nblib.library.kz - /elib/library.kz/jurnal/v_2007_1/

(1)

60

2007. 1

-

, -

- .

3.

-

. -

- ,

- .

1. . – -

// . 1975. 3.

2. . -

// . 1972. . 5. . 182-188.

3. . . .,

1958. . 122.

4. ., . -

, -

// .

2005. 6. . 73-78.

5.Drude P. Wied. Ann. 36. 532 865 (1889).

6. . . , 1935.

7. . -

// .

2003. 5.

8. ., . -

// . 1986. . 36.

9. . -

// - . 2003. 3.

10. .( .) . -

// .

2004. 11.

i i

-

i .

Summary

In this article the regulation task of temperature on of as- phalt and cement density due to selective surface covered onto glass.

20.10.06 .

. , .

.

)

, 0 ( ) , 0

( H T

)

( z

T z t

c T , 0 < z <H,

t ( 0 , t

₀

)

, (1)

),

( ) 0 ,

( z T

₀

z

T

0 < z <H, (2)

0 z i z

T

, i=1, 2, … ,k, (3)

T(0, t) = T₁, 0 < t < t₀, (4) )

, 0 ( ) , 0

(z t f z t

f

f – -

, ₁ = const,k – .

- ,

.

h(z), -

– h₁(z). h(z)

, h₁(z)

1, ₁ < . -

, .k=2.

k.

:

)) ( (T T₀ z z

T , (5)

T₀(z) – (

).

z =h(t)

dz p dh z

T

, (6) z=h₁(z)

z 0

T

. (7)

(2)

61

, (1)

,

c =c(T), = (T). (8)

(8) .

- ,

.

c = c(T) = (T) ,

|T| < ,

1

0

( )

0 c c T c

,

0

₀

( T )

₁,

2

)

( c

T T

c , ( ) ₂

T

T . (9)

, (1)–(9)

. -

, -

(1)–(9) .

) , 0 ( ) , 0

( H t

₀

t j t h

z

_i

) ;

_j

;

2 1 1 (

12

M j

N

i 1 , 2 ,..., ; 1 , 2 ,...,

;

N h H ;

M t t⁰ .

, z_i

z_i, i = 1,2,…,k. ,

k = 2.

(1)–(9):

x x i i t

i

Y

i

Y Y

Y

c ( ) ( ( ) )

12

12 ,

i I , j J

, (10)

) (

12 2 0

1 i

i T z

Y , i I, (11)

1 0

12

T

Y

_i _, _i _I, (12) )) ( (

)

( ¹ ₀

12 N j

N N

N Y T t

h Y

Y Y , (13)

), , ( _i _j ₁

i Y z t

Y

_i

Y ( z

_i

, t

_j

)

,

2 / )

(

₁

12 i i

i

Y Y

Y

– .

. (z, t) -

(1)–(9). ,

)) , 0 ( , , 0 ( )

,

(z t W₂² t₀ W₂³ H

T , -

(10)–(13)

( z+h) -

) )

((

² ²

1

2

t C t h

Y T Y

T x a m

t

x

t x .

.

(1) t=(n+1) t z

12

z1 12

z1 .

x z

z

d h

t t c T

h ( , ) 1 ( )

1

2 1 1 2 1 1

2 1 1

,

z

T , ¦U¦=(

U h

i i

2 )¹². U=T–Y

1 2

1 1 1

2 1 2

1

( , ) ( ) )

) (

(

ⁱ ^j _i_z _z

t

Y Y

z t z T T

U

c

,

h 1

1

T z t d

t t c T

z

i t

2 1 1

) , ) (

,

(

. (14)

z i j

i

Y Y

z t z

T T ( , ) ( )

)

(

₁₁₂ ¹² ¹ ₁₁₂

iz j

i

T

z t z

T T ( , )

)

(

₁ ₁₂ ¹² ¹

z i i iz i

i

Y T Y U

T ) ( ) ( )

(

₁₂ ₁₂ ₁₂

z i

i U

Y ) ( ₁₂

3

2 ,

2 iz

j

i T

z t z

T T( , )

)

( ₁₁₂ ¹² ¹ ,

3

( T

i ₁₂

) ( Y

i ₁₂

) T

iz. ,

2 4 2

1 C ( t) , ₂ ² C₅h²,

2 7 2 2

6 2

3 C T_t ( t) C U .

(3)

62

2007. 1

(2.14)

1 3 2 2

1

) )

(

_i _z _z

t

Y U

U

c

. (15)

T(z,t) – T₁. z = 0,

T(z,t) –T₁ Y_i –T₁ T(z,t)

Y_i. (15) 2Uh t -

i j h t :

t Uh U

j i

z j

i

t

2 ( ) / 2

2

,

3 2 ,

t Uh

j i

/ 2

,

1 . (16) (5) (13)

N N

N z

N

U U

Y

₁_/₂

)

₂_, ₃_,

(

. (17)

(16) - ,

t c h U U

t Uh U

j i

z z

j i

t

,

3 2 ,

) (

2 2

t c h

U U

j

i z

z ,

3 2

) 1 (

2

t c h U

j i,

2 1 .

, -

,

t U

C t U U

U

² ²

2

_z ₅ _z ₂ ₃

t U C t T U

U

C

_z

z i 7 1

6

max

. (18)

max T

_z

C

8

i , (18),

,

t U t

U U

t z t

z

2 2

2

2 t C

t U C

t t

2 3 2 2 2 1 10 2

9 .

, , -

2 11

2

( )

max U U t C h t

t i z

(19)

2

2 ( , )

) , (

maxT z t Y T z t Y t

t

j z i z j i j

i j i i

2 11(h t)

C _,

.

h , t 0

(10)–(13) -

(1)–(9).

1.

(3), (6) (7), (16) -

.

2. (5) -

)

2

⁰

(

1 1

2

1 j

N N N

N

Y Y T t

h Y

Y

,

h 1

E ,

) 1 (

1 1

0

1 j

N

N T t

E Y E

E

Y E .

.

1. ., ., . -

. .: , 1971. 451 .

2. . . : -

, 1967. 457 .

3. . . :

, 1986. 239 .

4. . -

- //

. 2001. . 4, 3. . 295-303.

5. .

// . 2005. 2(42).

. 45-50.

6. ., . -

-

// . 2005. 4. . 54-57.

i . i

i.

Summary

In activity suggested a difference scheme for equations of conductive thermoexchange in multilayer area. The convergence of an approximated problem’s solution to the solution of an initial problem in Sobolev spaces are demonstrated.

26.10.06 .