681.2:536.083

.. 1, .. 1, .. 2
ї, , . (1); ї,
. .. (2)
.. ..
: ; ; ; .
: . . .

, - ; - , 2/;
- /(3-);
d - , ;
(), () - ;
= /2 - ; - , ; () - , /2; Q() - , , , ;
Q ( , ) - , 1 , /2;
Q (, ) - , , /2;
=( X)2 + (-6)2 -
(X; 6) (; ), ;
, - , ;
- , ;
- , ; , , , , ^, 0 - , ;
S - , 2;
5 - ; (, , ), (, ), (, , ), (, ) - , ; (), 2() - (,{) (2,^2), ;
(, , )- , ; - , ;
V, - ; - , ; - , ;
0, - , ;
X - , /( );
^ - , /( ); - , ;
, - , , ;
- , .
, , , . , , .
. . , . , , , . , , . . , - [4]. .
, (. 1) (. 2) .
(X, 0, ) = () , (1)
X [0; ], 0 [0; ] - ; X [-; ], 0 [-; ] - .
'rZ
. 1
, :

| X (X, 0, ) 0 = | () = Q ()
^
(2)
( (2, >):
/( = = 1, = 0) = 7\();
(3)
/( = 2, = 2, = 0) = 2().
XI , - 0 , , X! . .
, .
, = 0 ( = X, = 9), Q. :
. | 2 | = .
2 | )
(4):
1) ^-0 0
2 Q ( , ) = 2 Q ( , ) - [ 2/(, ) : 2
(4)
4 pr


(5)
2) 1 ( [1; 2]), 1 2 0 :
\ Q (, ) I - I = 1 [ [ / (1, ) - / (, )] + [ [ 2 / (, ) . (6)
11 21 0 2
(5) (6), : X 0 9 0 ; 0 0 2 .
2 z
dz 2,
Qr = Ql + Q1C + Q2C

Qr - dQ(); Qi=1 j[^() - 72 ()]d ;
(7)
0


Q1c - Jjf - Ijr2t(r,)dr dXd0 ;
0 0 v ri r2 J

LRr2
Q2C = 4 ( r. t) "Xq ; = - ±] dx dq ;
r1 0 0 v 12 '
r =V(x-X)1 + (y-0)2. i = 1. 2;

p r ( 1 1 Vr 2
QlC = i|-|i r t ( r. t ) r e y ;
0 0 v ri r2 ' 0
2PRr2 z 2pR ( . .
Q2C = iii ii r2'(r. t)drd edy ; d= ii( 7 - r
4
dedy ;
ri = J xi2 - 2 ex cos y+e2
i = 1. 2.
S. , , (X; 0) [5]:
T(r, 0) = T0 = const,
At ( r. t ) = T ( r. t ) - T0 =
Q
erfc
1
4 plr 2^F
(8)
erfc
24F
= 1 - erf
24K'
: = 10-7 2/, X = 0,1 /(-), 1 = 10-3 , 2 = 3 -10-3 , = 0,991, = 2-10-3 , 1 = 2 = 0,5; = 10-7 2/, X = = 0,1 /(-), 1 = 10-3 , 2 = 3-10-3 , = 0,991, 1 = 2 = 0. . 3. (7) .
,
. 3
1
1
(7) QIC Q'lC . :
LR

0 0
(xi -x)2 +(y -0)2
x1 -X)2 + (yi -0)2 V(x2 -X)2 + (y2 -q)2
r2t( r, t) drd X d 0 =
LR
V( x2 -X)2 +( 2 -0 )2
ii J
00
V( xi-x )
dz
_2
(X > >^
i=i
(9)
X [0;R] ; y [0;L] ;
z m
J r2t(r,t)drdXd0 ї ^Vjt(Xj ,yy-,t),
2 +( yi -0 )2
V( xi-X )2 +( yi-0 )2
x, e[xi; x2 ] ; y, ebi;y2 ]
j=i
(i0)
.
(9), (10) , , [3]. /(, , ) (1, 1) (2, 2) (9) , (10) - .
(9), (10) (2) , (3) (7)

() = 1 $[ ()-2 ()]d + [(01 () + 12 ())-(01 (0) + 12 (0))], (11)
0 =w0 + V0; Pi = Vi;
, LR
d=ff
4pJ J
0 0
(xi -X)2 + (yi -0)2 V(X2 -X)2 + (y2 -0)2
d X d 0 - -
;
d = 4 p
0 0
\
V2 2 2 2
xj - 2 xj cos a + e 4X2 - 2 ex2 cos a + e
d e d a -
.
0, 1: 1 = 10-3 , 2 = 3 -10-3 , = 0,991, = 2-10-3 , 1 = 2 = 0,5 -0 = 6,395-10-7, 1 = 3,639-10-7; 1 = 10-3 , 2 = 3 -10-3 , = 0,991, 1 = 2 = 0 - 0 = 3,348-10-4, 1 = 4,487-10-7.

i
i
0
n
0
\
i
i
J
i
i
, (11) [1].
,
(, , 0) = (, , ). (12)

1=-----------------. 03)

$ [!( ) - ( )] d
0
(13) (12), . . , . , .
:
/ (, , ) = ~\~ ^ , (14)
4 2^
1 1
;= = 1 - "-
270 2^'
, ,
1
/ (, , ) = $ d0 $ / (, , ) dX . (15)
0 0
(13) , X, .
: X = (0,03... 0,30) /(-), = (10-7 ... 10-6) 2/.

= 1() . (16)
. 0,002.0,03,
3 . . 4. , .
. 4
( ). , , . 5.
0, 1 ,
[0^() + /^()] = 01(0) + ^^( = ^ + 2(. (13)
( -0)
1 = -
(i7)
(i8)
J [7i(t) - T2(t )] dt
t0
, (13). 0,1. 0,3. = 3, 2 . . 6.
. 4 6 .
, (13), (18), (. 7).
1, 2, . 2 3 3,2 1,6 0,6 3. 4 2 - 1. 5 (1, 1) (2, 2), (13), (18).

UH a
j ( t ) dt
1 = -
0
g
(19)
| () d

= /(^5), = --/( 5) - .
d, , , , , , , X (19) .

- <5
, X = (0,05... 0,40) /(-) , [2] 5 = 3 %.
, (19). Mahtcad .
5 < 7 %.
, , X = (0,05.0,40) /(-) 5 < 10 % .

1 , .. - / .. // - . - 1998. -. 71. 5. . 811 - 818.
2 , .. / .. // , 2000, 6. . 27 - 32.
3 , .. / .. - ., 1979. - 256 .
4 , .. / .. . - ., 1977. -656 .
5 / .. , .. , .. , .. ; . . .. . - .: , . -, 1986. - 256 .
Method of Non-Destructive Control over Thermal Conductivity of Heat-Insulating Materials on the Basis of Integral Form of Fourier Equation
I.V. Kovalyova1, I.V. Korablyov1, Yu.I. Azima2
Department MASK, Moscow State University of Environmental Engineering (1); Department Metrology and Quality Systems Novomoskovsk Institute of Russian Chemical Technological University after D.I. Mendeleyev (2)
Key words and phrases: integral Fourier equation; non-destructive control over properties; heat-insulating materials; heat measuring cell.
Abstract: Theoretical grounds of the method of measuring heat conductivity of heat-insulating materials are considered. The design of heat measuring cell is described. The results of the research are submitted.
Methode der nichtzerstrenden Kontrolle der Wrmeleitfhigkeit der Wrmedmmstoffe auf Grund der Integralform der Fourier-Gleichung
Zusammenfassung: Es sind die theoretischen Grunde der Methode der Messung der Wrmeleitfhigkeit der Wrmedmmstoffe betrachtet. Es ist die Konstruktion der Wrmemezelle beschrieben. Es sind die Untersuchungsergebnissen dargelegt.
Mthode du contrle non-destructif de la conductibilit thermique des matriaux thermoisolants la base de la forme intgrale des quations de Fourier
Rsum: Sont envisages les bases thoriques de la mthode de la mesure de la conductibilit thermique des matriaux thermoisolants. Est dcrite la construction de la cellule de la conductibilit thermique. Sont prsents les resultats des tudes.