normal lasuprafeele izoterme se determin cuecuaia lui Fourier:

THERMAL CONDUCTIVITY

COEFFICIENT

1. The principle of the work

The coefficient of thermalconductivity is a physical constant ofmaterials, which characterizes theirproperty to conduct the heat flux. Itdepends on temperature, the nature,phase, and form in which the material isin, and it can be determinedexperimentally.

In the hypothesis of plane plates,with parallel isothermal surfaces and of asteady-state heat transfer, the heat fluxdensity in normal direction to the isother-mal surfaces is determined using Fouriersequation:

= 2mWt q ; (1)

n care este coeficientul deconductivitate termic, - grosimeaplcii, t - diferena de temperatur ntresuprafeele plcii.

in which is the coefficient of thermalconductivity, - the board thickness, t - the temperature difference between theplates surfaces.


2/23

2

Prin urmare, coeficientul de conduc-tivitate termic este numeric egal cufluxul termic conductiv staionar, caretraverseaz unitatea de suprafa a unei

plci de grosime unitar, cnd diferena detemperatur ntre suprafeele exterioareeste egal cu unitatea. Deci:

Accordingly, the coefficient ofthermal conductivity is numerically equalto the steady-state conductive heat flux,which crosses the unit surface of a plate

with unit thickness, when the temperaturedifference between external surfaces isunity. Therefore:

=

mKW

t q . (2)

Determinarea acestui coeficientpresupune msurarea experimental amrimilorq , i t .

2. Schema instala iei i

modul de lucru

Schema de principiu a instalaiei de

determinare a coeficientului deconductivitate termic n domeniulvalorilor ( )mKW977,1...029,0= , al

materialelor izolatoare plane, omogene,microporoase, fibroase sau sub form departicule, numit Dr. Bock, esteprezentat n figura 1.

Determinarea coeficientului de con-ductivitate termic se bazeaz pe metodaplcii nc lzitoare cu un singur corp deprob .

The determination of this coefficientsupposes the experimental measurementof the quantitiesq , and t .

2. Scheme of experimental

installation and test procedure

The principled schematic of the

installation for the determination of thethermal conductivity coefficient in thevalues range ( )mKW977.1...029.0= ,

of plane, homogeneous, micro-porous,fibrous, or in-form-of particles heat-insulating materials, called Dr. Bock, isshown on Fig. 1.

The determination of the coefficientof thermal conductivity is based on the

method of the heating plate with a

single sampling body .


3/23

3

Fig. 1 . Schema de principiu ainstalaiei pentru determinarea

coeficientului de conductivitate termic

Fig. 1 . The principled schematic ofthe installation for the determination of

the thermal conductivity coefficient

Proba de material (1) se aeaz ntredou plci metalice plane, cea superioar (2) cu o temperatur mai mare - constant,ca urmare a unui aport de energieelectric, denumit nclzitoare, iar ceainferioar (3) cu o temperatur mai

sczut - constant, ca urmare a uneicedri de cldur, denumit rece. Placa nclzitoare este nconjurat de o plac cuaceeai temperatur, denumit plac deprotecie (4), eliminndu-se n acest mod

The sample (1) is placed betweentwo plane metallic plates, the superior (2)with a higher temperature - that isconstant, as a result of an addition ofelectric power - called heating plate, andthe inferior (3) with a lower temperature -

that is constant too, as a result of a heatrejection, called cold plate. The heatingplate is enveloped by a plate with thesame temperature, called protective plate(4); in this way the heat losses from the


4/23

4

pierderile de cldur de la placa nclzitoare i astfel, n condiiicvasistaionare, puterea electric furnizat plcii nclzitoare este proporional cu

fluxul termic care strbate proba dematerial.

Meninerea constant a temperaturiiplcii de protecie i a plcii reci serealizeaz prin conectarea lor la circuitulde nclzirei rcire al termostatelor (9)i(10) prevzute cu termoregulatoarele (9a)

i (10a). Apa de rcire, care circul prinserpentina termostatelor, pe al crei traseuse afl termometrul (15)i rotametrul(17), reduce ineria termic a apei determostatare n termostatul plcii caldeipreia cldura cedat ctre placa receirespectiv ctre termostatul aferent ei.

Utilizarea apei de termostatare, caagent termic, antrenat de pompe decirculaie, permite stabilirea cderii detemperatur n prob. Cu ajutorulperechilor de termometre (6)i (7) sepoate determina valoarea medie atemperaturii agentului termic din plcilemetalice i apoi calcula cderea detemperatur n prob.

Fluxul termic, care strbate proba dematerial de la suprafaa superioar la ceainferioar este datorat plcii nclzitoare,semi-ngropat n placa superioar de

heating plate being eliminated and thus,for quasi-stationary conditions, theelectric power supplied to the heatingplate is proportional to the heat flux that

crosses the sampling material.To keep the temperatures of the

protective plate and cold plate at constantvalues, they are connected to the heatingand cooling ciruit of thermostats (9) and(10) that are equiped with thermo-regulators (9a) and (10a). The cooling

water that flows through the coil of thethermostats and on whose route are placedthermometer (15) and rotameter (17),diminishes the thermal inertia of the waterfrom the hot plate thermostat and absorbsthe heat transferred to the cold plate andto its afferent thermostat, respectively.

The utilization of the thermostat wa-ter that is put in motion by circulationpumps, as thermal agent, allows to set-tling the temperature drop within thesample. By aid of the pairs of thermo-meters (6) and (7), the average value ofthe temperature of the thermal agent fromthe metallic plates can be determined andthen calculated the temperature drop inthe sampling material.

The heat flux that crosses the sam-pling material from the superior surface tothe inferior one is the result of the heating


5/23

5

protecie, care este prevzut cu orezisten electric, n circuitul creia esteintercalat reostatul cu dousprezecepoziii (14). Meninerea constant a

temperaturii plcii superioare calde petoat suprafaa de contact cu proba dematerial este realizat de termocuplul (5),care este conectat la milivoltmetrul (12).Dac temperatura plcii nclzitoare estemai mare dect a plcii de protecie,atunci acul indicator al milivoltmetrului

este deviat n stnga reperului zero, iarcircuitul rezistenei plcii nclzitoare se ntrerupe. Atunci, aceast rezisten nceteaz s mai furnizeze energieelectric. Cnd temperatura plcii nclzitoare scade sub temperatura plciide protecie, ca urmare a continuitii

transmiterii fluxului termic probei dematerial, atunci acul milivoltmetrului estedeviat n dreapta reperului zero,ref cndu-se circuitul rezistenei plcii nclzitoare i astfel se asigur reluareaprocesului de transfer termic prin probade material.

Consumul de energie electric furnizat plcii nclzitoare este nregistrat de un contor electric (13)amplasat n circuitul aceleiai rezistene.n circuitul de alimentare de la reea esteamplasat transformatorul variabil cuapte

plate, which is half-buried in the superiorprotection plate and equipped with anelectric resistance, on whose circuit isinserted rheostat (14) with twelve settings.

The maintaining of the superior hot plateat a constant temperature throughout thecontact surface with the sampling materialis attained by thermocouple (5) that isconnected to milivoltmeter (12). If thetemperature of the heating plate is higherthan that of the protecting plate, then the

pointer of the milivoltmeter is deflectedon the left side of mark zero, and thecircuit of the resistance from the heatingplate is interrupted. Then, this resistancestops the supply with electric energy.When the temperature of the heating platedrops below the temperature of the

heating plate, due to the continuity in theheat transfer to the sampling material,then the pointer of the milivolmeter isdeflected on the right side of mark zeroand the circuit of the resistance of theheating plate is restored. In this way thereiteration of the heat transfer processthrough the sampling material is assured.

The consumption of electric energythat is supplied to the heating plate isregistered by an electric counter (13)located in the circuit of the sameresistance. On the feed circuit of the


6/23

6

poziii (11).

Plcile metalice sunt nconjurate ntimpul msurtorilor de o cutie

protectoare, care are rolul de a reducepierderile de cldur n exterior.

Cu ajutorul a patru micrometre (8)fixate pe placa superioar se msoar grosimea probei de material.

n continuare se prezint modul de

lucru.

Preg tirea probelor de material

Probele din materiale de construcie,izolatoare sau plastice se confecioneaz sub form de plci ptrate sau circulare,cu suprafee plane i paralele, avnd

lungimea laturii sau diametrul cuprinse ntre 200 mmi 250 mm sau sub form dematerial mrunit omogen, cu porozitateredus i fibros (praf, granule, fibre). nacest caz, materialul se aeaz pe placainferioar rece, n interiorul unei rame cuconductivitate termic redus i cudimensiunile identice cu cele ale probeicompacte, dar cu o nlime puin maimic dect grosimea stratului de material.

Grosimea probelor este cuprins ntre 3i 70 mmi se stabilete n funciede valoarea estimat a coeficientului de

electric network is placed the variabletransformer with seven positions (11).

The metallic plates are surroundedduring the experimental measurements by

a protecting box, with the purpose toreduce the heat losses to the outside.

The thickness of the samplingmaterial is measured by aid of fourmicrometers (8) fixed on the superiorplate.

Next, the working routine will be

described.

Preparation of the sampling materials

The insulating or plasticconstruction sampling materials aremanufactured in form of quadratic orcircular plates, with plane and parallel

surfaces, having the length of one side orthe diameter comprised between 200 and250 mm, or in form of a homogeneouschopped material, with reduced porosity,and fibrous (dust, granules, fibers). In thiscase, the material is set on the coldinferior plate, inside of a frame with lowthermal conductivity and with the samedimensions as those of the compactsample, but with a height less than thethickness of the material layer.

The thickness of the samples iscomprised between 3 and 70 mm and is


7/23

7

conductivitate termic pentru acelmaterial cu ajutorul diagramei din figura2. Dac probele de material sunthigroscopice, avnd n vedere c valoarea

coeficientului de conductivitate termic depinde de coninutul de umiditate, sedetermin umiditatea medie a probei nstare umed ca medie aritmetic avalorilor obinute prin cntrirea probei nainte i la sfritul experimentului.Masa probei n stare anhidr se obine

prin cntrire.

settled as function of the estimated valueof the thermal conductivity coefficient forthat kind of material by use of thediagram shown on Fig. 2. In the case the

samples are hygroscopic, and taking intoaccount that the value of the thermalconductivity coefficient depends on themoisture content, the average moisturecontent of the moist sample is determinedas the arithmetic mean of the valuesobtained through weighing of the sample

before and at the end of the experiment.The mass of the sample in the anhydrousstate is obtained through weighing.

0 10 20 30 40 50 60 70 80

Grosimea probei [mm]

0

2

4

6

8

10

12

0 . 0 2 5

0 . 0 5

0 . 1

0 . 2

0 .4

0 .6 0 .8 1 .0

1 . 5

1 .7 [ k c a l / m h g r d ]

0 10 20 30 40 50 60 70 80

Grosimea probei [mm]

0

2

4

6

8

10

12

0 . 0 2 5

0 . 0 5

0 . 1

0 . 2

0 .4

0 .6 0 .8 1 .0

1 . 5

1 .7 [ k c a l / m h g r d ]

Fig. 2 . Diagrama de determinare agrosimii probelor de materiali a trepteide putere corespunztoare rezisteneiplcii de nclzire

Fig. 2 . The diagram for the deter-mination of the sampling materials thick-ness and of the power stage correspondingto the resistance of the heating plate


8/23

8

Fig. 3 . Vedere de ansamblu ainstalaiei de determinare a coeficientului

de conductivitate termic

Fig. 3 . The ensemble view of theinstallation for the determination of the

thermal conductivity coefficient

Starea aerului din ncperea n carese fac determinrile experimentale trebuies fie normal (temperatura de 1825oC

i umiditatea relativ de 5565%).

The state of the air inside the roomwhere the experimental determinationsare performed must be normal (thetemperature of 1825oC and the relative

humidity of 5565%).

Aezarea probei de material n instala ie

Se ndeprteaz cutia de protecie(1) (fig. 3), termoizolant, se ridic placasuperioar i se aeaz proba de materialpeste placa inferioar. Pentru o aderen ct mai bun se execut cteva micrilaterale. Se deurubeaz micrometreleplcii superioare de protecie, astfel nctele s nu vin pentru nceput n contact cu

The setting of the sampling material in

the installation

The protecting thermo-insulating box(1), (Fig. 3), is removed, the upper plate israised and the sampling material is set onthe lower plate. For a better adherence,several lateral movements are performed.The micrometers of the upper protectingplate are unscrewed, so that they shall not


9/23

9

contrauruburile fixate pe placainferioar. Apoi se aeaz placasuperioar peste proba de material, se nurubeaz micrometrele pn la o

atingere uoar de contrauruburi i semsoar grosimea probei cu ajutorul celorpatru micrometre, cu o precizie de 1/100mm. Pentru probe cu grosimi mai mari de25 mm se vor monta la cele patrucontrauruburi prelungitoare de 25 sau 50mm, lungimi care se vor aduga la

valorile indicate de micrometre. n finalse reaeaz capacul de protecie.

Punerea n func iune a instala iei

Se regleaz temperaturatermometrelor cu contact electric ale

termostatelor aflate n dulapul (3) cuajutorul unei chei magnetice la valoareade lucru a plcilor de rcirei nclzire.

Pn la realizarea temperaturilorimpuse fluidului de termostatare, ventilul(8) rmne nchis. Dup aceea doar, seregleaz debitul apei de rcire n celedou termostate prin manevrareaventilelor (8)i (9), astfel nct timpul de nclzire a lichidului din termostat s fieaproximativ egal cu timpul de rcire.

Durata acestor intervale de timp esteegal cu durata de aprindere, respectiv

come for the beginning in contact with thecounterscrews fixed on the lower plate.Then, the upper plate is put over thesampling material, the micrometers are

screwed until they reach slightly thecounterscrews and the thickness of thesample is measured with the four micro-meters, with a precision of 1/100 mm. Forsamples with higher thicknesses than 25mm, prolonging tools of 25 or 50 mm willbe fixed on the four counterscrews. These

lengths will be added to the valuesindicated by the micrometers. Finally, theprotecting cover will be relocated.

The starting of the installation

The temperature indicated by thethermometers with electric contact of the

thermostats that are placed in the closet(3) is adjusted by use of a magnetic key tothe operating value of the cooling andheating plates.

Until the temperature reaches the va-lues imposed to the thermostat fluid, thefaucet (8) is closed. Only afterwards, theflow rate of the cooling water from thetwo thermostats is adjusted through thefaucets (8) and (9), so that the heatingtime of the thermostat liquid shall beapproximately equal to the cooling time.

The duration of these time intervals


10/23

10

stingere a becurilor de control (10)i (11)de pe tabloul de comand (12). Becul decontrol (13) indic alimentarea cuenergie electric a rezistenei plcii

nclzitoare atunci cnd este aprinsi ntreruperea alimentrii ei, atunci cndeste stins.

n acest sens se stabilete treapta deputere pe diagrama din figura 2 n funciede grosimea mediei conductivitateatermic estimat a probei. Punctul de

intersecie al verticalei corespunztoaregrosimii medii a probei cu curbaconductivitii termice estimate se va afla n cmpul treptei de nclzire cutate.Cnd acest punct se afl la limita dintredou trepte, se alege iniial treapta deputere superioar. Verificarea alegerii

treptei de putere corecte se poate urmripe tabloul de comand. Astfel, timpul cteste aprins becul de control corespunztorplcii nclzitoare trebuie s fieaproximativ egal cu timpul ct este stins.

Durata minim de pornire ainstalaiei se recomand a fi de o or.

is equal to the lighting and turn-off dura-tions of the control bulbs (10) and (11)from the switchboard (12). The controlbulb (13) shows the electric energy supply

of the resistance from the heating platewhen it is lightened and the interrupting ofthe supply when it is dark.

Therefore, the power stage will beestablished on the diagram presented onFig. 2 as a function of the average thick-ness and the estimated thermal conducti-

vity of the sample. The intersection pointof the vertical corresponding to the ave-rage thickness of the sample with thecurve of the estimated thermal conduc-tivity will be placed in the field of thesearched heating stage. When this point isat the limit between two stages, the higher

heating stage will be chosen initially. Thechecking of the selection of the correctpower stage can be followed on theswitchboard. Thus, the time when thecontrol bulb corresponding to the heatingplate is turned on must be approximatelyequal to the time when it is turned off.

The minimum starting duration ofthe installation is recommended to be onehour.


11/23

11

Efectuarea m sur torilor

Dup intrarea instalaiei n regimstaionar de funcionare se facurmtoarele determinri, din 0,5 n 0,5

ore, care se nscriu n tabelul 2: ora i minutele indicate de ceasul (14); indicaia contorului de energieelectric (15);

temperatura agentului termic citit latermometrele (16)i (17) amplasate laintrare i la ieire din placa superioar

(t ci, t ce), respectiv la termometrele (18)i(19) ale plcii inferioare (t ri, t re);

temperatura ncperii; temperatura apei de rcire latermometrul (20);

Temperaturile se msoar cuajutorul unui sistem optic, compus dintr-o

lentil convergent (lup) i oglind, cu oprecizie minim de 2/100oC.

Raportul diferenei dintre dou citiriconsecutive ale energiei electrice lacontor, iE i al diferenei de timp

corespunztoare, i se consider

constant dac nu depete 2,5% din

valoarea medie a cel puin cinci citiri. nacest caz, determinarea experimental este ncheiat.

Instalaia se oprete prin manevrarea ntreruptorului principal (5). Se aduc n

The performing of the measurement

When the installation works instationary conditions the followingmeasurements will be performed every 0.5

hours that will be inscribed in Table 2: the hour and minutes indicated byclock (14);

the indication of the electric energycounter (15);

the temperature of the thermal agentread at thermometers (16) and (17) placed

at the entrance and exit from the superiorplate (t ci, t ce), and at thermometers (18)and (19) of the inferior plate (t ri, t re),respectively;

the room temperature; the temperature of the cooling water atthermometer (20);

The temperatures are measured withan optical system, made of a convergentlens (magnifying glass) and a mirror, witha minimum accuracy of 2/100oC.

The ratio of the difference betweentwo consecutive readings of the electricenergy on the counter, iE and of the

corresponding time interval, i isconsidered to be constant if it doesntexceed 2.5% of the mean value of at leastfive readings, the experimental determi-nation being finished.


12/23

12

poziia iniial butonul transformatorului(7) i butonul reostatului (4). Se ntrerupecirculaia apei de rcire a termostatelorprin nchiderea robinetului (8).

Se ndeprteaz din nou cutia deprotecie i se msoar grosimea probei lasfritul experimentului cu ajutorul celorpatru micrometre. Valorile se nscriu ntabelul 1.

Se nltur proba de material dininstalaie prin intermediul brauluipivotant (2) i se msoar apoi princntrire din nou masa acesteia.

Plcile metalice se suprapun apoi,iar indicaiile micrometrelor pn la

oprirea lor n contrauruburile fixate peplaca inferioar reprezint erorile deplaneitate. n calcule se impun coreciileacestor erori.

La sfrit se aeaz pe instalaiecutia termoizolant.

Mrimile msurate se nscriu ntabelele 1i 2.

The installation is turned off bypushing the main switch (5). There arebrought in initial position the button oftransformer (7) and the button of rheostat

(4). The circulation of the cooling waterfrom the thermostats is interrupted byturning off the tap (8).

The protecting cover is taken offagain and the thickness of the sample ismeasured at the end of the experiment byuse of the four micrometers. The values

are marked in Table 1.The sampling material is taken out

by use of the revolving support (2) and itsmass is determined again throughweighing.

The metallic plates will be thenoverlapped, and the indications of the

micrometers when they are stopped by thecounterscrews, which are fixed on theinferior plate, represent the errors ofplanarity. In calculations, corrections ofthese errors are required.

Finally, on the installation thethermo-insulating box is set.

The measured quantities are markedin Tables 1 and 2.


13/23

13

Valoarea obinut la citireaThe value obtained at readingMrimi msurate

The measured quantities SimbolSymbol

Unitatea demsur The unit ofmeasurement 1 2 3 4 5 6

Timpul

Time

ore

hoursTemperatura apei dercireThe temperature of thecooling water

wt oC

Tab . 1. Grosimea probei de material Tab . 1. The thickness of thesampling material

Grosimea probeide material la nceputul i sfr-itul msurrilor/The thickness ofthe sampling ma-terial at the be-ginning and at theend of the mea-

surements

UnitateUnit

Valori msurate

Measured values

Erori

Errors

Valori corectate

Corrected values

i1 f 1 mm 1k +0,04mm

i2 f 2 mm 2k +0,24 mm

i3 f 3 mm 3k +0,04 mm

i4 f 4 mm 4k +0,05 mm

Tab . 2. Mrimi msurate Tab . 2. The measured quantities


14/23


15/23

15

Temperatura apei laieire din placainferioar The temperature of

water at the exit fromthe inferior plate

ret oC

Treapta de putereThe power stage

- -

3. Prelucrarea datelor experimentale

Determinarea grosimii medii corectate a

probei de material:

3. Experimental data processing

The determination of the corrected

average thickness of the sampling

material:

( )

[ ]m2

44iif iii k k +

= , (3)

n care valorile se preiau din tabelul 1.Este necesar exprimarea rezultatului nunitatea fundamental pentru lungime nSI.

Determinarea fluxului termic unitar:

where, the values are taken from Table 1.It is necessary to express the result in thefundamental unit for length in SI.

The determination of the heat flux

density:

=

= 2mWk E k E q i

i , (4)

unde iE E = reprezint consumul

total de energie electric exprimat nkWh, nregistrat de contor n intervalul de

where iE E = is the total

consumption of electric energy expressedin kWh, which is registered by the counter


16/23

16

timp [h] n care instalaia a lucrat nregim staionar i egal cu sumaconsumurilor de energie electric iE ,

rezultate din minimum cinci citiriconsecutive la intervale egale de timp

h5,0= i , i= - intervalele de

timp corespunztoare lui E , respectiv

iE , exprimate n ore;k - o constant a

treptei de putere, care depinde att deraportul dintre puterea electric consumat de placa de nclzire (decitransformat n flux termic util)i putereaelectric total preluat de la reostat(energia electric corespunztoare ei fiindmsurat cu ajutorul contorului electric),ct i de aria suprafeei plcii de nclzire.

n tabelul 3 sunt nscrise valorileconstantei k pentru cele dousprezece

trepte de putere, respectiv constantar a,care reprezint rezistena termic a celuleide msurare.

in the time interval [h], during whichthe installation has worked in stationaryconditions, and that is equal with the sumof electric energy consumptions iE ,

resulted from minimum five consecutivereadings at equal time intervals

h5.0= i ; i= - the time

intervals corresponding toE and iE

respectively, expressed in hours;k - aconstant corresponding to the power stage,which depends both on the ratio betweenthe electric power consumed by theheating plate (and thus transformed inuseful heat flux) and the total electricpower taken from the rheostat (itscorresponding electric energy beingmeasured by the electric counter), and onthe area of the heating plate surface.

In Table 3 are written the values ofconstant k for the twelve power stages,and constant r a, respectively, whichrepresents the thermal resistance of themeasuring cell.


17/23


18/23

18

unde rericeci t t t t ,,, reprezint tempera-

turile la intrare, respectiv la ieirea apeidin placa superioar i cea inferioar, n -numrul de citiri, tretritcetci k k k k ,,, -

coreciile de temperatur pentru celepatru termometre ale instalaiei, cuprinse n tabelul 4.

where, rericeci t t t t ,,, are the temperatures at

the entrance and at the exit of the waterfrom the superior plate and the inferiorone, respectively,n number of readings,

tretritcetci k k k k ,,, - the temperature

corrections for the four thermometers ofthe installation, included in Table 4.

Tab. 4. Coreciile de temperatur Tab. 4. The temperature corrections

Coeficieni de corecie [ ]C

Correction coefficients[ ]C TemperaturaTemperature

[ ]C tcik tcek trik trek

20 + 0,05 + 0,08 + 0,07 + 0,11

25 - 0,02 + 0,05 + 0,09 + 0,0830 + 0,07 + 0,06 + 0,05 + 0,0835 + 0,01 + 0,05 + 0,02 + 0,02

ntruct coeficientul de conducti-vitate termic depinde de temperaturaprobei, valoarea ei medie se determin curelaia:

Because the coefficient of thermalconductivity depends on the temperatureof the sample, its average value will bedetermined with relation:

[ ]C2

+

= mr mcmt t t . (8)

Determinarea coeficientului de

conductivitate termic se efectueaz curelaia:

The determination of the coefficient

of thermal conductivity is accomplishedwith relation:

=

mKW

ar qt q , (9)

n care:q reprezint fluxul termic unitar; where: q is the heat flux per unit area; -


19/23

19

-grosimea medie corectat a probei de

material; t - cderea de temperatur nproba de material, ar - constant a

aparatului careine seama de rezistenatermic la trecerea fluxului termic ntrefluidele de termostatarei suprafaa decontact a probei de material.

Mrimile calculate se centralizeaz n tabelul 5.

the corrected average thickness of the

sampling material, t - the temperaturedrop in the sampling material,ar - the

constant of the apparatus, which takesaccount of the thermal resistance of theheat flux transfer between the thermostatfluids and the contact surface of thesampling material.

The calculated quantities will becentralized in Table 5.

Tab . 5. Mrimi calculate Tab . 5. The calculated quantities

Mrimi calculateCalculated quantities

SimbolSymbol

Unitateademsur Unit ofmeasure

ValoareValue

Grosimea medie calculat a probei de material

The calculated average thickness of the samplingmaterial

m

Consumul total de energie electric The total electric energy consumption

iE E = kWh

Intervalul total de timpThe total time interval

i= hours

Fluxul termic consumat

The consumed heat flux

E kW

Fluxul termic unitarThe heat flux per unit surface

q 2mW

Numrul de citiriThe number of readings

n -


20/23

20

Temperatura medie corectat a plcii superioareThe corrected average temperature of thesuperior plate

mct Co

Temperatura medie corectat a plcii inferioare

The corrected average temperature of the inferiorplate

mr t Co

Cderea de temperatur n proba de materialThe temperature drop in the sampling material

t Co

Temperatura medie a probei de materialThe average temperature of the sampling material

mt Co

mK

W Coeficientul de conductivitate termic al probei

de materialThe coefficient of thermal conductivity of thesampling material

mhgrdkcal

4. Calculul erorilor i

interpretarea rezultatelor

Prin logaritmarea ecuaiilor (2)i (4)i apoi prin difereniere, se obin relaiile:

4. The errors calculation and

the results analysis

Through the logarithmation ofequations (2) and (4) and then throughdifferentiation, the following relations willbe obtained:

( )t t

qq

+=

dddd ; (10)

( ) ( )i

i

i

i

i

ik k

E E

qq

+

= dddd ; (11)

A A

k k i

i dd = . (12)


21/23


22/23


23/23

Tab . 5. Conductivitatea termic pentru lemn

Tab . 5. Thermal conductivitycoefficient for wood

Coeficientul de conductivitate termic Thermal conductivity coefficient

[W/mK]

Specie delemnWoodspecies

DensitateDensity

[kg/m3]

UmiditateMoisturecontent

[%] longitudinal radial tangentialMolidSpruce 410 16 0,2219 0,1227 0,1047BradFir 450 - 0,279 0,107

FrasinAsh 740 15 0,306 0,1758 0,1633Nuc

Walnut 650 12 0,3285 0,1465 0,1382Stejar

Oak650 10 0,244-0,3489 0,1593-0,1803

6. Bibliografie 6. References

1. Badea A. Necula H., Stan M., Ionescu L., Blaga P., Darie G.Echipamente iinstala ii termice. Editura Tehnic, Bucureti, 2003.

2. Kreith F. Handbook of thermal engineering, CRC, Boca Raton, Florida, 2000.

4. Bcanu, G. Termodinamic , transfer de c ldur i mas . Editura DealulMelcilor, Braov, 1998.

5. Pop M.G., Leca A., Prisecaru I., Neaga C., Zidaru G., Muatescu V., IsboiuE.C. ndrumar. Tabele, nomograme i formule termotehnice. Editura Tehnic,Bucureti, 1987.

6. *** Wrmedurchgangsprfer nach Dr. Bock BedienungsanweisungFEUTRON Fabrik Elektro-Physical Gerte Greitz, 1962.

7. *** EN 12667/2001. Determination of thermal resistance by means ofguarded hot plate and heat flow meter methods products of high and mediumresistance.

Cuprins Contents
http://.cuprins%20-%20contents.pdf/http://.cuprins%20-%20contents.pdf/http://.cuprins%20-%20contents.pdf/http://.cuprins%20-%20contents.pdf/

Thermal Conductivity Coefficient

Documents

Transcript of Thermal Conductivity Coefficient