ÍNDICE
No. DE PÁGINA
» OBJETIVOS…………………………………………. 2
» INTRODUCCIÓN…………………………………… 2-5
» EJEMPLOS DE APLICACIÓN…………………….. 5-7
» METODOLOGÍA……………………………………. 8
» RESULTADOS DISCUSIÓN……………………. 8-!5
» CONCLUSIÓN………………………………………. !"
» BIBLIOGRA#ÍA……………………………………... !"
1
» O$%&'()o* M&+(, +(*',($/0(1 +& '&34&,'/,* o ,o +& / */4&,6(0(& &'&+(+ 0o34,, o* ,&*/'+o* 0o / 9(*(* '&1,(0o. O$'&&, 0o+/00(1 4:,+(+* +& 0o, o$ 4o, 0o+/00(1 0o)&00(1. R&(;, / 9(*(* 6/+3&'+o '&1,(03&'& 4, ('&,4,&'0(1 +& o* ,&*/'+o* o$'&(+o*.
» I',o+/00(1.
T,*6&,&0( +& 0o, & */4&,6(0(&* &'&+(+*. L ',*6&,&0( +& 0o,< &* ,&0(1 +& ('&,03$(o +& 0o, 4o, 0o)&00(1 +& / *1(+o / 6/(+o. E* +&0(,< / *1(+o =/& &4&,(3&' ',*6&,&0( +& &&,> 4o, 0o)&00(1 &',& */* >3('&* o* ,&+&+o,&*. E & +(*&?o 0o*',/00(1 +& &=/(4o* +& ',*6&,&0( +& 0o, *& /'((; 6o,3* *(34&* 0o3o 0((+,o*< 40* 4* $,,*< * 0/&* *o /'((;+* 4, 4,o3o)&, & 6/%o +& 0o, &',& / 6/&'& & 3&+(o. C/+o / */4&,6(0(& 4,(3,( *& & ,& */4&,6(0(&* +(0(o&*< &*'* *o 0oo0(+* 0o3o */4&,6(0(&* &'&+(+* o &'*.
C*(6(00(1. U &' ,&0' &* 0/=/(&, */4&,6(0(& 4,oo+ =/& *& /& / 4,&+ 4. P/&+& *&, +& 9,& ',*)&,* /(6o,3& @ o o /(6o,3& @$ / &' /, &* =/& =/& *& /& +& 6o,3 0(,0/6&,&0( / 0((+,o */ *&00(1 ',*)&,* ),( 0o & ,+(o +&*+& >& 0&', +& 0((+,o @0.
U &' +& /% o *4(&< &* / */4&,6(0(& 4,oo+ +& *&00(1 ',*)&,* 0(,0/, /(6o,3& o o /(6o,3&. P&,o &* 0o3 & 0/=/(&, *&00(1 +& / 0o6(/,0(1 +& &'* +&4&+& +& &*40(o< 4&*o< 6$,(00(1 0o*'o*< *> 0o3o +& 4/'o =/& * &'* ,&+/0& & 0o&6(0(&'& +& 0o)&00(1 +& */4&,6(0(& /3&' 0>+ +& 4,&*(1 *o0(+ 0o / 6/%o *o$,& * &'*. 2
S& 4/&+& ,&(;, *(/(&'& 0*(6(00(1 A&'* +& *&00(1 ',*)&,* 0o*''& A&' ,&0'/,. A&' *4(&. A&' /, o 0(,0/6&,&0(. A&'* +& *&00(1 ',*)&,* ),($& A&' ',(/,. A&' 0(,0/6&,&0( ),($&. A&' +& /% 4,$1(0 L* &'* *o *1(+o* =/& ',*6(&,& 0o, 4o, 0o+/00(1 o ,o +& */ &o3&',> 4o, 0o)&00(1 ',):* +& */ &'o,o< *o *(*'&3* 0o 0o+/00(1 0o)&00(1. L* &'* *& /* 0/+o & 0o&6(0(&'& +& ',*6&,&0( +& 0o, 4o, 0o)&00(1 F &* 4&=/&?o< &*'* /3&' )&o0(++ +& ',*6&,&0( +& 0o,< +&*+& */ */4&,6(0(& &4o&, / 9,& 39* ,+& 0o)&00(1 ,+(0(1< 0o3o '3$(: /3&', & 0o, +(*(4+o 4o, 0o)&00(1 3$(&'&. L* &'* (0,&3&' & 6/%o +& 0o, &',& / *1(+o / 6/(+o< */ 3'&,( +&$& '&&, / ' 0o+/0'()(++ ':,3(0 4, 0/34(, */ o$%&'()o< =/& &* 6(3&'& & /3&'o +& 0o, +(*(4+o 4o, 0o)&00(1 3$(&'&. L 0o+/0'()(++ ':,3(0 &* +& , (34o,'0( & * */4&,6(0(&* &'&+(+*< +&$(+o =/& 4,'(, +& &*'& )o, *& &*0o& & 3'&,( 39* 4,o4(+o 4, 0o*',/00(1 +& +&'&,3(+ &'< +&39* '&(&+o & 0/&' =/& ',*6&,&0( +& 0o, & o &=/(4o* =/& /'((; &*'o* +(*4o*('()o*< & */ 3o,> *& + 4o, 0o)&00(1 F0( & 3$(&'&< &* (34o,''& 0o', 0o 3'&,(&* '3&'& 0o+/0'()o*< & o* 0/&* '&34&,'/, +& 'o+ &' *& o 39* 0&,0 4o*($& '&34&,'/, +& $*& +& 3(*3. 3
L +(*',($/0(1 +& '&34&,'/, 6/0(o 0o3o / ,+(&'& =/& & +(,&00(1 x” 3'(&& ',*6&,&0( +& 0o, 4o, 0o+/00(1 ('&,3&'&< 3(*3o '(&34o =/& F ',*6&,&0( +& &&,> 4o, 0o)&00(1 +&*+& */4&,6(0(&.
R+(0(1. L ,+(0(1 ':,3(0 &* &&,> &3('(+ 4o, 3'&,( =/& *& &0/&', / '&34&,'/, ++< *& 4,o+/0& +(,&0'3&'& +&*+& 6/&'& F0( 6/&, & 'o+* * +(,&00(o&*.
Co)&00(1 . L 0o)&00(1 &* & 3&0(*3o +& ',*6&,&0( +& 0o, 4o, 3o)(3(&'o +& 3* o 0(,0/0(1 +&',o +& */*'0(. P/&+& *&, '/, 4,o+/0(+ *oo 4o, * +(6&,&0(* +& +&*(++&* +& 3'&,(H o 6o,;+< 0/+o 3'&,( &* o$(+ 3o)&,*& +& / /, o',o< 4o, &%&34o & (,& 0o / )&'(+o, o & / 0o / $o3$. S1o *& 4,o+/0& & >=/(+o* *&* +o+& o* 9'o3o* 3o:0/* *o ($,&* +& 3o)&,*& & & 3&+(o. E 3o+&o +& ',*6&,&0( +& 0o, 4o, 0o)&00(1 *& &0/&', $%o o* 4,93&',o* +& & +& &6,(3(&'o +& N&'o.
L& +& E6,(3(&'o +& N&'o. L ',*6&,&0( +& 0o, &*'9 ,&0(o+ 0o o* 0/&,4o* 0(&'&* 6,>o* 3+o*H 6/&'& ,&0&4'o,< &)9+o*& 0$o & 4,o0&*o* 0o3o 0o+&*0(1< )4o,(;0(1< 0,(*'(;0(1< ,&00(o&* =/>3(0*< &'0. & +o+& ',*6&,&0( +& 0o,< '(&& */* 4,o4(o* 3&0(*3o* 0+ /o +& &o* 0/&' 0o */* 4&0/(,(++&*. L ',*6&,&0( +& 0o, &* (34o,''& & o* 4,o0&*o*< 4o,=/& &* / '(4o +& &&,> =/& *& &0/&', & ',9*('o< +&$(+o / +(6&,&0( +& '&34&,'/,* @,+(&'&< 4o, ''o &(*'& 4o*($((++ +& 4,&*&',*& & &6,(3(&'o< *( &3$,o &*' &&,> & /, +& 4&,+&,*& *( ( /*o &* */*0&4'($& +& ',*6o,3,*& & &&,> 3&09(0 4o, &%&34oH 4, 4,o+/0(, ',$%o< &&,, )4o,< 0&', / 0o,,(&'& 6,>< &'0. E )(,'/+ +& o '&,(o, &* (34o,''& F0&, / (',o+/00(1 0oo0(3(&'o +& o* 4,o0&*o* +& ',*6&,&0( +& 0o, ',):* +& +&'&,3(0(1 &4&,(3&' +& &0/0(1 &34>,(0 =/& ,&0(o '&34&,'/, +& &6,(3(&'o +& / 0'(++ +& */*'0( 0o ,&*4&0'o 3&+(o.
4
E4&,(3&'3&'& *& 4/&+& +&3o*',, $%o 0(&,'* 0o+(0(o&* o$'&&, / $/& 4,o(30(1 '&34&,'/, +& / */*'0( /*+o L& +& E6,(3(&'o +& N&'o. E*' 4/&+& &/0(,*& +& *(/(&'& 3&, L '&34&,'/, +& / 0/&,4o 03$( / )&o0(++ =/& &* 4,o4o,0(o +(6&,&0( +& * '&34&,'/,* &',& & 3&+(o &'&,o & 0/&,4o. S/4o(&+o =/& 0o*''& +& 4,o4o,0(o(++ &* 3(*3 *& =/& '&34&,'/, /3&'& o +(*3(/< &'o0&* &0/0(1 +(6&,&0( +& & +& &6,(3(&'o &* dT ∝ T − Tm dt dT = K (T −Tm ) dt •
S&4,+o ),($&* dT
( T −Tm ) •
=k dt
I'&,+o
∫ (T −dT Tm) = k ∫ dt •
R&*o)(&+o ln
e
( T −Tm) =kt + c
ln
( T −Tm )
=
e
kt
+ ec ce
T (t)=
5
kt
−Tm
» E%&34o* +& A4(00(1. L* */4&,6(0(&* &'&+(+* *& /* 0o ,&6&,&0( / *1(+o =/& &4&,(3&' ',*6&,&0( +& &&,> 4o, 0o+/00(1 +&',o +& */ >3('&< *> 0o3o */ ',*6&,&0( +& &&,> 4o, 0o)&00(1 @Ko ,+(0(1 &',& */* >3('&* */* ,&+&+o,&*. D& 3&, =/& F 3/0F* *('/0(o&* =/& (34(0 &6&0'o* 0o3$(+o* +& 0o+/00(1 0o)&00(1< 4(00(1 39* 6,&0/&'& &* =/& & =/& *& /* / */4&,6(0(& &'&+(+ +& 3&, &*4&0>6(0 4, /3&', ,4(+&; +& ',*6&,&0( +& 0o, &',& / *1(+o / 6/(+o 0o'(/o. A &*' */4&,6(0(& &'&+(+ *& +&o3( ALETAS. L* &'* +& &6,(3(&'o &*'9 F&0F* +& 3'&,(&* ('&*3&'& 0o+/0'o,&* 0o3o & /3((o. M&%o, ',*6&,&0( +& 0o, +&*+& / */4&,6(0(&* &4o&, / 9,& 39* ,+& 0o)&00(1 ,+(0(1H *o +& /*o 0o3 & 4,90'(0 4, 3&%o,, ',*6&,&0( +& 0o, 3&/+o (0,&3&' )&o0(++ +& &** ',*6&,&0(* +&*+& / */4&,6(0(& 0o ),(o* +o$&0&*.
I'&,03$(+o,&* +& 40 &' E*'& '(4o +& ('&,03$(+o, +& 0o, /'((; *+(0F =/& 0o'(&& 4*%&* +& &'* 4, /3&', &6&0'()(++ +& /(++. Lo* +(*&?o* *o +& 6/%o 0,/;+o 0o',0o,,(&'&< %/'o 0o +(6&,&'&* 0o6(/,0(o&* +& &'< 0o3o &'* ,&0'*< * &'* * &'* 0o34&*, o+/+o. M/, o* ('&,03$(+o,&* +& 0o, +& &' *o &&,3&'& F&0F* +& &0(o&* +& /3((o =/& 4,o4o,0(o / 3o, &6(0(&0( +& ',*6&,&0( +& 0o,. E 3'&,( 4&,3('& =/& & *(*'&3 6/0(o& / '&34&,'/, 39* $% ,&+/0(, & 4&*o +& &=/(4o. M/, o* ('&,03$(+o,&* +& 0o, +& &'* *& /'((; *o$,& 'o+o 4, o* *&,)(0(o* +& $% '&34&,'/, 0o3o & * '/,< & F&(o (0/&600(1 +& o>&o< * 4'* +& *&4,0(1 +& (,& & ',*4o,'& 0o3o /'o31)(&* 3o'o,&* +& &,o)&*.
Ventajas de la placa y los intercambiadores de calor de la aleta: 6
•
•
•
•
A' &6(0(&0( +& ',*6&,&0( +& 0o,< &*4&0(3&'& & & ','3(&'o +& *. T,*6&,&0( +& 0o, +& 39* ,+& 9,&. A4,o(3+3&'& 5 )&0&* 39* (&,o =/& & +& SF& / ('&,03$(+o, +& 0o, +& '/$o*. C4; +& *o4o,', ' 4,&*(1.
Desventajas de la placa y los intercambiadores de calor de la aleta: •
Po+,> 0/*, o$*',/00(1 & * )>* *o 3/ &*',&0F*.
•
D(6>0(&* +& (34(, * )>* +& ('&,03$(+o,&* +& 0o, +& 6/(+o*.
E*'& &* / ('&,03$(+o, +& 0o, 0o / * =/& 4* F0( ,,($ ',):* +& / /)( +& >=/(+o +& / @ 3&/+o< & >=/(+o *& 'o3 &'o0&* & o',o* /,&* '&* +& *&, &6,(+o. E*'o &* 0o33&'& /'((;+ 4, ,&6,(&,0(1 +& o* *&* 3(*3o '(&34o =/& &(3(0(1 +& 0(&,'* (34/,&;*< 4o, o =/& *o/0(1 +& +o* 4,o$&3* )&;. E* 34(3&'& /'((;+o & 39=/(* +& 06: &4,&*o 0o3o / 3:'o+o +& Fo,,o +& &&,> +& &6,(3(&'o +& / *4&, 0&'+ *&, /'((;+o & &',00(1 +& 06: &4,&*o.
» M&'o+oo>. 7
E=/(4o '-!5 A,36(&+. M&+(, & +(93&',o +& 0((+,o. A%/*'& & ()& +& 0&'3(&'o. R&(*',& '&34&,'/, 6,&0/&'&3&'& F*' =/& :*' *& &*'$((0&< &'o0&* ,&+/;0 & ()& +& 0&'3(&'o 4&,3(' +& /&) 0/&' =/& '&34&,'/, *& &*'$((0&. P, )o'%&* +& 5< ! !5 V< ,&(*',& 0o,,(&'& /*+ '&34&,'/, & 0+ 4o*(0(1 o ,o +& 0((+,o< &* +&0(, +& T! T *(&+o T7 /&*', '&34&,'/, 3$(&'& @'o3+ *> 4o, 0o*',/00(1 +& &=/(4o
» R&*/'+o* +(*0/*(1. C90/o* E *(/(&'& '$ *& 3/&*', * '&34&,'/,* o$'&(+* +(6&,&'&* )o'%&* 5V
X
T(°C)
10 V
X
T(°C)
15 V
X
T(°C)
1 (w)
0
29.6
1 (w)
0
54.2
1 (w)
0
86.4
2
0.05
26.7
2
0.05
43.8
2
0.05
65.2
3
0.1
25
3
0.1
37
3
0.1
50.9
4
0.15
23.6
4
0.15
32.1
4
0.15
41.6
5
0.2
23
5
0.2
29.4
5
0.2
35.7
6
0.25
22.7
6
0.25
27.4
6
0.25
31.9
7
0.3
22.5
7
0.3
26.1
7
0.3
29.4
8
0.35
22.2
8
0.35
26.2
8
0.35
29
Co / '&34&,'/, 3$(&'& +& 2.5 C 4, o* )o'%&* +& 5V !V< 4, & )o'%& +& !5V *& o$'/)o / '&34&,'/, 3$(&'& +& 2.7 C. A 4,'(, +& &*'o* +'o* o$'&(+o* *& o0/41 *(/(&'& &0/0(1 ∅
exp=
Tx −T ∞ Tw −T ∞
Do+& 8
Tx
T∞
Tw
&* '&34&,'/, & 4o*(0(1 &* '&34&,'/, 3$(&'& &* '&34&,'/, +& 4,&+ +& ),(
O$'&(&+o o* *(/(&'&* ,&*/'+o* 5 V
∅
exp
10 V
exp
∅
1
1 (w)
1
0.681318
0.677321
66
16
2
2
0.494505
0.489614
49
3
0.459665
24
14
3
3
0.340659
0.344213
34
4
0.318112
65
63
4
4
0.274725
0.264094
27
5
0.228310
96
5
5
5
0.241758
0.204747
24
6
0.170471
77
84
6
6
0.219780
0.166172
22
7
0.132420
11
09
7
7
0.186813
0.169139
19
8
1 (w) 0.691394
68
0.126331
47
81
8
8
':,3(0 *& /'((; o *(/(&'& ,&0(1 ( q x x
2
− qx x +∆x )π r =
H T As (Tx − T∞ )
I/+o 0&,o &4,&*(1 '&,(o, ( q x x
exp 1
1 (w)
2
∅
15 V
2
− qx x +∆x )π r − H T As (Tx − T∞ ) = 0
Do+& A s V
= 2π r ∆x 2
= π r ∆x 9
P, o$'&0(1 +& 0o+/0'()(++
E'o0&*H */*'('/&+o * &0/0(o&* '&,(o,&* +()(+(&+o &',& & )o/3& *& '(&& *(/(&'& &4,&*(1 ( q x x
2
− qx x +∆x )π r − H T (2π r ∆x )(Tx − T∞ ) = 0 2
π r ∆x
E(3(+o ':,3(o* 0o3/&* 3((3(;+o &0/0(1< o* =/&+ o *(/(&'& ( q x x
− qx x +∆ x )
2 H T (Tx
−
∆ x
− T ∞ )
=
r
0
A4(09+o& >3('& &0/0(1 ,&*/''& '&,(o, 0/+o
lim
(qx x
− q x x+∆ x )
−
2 H T (Tx − T ∞ )
∆ x
∆ x →0
r
=
∆ x → 0 :
0
R&*/' o *(/(&'& dq
−
2 H T (Tx
dx
− T ∞ )
=
r
0
O $(&< +&,()+o 4, o$'&&, *&/+ +&,()+ o$'&&, &4,&*(1 & ':,3(o* +& T&34&,'/, d 2T dx
2
−
2
H T (Tx − T ∞ ) = 0 rk
0(&+o * *(/(&'&* 0o*(+&,0(o&* θ =
T x
− T ∞
Tw − T ∞ m2
=
2 H T rk
m=
O $(& 10
2 H T rk
S& */*'('/& & &0/0(1 +(6&,&0( +& *&/+o o,+& d 2θ dx
2
2
−m = 0
R&*o)&3o* &0/0(1 +(6&,&0( +& *&/+o o,+& n2 − m2
=
0
n2
=
0
=
m2
n = ±m θ (0) = 1
d θ
=
dx x = L
0
NOTA E*'o* '(3o* 4*o* +&*o*+o* +&'+3&'& *& &0/&', & 4,'& +& (',o+/00(1. L&+o 6(3&'& *(/(&'& &0/0(1 ∅
( x )=
cosh [ m ( L − x )] cosh ( mL )
2∗ Ht Do+& m= r∗k
L Lo('/+ Po*(0(1 , R+(o Q Co*''& +& 0o+/0'()(++ ':,3(0 Ht = Hr + Hc
' Co&6(0(&'& +& ',*6&,&0( +& 0o, 'o' , Co&6(0(&'& +& ',*6&,&0( +& 0o, 4o, ,+(0(1 11
0 Co&6(0(&'& +& ',*6&,&0( +& 0o, 4o, 0o)&00(1. 4
σ ∗φ∗(Ts −T ∞ Hr = Ts− T ∞
4
)
−9
σ =56.7∗10
0.25
Ts−T ∞ Hc=1.32∗[ ] D
A 4,'(, +& &*'* &0/0(o&* *& F0& & 090/o +& 0o*''& +& 0o+/0'()(++ ':,3(0< /'((;+o & *o6',& 4o3'F 4o(&+o * &0/0(o&* 0o3o / *(*'&3 +& &0/0(o&* o (&&*< 'o3+o & 0/&' =/& 0o 0+ '&34&,'/, *& 00/ / 0o*''& +& 0o+/0'()(++ ':,3(0 +&39* =/& ∅
(0 ) ≈ 1
To3+o & 0o*(+&,0(1 &*'o *& 4/&+& F0&, / $/& 4,o(30(1 )o, &4&,(3&'.
12
13
NOTA L* 04'/,* '&,(o,&* 6/&,o ' *1o & +& / 3&+(0(1< * 0/9&* 4, o$'&&,* +& 0+ / +& * '&34&,'/,* +& */4&,6(0(& +& 0+ /o +& o* '&,3o4,&* +& &=/(4o +& 6/&,o 3o+(6(0+o /o 4o, /o ,&*4&0'()3&'&. Po, 3&+(o +& &*'& 3:'o+o *& o$'/)o o* *(/(&'&* +'o*. 5V
T(°C)
1 (w) 2
3 4
k(w/m°C )
29.6
107.9342
26.7
107.9825
25
5
23.6 23
108.0176 108.0575 108.0798
6
22.7
108.0928
7
22.5
108.1024
8
22.2
108.1188
14
S0+o & 4,o3&+(o Kp=
k 1 + k 2 + k 3 + k 4 + k 5 + k 6 + k 7 + k 8 8
Kp=108.0482
w m °C
10 V
T(°C)
1 (w) 2
k(w/m°C )
3
54.2
107.7692
43.8
107.8221
37
107.8649
4
32.1
107.9074
5
29.4
107.9386
6
27.4
107.9681
7
26.2
107.9897
8
26.1
107.9917
S0+o & 4,o3&+(o
Kp=
k 1 + k 2 + k 3 + k 4 + k 5 + k 6 + k 7 + k 8 8
Kp=107.9064625
w m ° C
15 V
k(w/m°C )
T(°C)
1 (w)
86.4
107.6765
2
65.2
107.7361
3
50.9
107.7871
15
4
41.6
107.8342
5
35.7
107.8755
6
31.9
107.9109
7
29.4
107.9409
8
29
107.9464
S0+o & 4,o3&+(o Kp=
k 1 + k 2 + k 3 + k 4 + k 5 + k 6 + k 7 + k 8 8
Kp=107.83845
w m° C
Co &*'o* ,&*/'+o* *& 4/&+& F0&, / 0o34,0(1 +& 0o*''& +& 0o+/0'()(++ ':,3(0 &4&,(3&' +& '1 0o', * 0o*''&* 00/+*
&4&,(3&' ! ! !
00/+ !8.82 !7.""25 !7.885
+& &,,o, .872!! !.25 !."5"22
Po, ''o *& 4/&+& o$*&,), =/& o* )o,&* 00/+o* &*'9 4&,6&0'3&'& 0o,+& o* )o,&* &4&,(3&'&*H &*o =/(&,& +&0(, =/& 'o3+o 0o*(+&,0(1 +& =/& ∅ (0 ) ≈ 1 6/& 0&,'+.
16
»Co0/*(o&*. E ',*6&,&0( +& 0o, *& +(*'(/& ',&* '(4o* +& 3&0(*3o* 0o+/00(1< 0o)&00(1 ,+(0(1. E &*' 4,90'(0 *& +&*0,($& o* 3&0(*3o* +& ,+(0(1 0o)&00(1. Po, o =/& *& o$'/)o 4o, F&,,3(&'* 3'&39'(0* @4o3'F * 0o+/0'()(++&* ':,3(0* 3/ 4,o(3+* &4&,(3&'< &*'o *& 0o34,o$1 o$'&(&+o / &,,o, !.
» B($(o,6>. •
W
B(,+< R. B. Fenómenos de Transporte. Primera Edición México D.F: Reverte Ediciones< 2!. //* A. X&&< Transferencia de Calor !" edición Mc#ra$%&ill México 2.
W
I0,o4&,< D&Y(''< B&,3< L)(&< F'ndamentals of &eat and Mass Transfer (t) edition *o)n +ille, - ons !//0.
W
#. ,&('F M. S. BoF< Principios de Transferencia de Calor (" edición TFo3*o< M+,(+< 22.
W
J. P. o3< Transferencia de Calor 1" edición Mc#ra$%&ill Madrid 2331.
W
A. J. CF43< Transmisión del Calor !" edición Ediciones 4nterciencia M+,(+< !"8.
W
J. R. Y&'< C. E. Y(0Q*< R. E. Y(*o< F'ndamentos de Transferencia de Momento Calor , Masa !" edición Editorial 5im'sa México 2333.
W
E. To,,&< J. M. P(;o< R. C$&o< Transmisión de Calor 2" edición S&,)(0(o +& P/$(00(o&* +& U()&,*(++ Po(':0(0 +& V&0(< V&0(< !.
17
