:
, . ( ):
w = + b + 2 + d3 (a)
.
= 0 w = 0 ( ), , (2w/2) = 0.
= d ( ) w0 = w (w/) = 0.
() ,
= 0; = 0;b = 3/2w0/d; d = - 1/2w0/d3.
:
()
()
-
, :
, d . , d. () d.
:
= 0 u ( u = ) (u/)=0 = const Þ (2u/2) = 0, , , , .
= k ( ) u = u0 = const (u/)=k = 0.
.
, ,
u/u0 = 1,5 (/k) 0,5 (/k)3 ()
:
,
Re = w0/n; r = n/.
k/d , r.
r ³ 1, Þ d³ k.
r = 0,6 1 ( r 0,7). k>d.
, Þ =0 , ( ), ²-² :
()
( k, a Þ ).
() ( /l ):
()
Nux = ax/l = a /l x/ = NuX; Rex = w0x/n = w0 /n x/ = ReX; Pr = n/a; .
() , , , .
, , . . , , . (Pr/ Pr)0,25, . (Pr/ Pr)0,25 Þ 1.
|
|
- , Pr ; - .
1 ; 2 ; 3 ; 4 () .
. .
, .
Re:
Re 1 = w01/n Re 2 = w02/n,
, . Re 1 Re 2 1 2, . ,
Re = 104 - 4×106
, , . , - ( Re ).
, . Re 1 Re 2 :
1) ;
2) , ;
3) ;
4) .
.
,
v¢2x, v¢2y, v¢2z ; w0 .
Tu , ( ).
Tu Re .
v (). v , v () . - .
:
q = - (l + l)× = - (l + req)× ,
S = (m + m)× = (m + res)× ,
S ; l, m - ; eq = l/r,es = m/r - - .
:
q = - l(1 + )× (1)
S = rn(1 + es/n)× (2)
Pr = es/eq; Pr = n/ = n/l/r
Pr . (1) (2)
= [(1 + ) ], (3)
= n [(1 + es/n) ]. (4)
Pr = 1 ( = n) Pr = 1, (3) (4) . u v .
|
|
, (3) (4), es eq.
:
d
II d I | . ; (I (); II ). , (), , |
. . . . .
.
.
Pr = 1 d k .
, ( ). .
, .
St º
Pr = 1 Pr = 1 - .
Nu = 0,0296 Re 0,8× Pr 0,43(Pr / Pr )0,25
0 ( Pr, ). , .
. ; (); -
.
( , ..), a 1. a . .