Avance Del Lunes FINAL (1)
74
Contenido 1. OBJETIVOS .......................................................... 2. MARCO TEÓRICO ..................................................... 2.1. REQUERIMIENTO DE CONSERVACIÓN DE LA ENERGÍA ...................2 2.2. CONSERVACIÓN DE LA ENERGÍA PARA UN VOLUMEN DE CONTROL ............................................................ 2.2.1.En un instant t ................................................. 2.2.2.En un int!"a#$ % ti&'$ ∆ t ..................................... 2.(. GENERACIÓN DE ENERGÍA ........................................... 2.(.1 C$n%u))i*n ...................................................... 2.(.2. C$n"))i*n ...................................................... 2.+. TRANS,ERENCIA DE CALOR EN SUPER,ICIES E-TENDIDAS ..........6 2. . ALETAS DE /REA DE SECCIÓN TRANSVERSAL UNI,ORME ............8 (. PLANTEAMIENTO DEL PROBLEMA ........................................ (.1. LITERAL A ....................................................... (.2. LITERAL B ....................................................... (.2.1 P!i&!a 'a!t ................................................... (.2.1 S0un%a Pa!t .................................................. (.(. LITERAL C ....................................................... + AN/LISIS DE VARIACIÓN DE LAS PROPIEDADES ............................. CONCLUSIONES ...................................................... ANE-OS ............................................................ 6.1 PROGRAMA EN MATLAB.............................................. 6.2 ANÁLII GRÁ!ICO................................................
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Transcript of Avance Del Lunes FINAL (1)
2.2. CONSERVACIÓN DE LA ENERGÍA PARA UN VOLUMEN DE
CONTROL........................................................................................................
2
2.2.1. En un instant t................................................................................2
2.(. GENERACIÓN DE ENERGÍA.................................................................3
2.(.1 C$n%u))i*n..........................................................................................4
2.. ALETAS DE /REA DE SECCIÓN TRANSVERSAL UNI,ORME............8
(. PLANTEAMIENTO DEL PROBLEMA.........................................................10
(.1. LITERAL A...........................................................................................11
(.2. LITERAL B...........................................................................................18
(.(. LITERAL C...........................................................................................37
CONCLUSIONES........................................................................................43
ANE-OS.....................................................................................................44
1.OBJETIVOS
E" o#$eti%o de" &i'(iente )*o+e,to- e& o*ient* ,e*, de (n int*od(,,i/n "o& odo& de t*n&e*en,i de ,"o*- ,on n&i& en "o& (ndento& de ,ond(,,i/n + ,on%e,,i/n- + de&)*e,indo " t*n&e*en,i de ,"o* )o* *di,i/n. e n"i*n )*o#"e& de t*n&e*en,i de ,"o* )o* ,ond(,,i/n (nidien&ion" + ("tidien&ion"- en e&tdo e&t#"e- t*%& de todo& n"ti,o& + n(*i,o&.
E" o#$eti%o )*in,i)" de e&te )*o+e,to e& )"i,* e" todo de die*en,i& nit& en " *e&o"(,i/n de )*o#"e& de ,ond(,,i/n (nidien&ion" + #idien&ion" en e&tdo e&t#"e.
2.MARCO TEÓRICO
2.1. REQUERIMIENTO DE CONSERVACIÓN DE LA ENERGÍA
L te*odini,- + " t*n&e*en,i de ,"o*- &on do& ,ien,i& (e e&tn ntiente *e",iond& + (e " te*odini,- t*t &o#*e " velocidad " (e &e t*n&e*e ,"o*- ient*& (e " t*n&e*en,i de ,"o*- &e ,on&ide* (n e9ten&i/n de " te*odini,. E" (&o de " )*ie* "e+ de " te*odini,- e& de,i*- " ley de la conservación de la energía, $(e' (n ))e" i)o*tnt&io- en e" de&**o""o de "o& )*o#"e& de t*n&e*en,i de ,"o*.
2.2. CONSERVACIÓN DE LA ENERGÍA PARA UN VOLUMEN DE CONTROL
P* )"i,* " )*ie* "e+ de " te*odini,- &e de#e identi,* )*ie*o- e" %o"(en de ,ont*o"- e" ,(" *e)*e&ent (n *e'i/n t*idien&ion" en e" e&),io- "iitd )o* (n &()e*,ie de ,ont*o"- t*%& de " ,("- )(eden in'*e&* " ene*' + " te*i. L )*ie* "e+ de#e &ti&,e*&e &o#*e ,("(ie* inte*%"o
de tie)o t )* e&te inte*%"o- de#e e9i&ti* (n #"n,e ene*'ti,o- ent*e
"& ,ntidde& de todo& "o& ,#io& de ene*'- edido& en :o("e&.
2.2.1. En un instant t L %e"o,idd " (e " ene*' t*i, + e,ni, in'*e& en (n %o"(en de ,ont*o"- & " %e"o,idd " (e &e 'ene* ene*' t*i, dent*o de" %o"(en de ,ont*o"- eno& " %e"o,idd " (e &"e ene*' t*i, + e,ni, de" %o"(en de ,ont*o" de#e &e* i'(" " %e"o,idd de in,*eento de " ene*' ",end dent*o de" %o"(en de ,ont*o".
2
2.2.2. En un int!"a#$ % ti&'$ t
L ,ntidd de ene*' t*i, + e,ni, (e in'*e& en (n %o"(en de ,ont*o"- & " ,ntidd de ene*' t*i, (e &e 'ene* dent*o de" %o"(en de ,ont*o"- eno& " ,ntidd de ene*' t*i, + e,ni, (e &"e de" %o"(en de ,ont*o" de#e &e* i'(" " in,*eento en " ,ntidd de ene*' ",end en e" %o"(en de ,ont*o".
E" )*ie* )&o en e&t *e&o"(,i/n- ,on&i&te en identi,* " &()e*,ie de ,ont*o"- t*ndo (n "ne )(nted. E" &i'(iente )&o- ,on&i&te en identi,* "o& t*ino& de ene*'- e&to& t*ino& in,"(+en; L ene*' t*i, + e,ni, (e ent* + &"e de" %o"(en de ,ont*o" de& de e&to- e& )o&i#"e 'ene** ene*' t*i, dent*o de" %o"(en de ,ont*o"- de#ido " ,on%e*&i/n de ot*& o*& de ene*'- e&te )*o,e&o- e& ,ono,ido ,oo 'ene*,i/n de ene*'. L e,(,i/n- de" #"n,e ene*'ti,o- (ed &;
´ Eent + ´ Eg− Esale= dEalm
dt ≡ ´ Ealm
<e donde;
´ Eent = Energía térmica y mecánica que entraal volumen de control[W ]
´ Esale= Energíatérmica y mecánica que sale del volumen de control[W ]
´ E g=Cantidad de energía térmicaque se genera dentro del volu mende control[W ]
dEalm
dt =Velocidadde cambiodela energíaalmacenadadentrodelvolumende control[W ]
Conservación de la energía para un volumen de control. Aplicación en un instante.
2.(. GENERACIÓN DE ENERGÍA E" t*ino 'ene*,i/n de ene*'- &e &o,i ,on " ,on%e*&i/n de ot* o* de ene*' =(i,- e",t*i,- e"e,t*o'nti, o n(,"e*> ene*' t*i,. E& (n fenómeno volumétrico.
E9i&ten t*e& odo& de t*n&e*en,i de ,"o*;
3
2.(.1 C$n%u))i*n
e ,on&ide* ,oo " t*n&e*en,i de ene*' de "& )*t,("& & ene*'ti,& "& eno& ene*'ti,& de (n &(&tn,i- de#ido "& inte*,,ione& ent*e "& i&&. P* e&te todo de t*n&e*en,i de ,"o*- " e,(,i/n o ode"o- &e ,ono,e ,oo " Ley de Fourier:
q } rsub {x} =-k {dT} over {dx} ¿
<e donde;
q } rsub {x} =Flujo de calor o transferencia de calor por unidad de área [W/ {m} {!} " ¿
dT
! =Conductividad térmica[W /m " # ]
E" &i'no eno&- e indi,- (e &e t*n&e*e ,"o* en " di*e,,i/n de " te)e*t(* de,*e,iente.
E&t e,(,i/n- &e ode" en " &i'(iente '(*;
4
2.(.2. C$n"))i*n
E" odo de t*n&e*en,i de ,"o* )o* ,on%e,,i/n &e &(&tent tnto en e" o%iiento o"e,("* "eto*io ,oo en e" o%iiento %o"(t*i,o de" ?(ido en " ,) "ite. L ,ont*i#(,i/n de#id " o%iiento o"e,("* "eto*io =di(&i/n> doin ,e*, de " &()e*,ie donde " %e"o,idd de" ?(ido e& #$.
E&te odo de t*n&e*en,i de ,"o*- &e ,"&i, de ,(e*do ,on " nt(*"e de" ?(ido e9i&ten do& ti)o& de ,on%e,,i/n;
1 C$n"))i*n 3$!4a%a5 C(ndo e" ?($o e& ,(&do )o* edio& e9te*no&- ,oo (n %enti"do*- #o#& o %iento& to&*i,o&.
2 C$n"))i*n #i6! 7natu!a#5 E" ?($o e& ind(,ido )o* (e*& de e)($e- (e &(*'en )*ti* de die*en,i& de den&idd o,&iond& )o* %*i,ione& de te)e*t(* en e" ?(ido.
in i)o*t* " nt(*"e )*ti,("* de" )*o,e&o de t*n&e*en,i de ,"o* )o* ,on%e,,i/n- " e,(,i/n o ode"o )*o)ido e& de " o*;
q =#$ {T} rsub {s} - {T} rsub {%} &
<e donde;
T s=Temperaturadela super$icie[ # ]
" # ]
C#e *e,",* (e e" ,oe,iente de t*n&e*en,i de ,"o* )o* ,on%e,,i/n- de)ende de "& ,ondi,ione& en " ,) "ite- en "& (e in?(+en " 'eoet* de " &()e*,ie- " nt(*"e de" o%iiento de" ?(ido + (n &e*ie de )*o)iedde& te*odini,& de" ?(ido + de t*n&)o*te.
Dsa!!$##$ % #a )a'a #8&it n #a t!ans3!n)ia % )a#$! '$! )$n"))i*n
En e" de&**o""o de e&te )*o+e,to- e" todo de " t*n&e*en,i de ,"o* )o* *di,i/n- &e ,on&ide*/ de&)*e,i#"e.
2.+. TRANS,ERENCIA DE CALOR EN SUPER,ICIES E-TENDIDAS
@n %e- (e &e t(%ie*on ,"*o& todo& "o& ,on,e)to& e9)"i,do& )*e%iente. e de#e ,ono,e* (e e" de&**o""o de n(e&t*o )*o+e,to- ,on&i&ti/ en " t*n&e*en,i de ,"o* )o* ,ond(,,i/n + ,on%e,,i/n- )e*o t*%& de supercies extendidas. E&t *&e- ,e *ee*en,i (n &/"ido (e e9)e*ient t*n&e*en,i de ene*' )o* ,ond(,,i/n + ,on%e,,i/n dent*o de &(& "ite& + "o& "*ededo*e&. E9i&ten (,& &it(,ione& (e i)"i,n ee,to& ,o#indo& de ,ond(,,i/n + ,on%e,,i/n- " )"i,,i/n & *e,(ente- e& (e"" en " (e &e (& (n &()e*,ie e9tendid de ne* e&)e,, )* aumentar " *)ide de t*n&e*en,i de ,"o* ent*e (n &/"ido + (n ?(ido ,onti'(o e&t &()e*,ie e9tendid- &e denoin aleta.
6
Us$ % a#tas 'a!a au&nta! #a t!ans3!n)ia % )a#$! %s% una 'a!% '#ana. Su'!9)i )$n a#tas.
A" e9in* " '(* nte*io*- &e )(ede )*e,i* (e " t*n&e*en,i de ,"o*- &e in,*eent (entndo e" *e de " &()e*,ie t*%& de " ,(" o,(**e " ,on%e,,i/n. E&to &e "o'* ,on e" e)"eo de aletas (e &e extienden de&de " )*ed " ?(ido ,i*,(ndnte.
Di3!nts )$n90u!a)i$ns % a#tas5
1 A#ta !)ta % s))i*n t!ans"!sa# uni3$!&5 E& ,("(ie* &()e*,ie )*o"on'd (e &e (ne (n pared plana ,on *e t*n&%e*&" ,on&tnte. =E&te e& e" ode"o de e$e)"o de n(e&t*o )*o+e,to>.
A#ta !)ta % s))i*n t!ans"!sa# uni3$!&
7
2 A#ta !)ta % s))i*n t!ans"!sa# n$ uni3$!&5 E& ,("(ie* &()e*,ie )*o"on'd (e &e (ne (n pared plana ,on *e t*&%e*&" %*i#"e.
A#ta !)ta % s))i*n t!ans"!sa# n$ uni3$!&
( A#ta anu#a!5 A(e"" (e &e (ne de o* ,i*,(ne*en,i" (n ,i"ind*o- + &( &e,,i/n t*n&%e*&" %* ,on e" *dio de&de " "ne ,ent*" de" ,i"ind*o
A#ta anu#a!
+ A#ta % a0u:a5 ()e*,ie )*o"on'd de &e,,i/n t*n&%e*&" ,i*,("*
A#ta % a0u:a
2.. ALETAS DE /REA DE SECCIÓN TRANSVERSAL UNI,ORME
Cd "et &e (ne (n &()e*,ie #&e de te)e*t(* T (( )=T b + &e
e9tiende (n ?(ido de te)e*t(* T %' P* "& "et& (e &e e&t#"e,en-
A, e& (n ,on&tnte + A& P9- donde A& e& e" *e de " &()e*,ie edid de " #&e 9 + P e& e" )e*et*o de " "et.
e denen "& &i'(iente& e,(,ione&;
( ( x )=T ( x )−T %
m !=
! *c
(
cos# m++( &m! )sen& m+
Ade& de e&to- e&to& inte*e&do& en e" ,"o* tot" t*n&e*ido )o* " "et- ddo )o* " &i'(iente e,(,i/n;
q$ =√ &)! *c "(b
(.PLANTEAMIENTO DEL PROBLEMA
e end(*e,e (n )", edinte (n &e*ie de ,o&ti""& "on'it(din"e& (e tienen (n &e,,i/n t*n&%e*&" *e,tn'("* ,on (n "on'it(d L 8 + n,o D 4 . L #&e de " )", &e ntiene (n te)e*t(* (nio*e T # 45 C- ient*& (e "& &()e*,ie& de "& ,o&ti""& de e9)onen " i*e (n
te)e*t(* de T % 25 C + (n ,oe,iente de ,on%e,,i/n de 600 F
2. H.
a @&ndo e" todo de die*en,i& nit& ,on 9 + 2 + (n
tot" de 5 9 3 )(nto& nod"e& + *e'ione&- e&ti* " di&t*i#(,i/n de " te)e*t(* + " t*n&e*en,i de ,"o* de " #&e. Co)*e e&to& *e&("tdo& ,on "o& (e &e o#t(%ie*on " &()one* (e " t*n&e*en,i de ,"o* en " ,o&ti"" e& (nidien&ion" + )o* e""o &ee$nte " ,o)o*tiento de (n "et.
6 E" e&),ido de " "" (e &e (& en " &o"(,i/n nte*io* de die*en,i& nit& e& #(*d- "o (e tiene ,oo *e&("tdo (n )*e,i&i/n )o#*e )* "& e&ti,ione& de te)e*t(*& + de " t*n&e*en,i de ,"o*. In%e&ti'(e e"
ee,to de *eniento de " "" " *ed(,i* e" e&),ido nod" 9
>.
) In%e&ti'(e " nt(*"e de " ,ond(,,i/n #idien&ion" en " ,o&ti"" + dete*ine (n ,*ite*io )* e" (e &e *on#"e " )*o9i,i/n (nidien&ion". ' e&to e9tendiendo &( n"i&i& de die*en,i& nit& )* dete*in* " t& de ,"o* de " #&e ,oo (n (n,i/n de " "on'it(d de "
,o&ti"" )* e" inte*%"o de 1.5 , LD , 10- nteniendo " n,(* D
,on&tnte. Co)*e &(& *e&("tdo& ,on "o& dete*indo& edinte " )*o9i,i/n de " ,o&ti"" ,oo (n "et.
(.1. LITERAL A
L8 D 4 T b=)* 0C J 10 W
m!
m ! !
x= y=!mm - Co)*e e&te ,"o* ,on e" o#tenido &i &e &(e
(n "et
Su'ust$s
• Condi,ione& de E&tdo E&t#"e • P*o)iedde& ,on&tnte& • ,oe,iente de ,on%e,,i/n • Coe,iente de ,on%e,,i/n (nio*e &o#*e "& &()e*,ie& de "& ,o&ti""
N$ta5 )* "o& ,",("o& )o&te*io*e& , e& e" ,"o* )o* ,on%e,,i/n (e &e en,(ent*
T %=!* (
C.
Ade& T b e& " te)e*t(* en " #&e - + T b=)* 0C
N$%$ 1
9 = T %−T + > K J y
!
y
(T *−T +) y 0
9 = T %−T + > K !
! (T b−T +) K
! (T !−T +) K J (T *−T +) 0
=600> =29 103> =25 T1> K 5 = )*−T + > K 5 = T !−T + > K 10 = T *−T + > 0
30 1.2T1 K22.5 5T1 K 5T2 5T1 K 10T5 10T1 0
21.2 T1 5 T2 10T5 255
N$%$ 2
9 = T %−T ! > K J y
!
y
(T -−T !) y 0
9 = T %−T ! > K !
! = T ,−T ! >K ! = T −T ! > 0
=600> =29 103> =25 T2> K 5 = T +−T ! > K 5 = T ,−T ! > K 10 = T −T ! > 0
30 1.2T2 K 5T1 5T2 K 5T3 5T2 K 10T6 10T2 0
21.2 T2 5 T1 5T3 10 T6 30
N$%$ (
13
9 = T %−T , > K J y
!
y
(T .−T ,) y 0
=600> =29 103> =25 T3> K 5 = T !−T , > K 5 = T )−T , > K 10 = T .−T , > 0
30 1.2T3 K 5T2 5T3 K 5T4 5T3 K 10T7 10T3 0
21.2 T3 5 T2 5T4 10 T7 30
N$%$ +
x
x
T −T ) > 0
15 0.6T4 K 15 0.6T4 K 5T3 5T4 K 5T8 5T4 0
11.2 T4 5 T3 5T8 30
N$%$
14
J x (T +−T *)
y K J y
y
2T5 T1 0.5T6 22.5
J x (T !−T )
y K J y
y
2T6 T2 0.5T5 0.5T7 0
N$%$ ;
2T7 T3 0.5T6 0.5T8 0
N$%$ <
15
x
5 (T .−T /) K 5 (T )−T /) K 600 (! x+(−,)
! =25 T >
10.6T8 5T7 5T4 15
( !+0! −*
−* !+0!
qC + y
m
q!
W
m
16
W
m
Coo (n "et
P 2=1> K 2D 2 K =2>=4 9 103> 2.008
*c " D 4 9 10 3
T=0> T# 450C
K C ! e −mx
e'(nd ,ondi,i/n - 9 L
E" ,&o en e" (e no& en,ont*o& e& t*n&e*en,i de ,"o* )o* ,on%e,,i/n en e" e9t*eo
A, T=L> T % J * c
/T
e &(e T=L> 1 32.320C
-
7.32 =20 C ! > e (+.,0**)( x +(
−,) K C ! e
3.76 C !=.!0*
( =9> 0.625 C ! e +.,0** x
K 1.375> e −+.,0** x
√ &)! *c (b sen& ( m+)+(&/m! ) cos# (m+) cos# (m+ )+(& /m! )sen&(m+)
√ -(((!0(()(+()() x +( −,) =20>
Qe**o* |+,(0-1−+,(0
+,(0-1 | 100Q 0.0842Q de e**o*
on %"o*e& (+ )*o9ido&- e" todo de die*en,i& nit& en e&tdo e&t#"e e& (n )*o9i,i/n (+ #(en.
P* &e* ,o)*o#* (e "o& *e&("tdo& o#tenido& ,on e" ,"o* de (n "et &e io (n e&t(dio (nidien&ion" de " t*n&e*en,i de ,"o*.
1
! y (T ,−T ) )
21
Ca#$! %s% #a 6as
qbase=¿ 132.126
e o#&e*% (e e" ,"o* de " /*(" de " "et (nidien&ion" &e )*e,e (,o " ,"o* o#tenido ,iendo (n n"i&i& (nidien&ion" de ,"o*e& en e&tdo e&t#"e.
P* ne& did,ti,o&- &e * (n n"i&i& de die*ente& te*i"e& de " ,o&ti"" e& de,i*- %o& to* %"o*e& die*ente& de J. Tondo (n #(en ,ond(,to*
,oo e" o*o =J317 W
m! > + (n " ,ond(,to* ,oo e" )ino =J0-12 W
m! >.
A ,ontin(,i/n &e )*e&entn "o& %"o*e& de te)e*t(*& en "o& die*ente& nodo& )* )ode* &e* ,o)*do&- *e,o*dndo (e )* e" n"i&i& (e ,on&ide*d " &iet* + "& te)e*t(*& o#tenid& '*,i& " )*o'* de Mt"# )*e&entdo en " &e,,i/n de ne9o&.
Tabla . Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- &iendo x= y=! mm
N$%$ =>1? =>(1; =>?@12 1 3-32 44-656 26-351 2 35-73 44-38 25-204 ( 33-45 44-217 25-048 + 32-17 44-108 25-004
22
45.00 00
40 44-686 31-113 36-36 44-434 26-748 ; 33-7 44-253 25-471 < 32-61 44-144 25-040 3-32 44-656 26-351 1? 35-73 44-38 25-204 11 33-45 44-217 25-048 12 32-17 44-108 25-004
1 2 3 4 5 6 7 8 10 11 12 0 5
10 15 20 25 30 35 40 45 50
Co)*,i/n de Te)e*t(*&
H10 H317 H0-12
Nodo
Te)e*t(* =C>
!r"ca . Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- (ti"indo '*,o de #**&.
Coo &e o#&e*% en " t#" 1- "o& %"o*e& de te)e*t(* )* (n #(en ,ond(,to* )e*ne,en ,e*,no& "o "*'o de " ,o&ti"" ient*& (e )* (n " ,ond(,to*- " te)e*t(* die*e de&de " te)e*t(* de " )*ed =45C> &t e" e9t*eo de " ,o&ti""- donde &( te)e*t(* e& ,e*,n " de" #iente =25C>.
(.2. LITERAL B (.2.1 P!i&!a 'a!t
x= y=+mm
!(0-T +−*T !−+(T 1=!)(
!(0-T !−*T +−*T ,−+(T +(=+*
24
N$%$
N$%$ ;
+(0- T −*T .−* T +-=+*
! (T +−T 1 )+! (T +(−T 1)+! ()*−T 1)+! (T +.−T 1)=(
T ++T +(+)*+T +.−) T 1=(
)T 1−T +−T +(−T +.=)*
N$%$ 1?
)T +(−T !−T ++−T 1−T +=(
N$%$ 11
N$%$ 12
N$%$ 1(
N$%$ 1+
N$%$ 1
N$%$ 1
!(0-T +-−+(T +*−*T /−*T !)=+*
!(T +.−+(T 1−* T +=!!*
!(T +−* T +.−* T +1−+(T +(=(
N$%$ 1
N$%$ 2?
27
+(0,T !)−*T +-−*T !,=.0*
m
m
Ao* ,o)*o#*eo& e" ,"o* de "et ,on (n n"i&i& (nidien&ion" de ,"o*e& + " ,e* "o& #"n,e& de ene*'& ,o**e,t& en ,d nodo + &(iendo T1 ,oo " te)e*t(* de " #&e- &e o#t(%ie*on "o& &i'(iente& *e&("tdo&;
Ca#$! %s% #a 6as
qbase=+,(0,()
T + T ! T , T ) T * T - T . T T 1
45.00 00
42.02 2
A ,ontin(,i/n &e )*e&entn "o& %"o*e& de te)e*t(*& en "o& die*ente& nodo& )* )ode* &e* ,o)*do&- *e,o*dndo (e )* e" n"i&i& (e ,on&ide*d " &iet* + "& te)e*t(*& o#tenid& '*,i& " )*o'* de Mt"# )*e&entdo en " &e,,i/n de ne9o&. Tondo (n #(en ,ond(,to* ,oo
e" o*o =J317 W
m! > + (n " ,ond(,to* ,oo e" )ino =J0-12 W
m! >.
Tabla #. Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- &iendo x= y=+mm
N$%$ =>1? =>(1; =>?@12 1 41-6 44-80 27-887 2 3-2 44-64 25-14 ( 37-2 44-512 25-415 + 35-6 44-33 25-203 34-4 44-23 25-101 33-4 44-212 25-04 ; 32-6 44-14 25-021 < 32-1 44-104 25-003 42-2 44-830 34-751 1? 3-8 44-675 2-747 11 37-8 44-53 27-345 12 36-1 44-421 26-166 1( 34-8 44-321 25-578 1+ 33-8 44-23 25-27 1 33-0 44-176 25-120 1 32-4 44-131 25-01 1; 42-3 44-836 36-370 1< 40-0 44-684 30-7 1 37- 44-548 28-052 2? 36-3 44-430 26-537 21 34- 44-330 25-766 22 33- 44-248 25-371 2( 33-1 44-185 25-15 2+ 32-5 44-140 25-025
31
1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 1 20 21 22 23 24 0.0 5.0
10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
Co)*,i/n de Te)e*t(*&
H10 H317 H0-12
Nodo
Te)e*t(* =C>
Coo &e o#&e*% en " t#" 2- "o& %"o*e& de te)e*t(* )* (n #(en ,ond(,to* )e*ne,en ,e*,n& "o "*'o de " ,o&ti"" ient*& (e )* (n " ,ond(,to*- " te)e*t(* die*e de&de " te)e*t(* de " )*ed =45C> &t e" e9t*eo de " ,o&ti""- donde &( te)e*t(* e& ,e*,n " de" #iente =25C>.
32
(.2.1 S0un%a Pa!t x= y=(0*mm
P* e" n"i&i& &(io& (e )* ,d nodo e" ,"o* in'*e&.
N$%$ 1 )
33
−*T ++!(0,T !−*T ,−+(T +=.0*
N$%$ (
! ( y
−*T !+!(0,T ,−*T )−+(T +1=.0*
S $6s!"a un 'at!*n n #as )ua)i$ns@ '$! #$ u s si&'#i9)a asta # n$%$ 1
N$%$ +
N$%$
N$%$
N$%$ ;
34
N$%$
N$%$ 1?
N$%$ 11
N$%$ 12
N$%$ 1(
N$%$ 1+
N$%$ 1
N$%$ 1
35
N$%$ 1;
11;
−T ++)T +.−T +/−T ,,=)*
N$%$ 1
N$%$ 2?
N$%$ 21
N$%$ 22
N$%$ 2(
N$%$ 2+
N$%$ 2
N$%$ 2
N$%$ 2;
N$%$ 2<
N$%$ 2
N$%$ (?
N$%$ (1
N$%$ (2
1(2
(1(2 )
37
N$%$ ((
N$%$ (+
N$%$ (
N$%$ (
N$%$ (;
N$%$ (<
N$%$ (
N$%$ +?
N$%$ +1
N$%$ +2
N$%$ +(
N$%$ ++
38
N$%$ +
N$%$ +
N$%$ +;
N$%$ +<
N$%$ +
N$%$ ?
N$%$ 1
N$%$ 2
N$%$ (
N$%$ +
N$%$
N$%$
3
N$%$ ;
N$%$ <
N$%$
N$%$ ?
N$%$ 1
N$%$ 2
N$%$ (
N$%$ +
N$%$
40
N$%$
N$%$ ;
N$%$ <
N$%$
N$%$ ;?
N$%$ ;1
N$%$ ;2
N$%$ ;(
N$%$ ;+
N$%$ ;
N$%$ ;
N$%$ ;;
41
N$%$ ;<
N$%$ ;
N$%$ <?
/()+,0.*−(0+*T /(=(
O#teniendo n"ente "& te)e*t(*&;
T1 +(@? T2 41-550 T( 40-263 T+ 3-124 T 38-104 T 37-185 T; 36-358 T< 35-613 T 34-46 T1? 34-352 T11 33-824 T12 33-361 T1( 32-58
42
T1+ 32-612 T1 32-321 T1 32-083 T1; 43-384 T1< 41-37 T1 40-646 T2? 3-48 T21 38-446 T22 37-505 T2( 36-657 T2+ 35-83 T2 35-20 T2 34-58 T2; 34-057 T2< 33-582 T2 33-168 T(? 32-813 T(1 32-514 T(2 32-270 T(( 43-541 T(+ 42-165 T( 40-87 T( 3-73 T(; 38-687 T(< 37-733 T( 36-870 T+? 36-04 T+1 35-37 T+2 34-776 T+( 34-225 T++ 33-740 T+ 33-31 T+ 32-57 T+; 32-653 T+< 32-404 T+ 43-616 T? 42-285 T1 41-037 T2 3-884 T( 38-82 T+ 37-868 T 36- T 36-215
43
T; 35-511 T< 34-883 T 34-326 T? 33-836 T1 33-410 T2 33-044 T( 32-737 T+ 32-486 T 43-63 T 42-323 T; 41-082 T< 3-32 T 38-876 T;? 37-13 T;1 37-041 T;2 36-255 T;( 35-54 T;+ 34-18 T; 34-35 T; 33-868 T;; 33-440 T;< 33-074 T; 32-765 T<? 32-513
qaleta$rmula=+,(0-1 W
m
Ao* ,o)*o#*eo& e" ,"o* de "et ,on (n n"i&i& (nidien&ion" de ,"o*e& + " ,e* "o& #"n,e& de ene*'& ,o**e,t& en ,d nodo + &(iendo T1 ,oo " te)e*t(* de " #&e- &e o#t(%ie*on "o& &i'(iente& *e&("tdo&;
con x=(0* mm y y=) mm
qbase=¿ 130.5028
T +, 33.536
T +) 33.1183
T +* 32.7605
T +- 32.4610
T +. 32.2174
A ,ontin(,i/n &e )*e&entn "o& %"o*e& de te)e*t(*& en "o& die*ente& nodo& )* )ode* &e* ,o)*do&- *e,o*dndo (e )* e" n"i&i& (e ,on&ide*d " &iet* + "& te)e*t(*& o#tenid& '*,i& " )*o'* de Mt"# )*e&entdo en " &e,,i/n de ne9o&. Tondo (n #(en ,ond(,to* ,oo
e" o*o =J317 W
m! > + (n " ,ond(,to* ,oo e" )ino =J0-12 W
m! >.
Tabla $. . Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- &iendo x= y=(2*mm
N$%$ =>1? =>(1; =>?@12 N$%$ =>1? =>(1; =>?@12 1 43-05 44-86 30-03 41 35-37 44-367 25-778
45
2 41-550 44-806 27-271 42 34-776 44-320 25-543 ( 40-263 44-723 26-35 43 34-225 44-277 25-376 + 3-124 44-647 25-85 44 33-740 44-238 25-258 38-104 44-576 25-610 45 33-31 44-204 25-173 37-185 44-510 25-422 46 32-57 44-175 25-10 ; 36-358 44-44 25-24 47 32-653 44-150 25-05 < 35-613 44-32 25-205 48 32-404 44-130 25-017 34-46 44-340 25-143 4 43-616 44-16 40-15 1? 34-352 44-22 25-100 50 42-285 44-834 36-077 11 33-824 44-24 25-06 51 41-037 44-755 32-37 12 33-361 44-211 25-048 52 3-884 44-681 30-630 1( 32-58 44-177 25-032 53 38-82 44-610 28-72 1+ 32-612 44-148 25-020 54 37-868 44-545 27-75 1 32-321 44-123 25-011 55 36- 44-483 26-63 1 32-083 44-102 25-003 56 36-215 44-426 26-377 1; 43-384 44-07 36-541 57 35-511 44-374 25-64 1< 41-37 44-820 32-01 58 34-883 44-327 25-673 1 40-646 44-73 2-534 5 34-326 44-283 25-467 2? 3-48 44-663 28-044 60 33-836 44-245 25-320 21 38-446 44-52 27-087 61 33-410 44-211 25-214 22 37-505 44-526 26-446 62 33-044 44-182 25-135 2( 36-657 44-465 26-008 63 32-737 44-157 25-073 2+ 35-83 44-408 25-704 64 32-486 44-136 25-021 2 35-20 44-356 25-42 65 43-63 44-17 40-450 2 34-58 44-308 25-343 66 42-323 44-836 36-483 2; 34-057 44-265 25-238 67 41-082 44-757 33-327 2< 33-582 44-227 25-163 68 3-32 44-683 30-51 2 33-168 44-13 25-10 6 38-876 44-613 2-218 (? 32-813 44-163 25-06 70 37-13 44-547 27-75 (1 32-514 44-13 25-037 71 37-041 44-485 27-02 (2 32-270 44-118 25-011 72 36-255 44-42 26-46 (( 43-541 44-13 3-107 73 35-54 44-376 26-02 (+ 42-165 44-82 34-730 74 34-18 44-32 25-718 ( 40-87 44-750 31-715 75 34-35 44-286 25-4 ( 3-73 44-674 2-65 76 33-868 44-247 25-342 (; 38-687 44-604 28-247 77 33-440 44-213 25-22 (< 37-733 44-538 27-26 78 33-074 44-184 25-144 ( 36-870 44-476 26-588 7 32-765 44-15 25-078 +? 36-04 44-420 26-112 80 32-513 44-13 25-022
46
(.(. LITERAL C Lo (e &e )idi/ en e" "ite*" , e& %*i* e" %"o* de D )* die*ente& inte*%"o&- e in%e&ti'* "o& ee,to& (e e&to& )*od(,en en " t*n&e*en,i de ,"o* de&de " #&e de " ,o&ti"". @ti"indo e" inte*%"o de LD )*o)(e&to en e" en(n,ido &e o#t(%o " &i'(iente '*,;
Tabla %. S*i,i/n de" e&)e&o* D- nteniendo L $o- ,on J10 W
m! .
D => LD C"o* 1< =F> C"o* 2< =F> Q e**o* ?@<? 10-00 61-81 62-77 1-55 1@2 6-40 76-78 77-2 0-67 1@ 4-83 87-77 87-2 0-17 2@?; 3-87 7-1 6- 0-21 2@+; 3-23 105-50 104-4 0-53 2@<< 2-78 112- 112-08 0-81 (@2 2-43 11-86 118-58 1-07 (@;? 2-16 126-23 124-5 1-30 +@11 1-5 132-20 130-21 1-51 +@1 1-77 137-86 135-50 1-71 +@2 1-63 143-25 140-54 1-0 @(( 1-50 148-42 145-35 2-07
1.00 3.00 5.00 7.00 .00 0.00
1.00
2.00
3.00
LF
P$!)nta: % !!$! 7
!r"ca $. Po*,ent$e de e**o* %& LD- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
e (ti"i*on %"o*e& de D de&de 0.8 &t 5.33. e )(ede o#&e*%*- (e e" e**o* (e &e ,oete " &(i* (e e" ,"o* (e ?(+e de&de " #&e de " ,o&ti"" e& (nidien&ion"- % (entndo ,ono*e (ent e" %"o* de D. e ""e'/ e&t ,on,"(&i/n- de#ido (e e" *e&to de )*o)iedde& + ,ondi,ione& de" )*o#"e- &e nt(%ie*on ,on&tnte& e& de,i*- no %*i*on. En ot*& )"#*&- (e " &(i* (e "o& '*diente& de te)e*t(* t*n&%e*&"e& &on (+ )e(eo&- o en ot*& )"#*&- (e " te)e*t(* &o"o de)end de " di*e,,i/n en U9V &e %n ,oete* eno& e**o*e& &i &e di&in(+e D &t ,ie*to- "(e'o- e" e**o* e)ie (ent*- " '*, indi, (e e" ,"o* en *e"idd e&t ?(+endo en do& di*e,,ione&. Po* &(e*te )* e" inte*%"o de LD ddo- e"
47
e**o* ,oetido- no e& '*nde- )o* "o tnto- " &(n,i/n de ,"o* (nidien&ion" e& (+ ,e)t#"e. e )(ede o#&e*%*- (e &i &e tiene (n e&)e&o* (+ )e(eo- (n(e e" ,"o* &e t*n&it en do& di*e,,ione&- e" e**o* ,oetido " &(i* (e ?(+e en (n di*e,,i/n- e& i**e"e%nte.
+ AN/LISIS DE VARIACIÓN DE LAS PROPIEDADES
@no de "o& o#$eti%o& )*in,i)"e& e* e&t(di* e" ee,to ,(&do " ,#i* (n de "& )*o)iedde& de" )*o#"e ient*& "& de& no %*n.
m!
Tabla &. S*i,i/n de" e&)e&o* D- nteniendo L $o- ,on J0-12 W
m! .
Ca#$! 2D 7
!!$!
?@<? 10-00 6-7 13-72 102-06 1@2 6-40 8-4 14-50 70-80 1@ 4-83 -78 15-11 54-48 2@?; 3-87 10-2 15-64 43-24 2@+; 3-23 11-5 16-12 34-83 2@<< 2-78 12-0 16-54 28-21 (@2 2-43 13-7 16-3 22-81 (@;? 2-16 14-62 17-30 18-2 +@11 1-5 15-41 17-63 14-44 +@1 1-77 16-16 17-5 11-0 +@2 1-63 16-88 18-26 8-16 @(( 1-50 17-57 18-55 5-56
48
50.00
100.00
150.00
LF
P$!)nta: % !!$! 7
!r"ca %. Po*,ent$e de e**o* %& LD- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
m!
Tabla '. S*i,i/n de" e&)e&o* D- nteniendo L $o- ,on J317 W
m!
Ca#$! 2D 7
!!$!
?@<? 10-00 181-3 181-85 0-05 1@2 6-40 12-5 12-74 0-11 1@ 4-83 200-45 200-13 0-16 2@?; 3-87 206-7 206-54 0-21 2@+; 3-23 212-8 212-45 0-25 2@<< 2-78 218-68 218-05 0-2 (@2 2-43 224-1 223-46 0-33 (@;? 2-16 22-57 228-74 0-36 +@11 1-5 234-85 233-2 0-40 +@1 1-77 240-07 23-04 0-43 +@2 1-63 245-24 244-11 0-46 @(( 1-50 250-36 24-14 0-4
4
1.00 3.00 5.00 7.00 .00 0.00 0.10 0.20 0.30 0.40 0.50 0.60
% E!!$! "s. LF >?? >(1; 7O!$
LF
P$!)nta: % !!$! 7
!r"ca &. Po*,ent$e de e**o* %& LD- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
e o#&e*% (e e" e**o* (e &e ,oete " )*o9i* "o& %"o*e& de ,"o* de ne* (nidien&ion"- di&in(+en " oento (e &e tiene (n #(en ,ond(,to*.
Con e&te n"i&i& &e )(ede ,on,"(i* (e e" 9io e**o* en )o*,ent$e- " &(i* (e e" ,"o* ?(+e en (n dien&i/n- e& +o* en e" )ino (e en e" o*o. E&t& '*,&- &e "& *e"i*on nteniendo- e" *e&to de )*o)iedde& ,on&tnte& + (ti"indo e" i&o inte*%"o LD de" "ite*" ,. i e" te*i"- )o&ee e$o*e& )*o)iedde& de ,ond(,to*- "o& '*diente& de te)e*t(*- en ,d &e,,i/n t*n&%e*&" de " ,o&ti""- %n &e* & )e(eo& + " o* ,oo ?(+e e" ,"o*- % &ee$*&e e$o* (n ,o)o*tiento (nidien&ion" + e" e&t(dio de" ,"o* en do& dien&ione&- &e* eno& ne,e&*io- e&to o*** e&(e*o en ,",("o& de & nodo&.
P* )o+* Wn & n(e&t*& ,on,"(&ione& (e "o& '*diente& de te)e*t(* &on (+ )e(eo& &i e" te*i" e& (n e$o* ,ond(,to* o )o&ee (n '*n %"o* de ,ond(,ti%idd t*i, &e *e"i/ " '*, de '*diente de te)e*t(*&- tondo en ,(ent "& te)e*t(*& o#tenid& en (n n"i&i& (nidien&ion".
50
O*o =TC >
1 2-3 42-0 44-8 1-5 27-0 40-7 44-7
2 25- 3-6 44-7 2-5 25-4 38-5 44-6
3 25-2 37-5 44-5 3-5 25-1 36-7 44-5
4 25-0 35- 44-4 4-5 25-0 35-2 44-4
5 25-0 34-6 44-3 5-5 25-0 34-0 44-3
6 25-0 33-5 44-2 6-5 25-0 33-1 44-2
7 25-0 32-8 44-2 7-5 25-0 32-5 44-1
8 25-0 32-2 44-1
0 1 2 3 4 5 6 7 8 20
25
30
35
40
45
50
H &()(e&to
T&'!atu!as 7C
En " '*, o#tenid- not#"e (e " ,ond(,ti%idd *e'(" " U(nio*iddV de " te)e*t(* en " "et. C(ndo e&t )*o)iedd e& (+ "t =,oo e& e" ,&o de" o*o> e" '*diente e& ,&i n("o. A(e""o no o,(**e en "o& no ,ond(,to*e& ,oo e" )ino o en e" te*i" &()(e&to ,(+o '*diente e& )*on(n,ido. e de#e *e,o*d* (e e" te*i" &()(e&to ten (n %"o* de H i'(" 10 FH. e %e (e edinte (ent e" %"o* de H- " oento (e &e ,#i )o&i,i/n nod"- ,d nodo tiene (n eno* die*en,i de te)e*t(* ,on e" nodo %e,ino.
Ao*- &e %e* e" ee,to di*e,to de ,#i* "o& %"o*e& de H nteniendo "o& %"o*e& de "& de& )*o)iedde& ,on&tnte& de "o& "ite*"e& + #. e de#e en,ion* (e )* )ode* ,",("* e" ,o)o*tiento #idien&ion" de "o& ,"o*e& en ,d (no de "o& n"i&i& )*e%io& + en e" )*e&ente &e (ti"i/ (n &e)*,i/n de *endi$ de %K>%>?@&& + (e " )*o9i,i/n #idien&ion" &e* & )*e,i&. En *e&(en &e o#t(%ie*on e&to& %"o*e&;
Tabla (. S*i,i/n de " ,ond(,ti%idd- nteniendo $o- ,on d9d+0-5.
7F&= Ca#$! 1% 7
Ca#$! 2% 7
!!$!
1?@?? 130-6 128-78 1-46 2?@?? 165-51 163-78 1-05 (?@?? 183-54 181-6 0-86
52
+?@?? 14-5 13-12 0-76 ?@?? 202-06 200-68 0-68 ?@?? 207-45 206-14 0-63 ;?@?? 211-52 210-27 0-5 <?@?? 214-71 213-50 0-56 ?@?? 217-26 216-0 0-54 1??@?? 21-37 218-23 0-52 1?@?? 225-8 224-4 0-46 2??@?? 22-47 228-4 0-42 2?@?? 231-63 230-6 0-40 (??@?? 233-0 232-18 0-3 (?@?? 234-15 233-26 0-38 +??@?? 234-5 234-08 0-37
0.00 200.00 400.00 600.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
% E!!$! "s. L>< >+ >??
7C$NDUCTIVIDAD TRMICA
P$!)nta: % !!$! 7
!r"ca '. Po*,ent$e de e**o* %& J- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
E&to& *e&("tdo&- )o+n #&tnte " ,on,"(&i/n nte*io*- de (e &i (n te*i" e& e$o* ,ond(,to*- "o& '*diente& de te)e*t(* ent*e nodo + nodo- &on de&ido )e(eo&- + (e e" e**o* de &(i* (e e" ,"o* ?(+e en (n dien&i/n di&in(i*. <e e,o- &e )(do (ti"i* en " '*,- te*i"e& ,on e$o* ,ond(,ti%idd t*i,- )e*o "o& te*i"e& ,on ,ond(,ti%idd t*i, +o*e& 300 FH &on ,ono,ido& ,oo te*i"e& &()e*,ond(,to*e&. Lo&
53
te*i"e& &()e*,ond(,to*e&- )e&* de tene* #(en& )*o)iedde& de ,ond(,to*- &/"o (n,ionn ,oo ,ond(,to*e& ,ie*t& te)e*t(*& ,*ti,&- "& ,("e& &on (+ #$&- ="*ededo* de 1 H 20 H>. Ot*o dee,to de e&to& te*i"e&- e& (e &on (+ di,i"e& de ,on&e'(i*- + )o* "o tnto- &( )*e,io e& (+ "to. i &e % t*#$* (n e)*e& ,on e&to& te*i"e&- e" ,o&to de o)e** ,on e""o&- &e* t#in (+ "to- + (e &e de#e ,()"i* e&t*i,t& ,ondi,ione& de t*#$o. Po* e&o no &e &(ti"in ,ond(,ti%idde& & "t& en " t#" + en " '*, "o& )(nto& (ti"ido&- (e*on & (e &(,iente& )* ,o)*o#* n(e&t*& ,on,"(&ione& ,e*, de" ,#io de te*i"- en "o& "ite*"e& + #.
A" ,o)** "& t*n&e*en,i& de ,"o* o#tenid& ,iendo (n n"i&i& #idien&ion" ,on (no (nidien&ion" &e o#tiene "o& &i'(iente& *e&("tdo&;
110.00
160.00
210.00
@nidien&ion"
Bidien&ion"
T!ans3!n)ia % )a#$! 7
L )o, die*en,i ent*e & ,(*%& )o+ " ,on,"(&i/n de (e (n n"i&i& #idien&ion" no e& ne,e&*io )* die*ente& %"o*e& de J- de e,o e" te*i" " tene* e$o*e& )*o)iedde& de ,ond(,to* &e di&tin'(e eno& "& do& '*,&.
54
Ao* " )*o)iedd (e &e (ie*e %*i* e& e" ,oe,iente ,on%e,ti%o de" edio en e" (e &e en,(ent* " ,o&ti"" o en ot*& )"#*& e" edio en e" (e e&t &e (#i,.
e &,*on "o& &i'(iente& *e&("tdo&;
T#" 8. S*i,i/n de" ,oe,iente de ,on%e,,i/n- nteniendo J $o- ,on d9d+0-5.
7F&2=
Ca#$! 1% 7
Ca#$! 2% 7
P$!)nta: % !!$! 7
!r"ca (. Po*,ent$e de e**o* %& - tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
55
<e e&t '*, &e ""e' " ,on,"(&i/n (e e" e**o* ,oetido ,(ndo &e (ti"i (n edio ,on +o* ,oe,iente ,on%e,ti%o e)ie ,*e,e*. A(n(e &e o#&e*% (e e"
e**o* ,oetido " &(i* (e e" ,"o* ?(+e en (n dien&i/n e& (+ )e(eo )* de&)*e,i* " )o&i#i"idd de (e e" ,"o* ?(+ en (n &o" di*e,,i/n- &e * (n n"i&i& & )*o(ndo de" ,&o. e n"i* "o& '*,o& de '*diente de te)e*t(* de ,"o*e& (nidien&ion"e&- e&to& (e*on "o& *e&("tdo& o#tenido&;
56
<9= >
2J =TC
0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 0-5 44-6 44-3 44-0 43-8 43-6 43-4 43-3 43-2 43-0 42-
1 44-2 43-6 43-1 42-7 42-3 42-0 41-8 41-5 41-3 41-1 1-5 43-8 42- 42-2 41-6 41-2 40-7 40-4 40-0 3-7 3-4
2 43-5 42-3 41-4 40-7 40-1 3-6 3-1 38-7 38-3 38-0 2-5 43-1 41-8 40-7 3-8 3-1 38-5 38-0 37-5 37-1 36-7
3 42-8 41-3 40-0 3-0 38-2 37-5 36- 36-4 36-0 35-5 3-5 42-6 40-8 3-4 38-3 37-4 36-7 36-0 35-5 35-0 34-5
4 42-3 40-4 38- 37-7 36-7 35- 35-2 34-6 34-1 33-6 4-5 42-1 40-0 38-4 37-1 36-0 35-2 34-5 33-8 33-3 32-8
5 41- 3-6 37- 36-6 35-5 34-6 33-8 33-2 32-6 32-1 5-5 41-7 3-3 37-5 36-1 34- 34-0 33-2 32-6 32-0 31-5
6 41-5 3-0 37-1 35-7 34-5 33-5 32-7 32-1 31-5 31-0 6-5 41-3 38-7 36-8 35-3 34-1 33-1 32-3 31-6 31-0 30-5
7 41-2 38-5 36-5 35-0 33-8 32-8 31- 31-2 30-7 30-2 7-5 41-1 38-4 36-3 34-7 33-5 32-5 31-6 30- 30-3 2-8
Con &( *e&)e,ti% '*, de '*diente& de te)e*t(*;
0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 2
34
3
44
4
%K 7&&
T&'!atu!a 7C#sius
E&te '*,o (e&t* ,oo %* " di&t*i#(,i/n de te)e*t(* ,on *e&)e,to " ,oe,iente ,on%e,ti%o. i &e tiene (n ,oe,iente =100 )o* e$e)"o> " di&t*i#(,i/n e& ,&i n(" en ,#io )* %"o*e& "to& de =,oo 1000 )o* e$e)"o> " ,(*% )*e&ent (n )endiente & )*on(n,id + )o* ende (n ,#io & ,e"e*do de " te)e*t(* ,on *e&)e,to " )o&i,i/n nod". Po* e""o &e )(ede de,i* (e e" (ento de" ,oe,iente ,on%e,ti%o =(e de)ende de" ?(ido> ,e (e e" '*diente de te)e*t(* ,#ie ,on&ide*#"eente )e*o " %e (ent e" ,"o* e9)("&do )o* " "et.
Ao* &e )*o,ede* n"i* " ,(*% X %& ,oe,iente ,on%e,ti%o )* "o& do& n"i&i& *e"ido&.
57
@nidien&ion"
Bidien&ion"
7F&2=
T!asn3!n)ia % )a#$! 7
E&t '*, " ini,io (e&t* (n "ne (+ ,(*%. E" ,#io de" ,"o* )* %"o*e& de UV eno*e& 300 e& )*on(n,ido. C#io& "i'e*o& en e" ,oe,iente ,on%e,ti%o en e&t *e'i/n )*od(,i* ee,to& (+ ,on&ide*#"e& en e" ?($o de ,"o*. Pe*o de&)(& de e&te %"o* e" ,*e,iiento de " ,(*% &e ,o)o*t ,&i "ine"ente )o* "o (e &e )od* &(i* (e e" )*o,e&o &e Ue&t#i"iV + e" (ento de" ,oe,iente ,on%e,ti%o no e$o* de&ido " t*n&e*en,i de ,"o*. En e&t '*, &e )(ede die*en,i* e$o* #& '*,& ,ono*e &e (ent e" ,oe,iente ,on%e,ti%o- &e )(ede ,on,"(i* (e e" ,oe,iente ,on%e,ti%o tiene (n +o* in?(en,i en ,#i* "o& '*diente& de te)e*t(* ent*e "o& nodo& %e,ino&.
Ao* " %*i#"e ,#i* &e* " "on'it(d L de " ,o&ti""- ,on e&to &e )od* )*ede,i* " i)o*tn,i de " 'eoet* de e&t en " t*n&e*en,i de ,"o*.
e o#t(%ie*on "& &i'(iente& t#"& de *e&("tdo&;
58
L12
=TC>
L23
=TC>
L30
=TC>
L35
=TC>
L40
=TC>
0 45-0 45-0 45-0 45-0 45-0 45-0 0-5 43-5 43-4 43-3 43-3 43-3 43-3
1 42-2 41- 41-8 41-8 41-8 41-8 1-5 41-0 40-5 40-4 40-4 40-4 40-4
2 40-0 3-3 3-1 3-1 3-1 3-1 2-5 3-0 38-1 38-0 38-0 38-0 38-0
3 38-1 37-1 36- 36- 36- 36- 3-5 37-4 36-1 35- 35- 35- 35-
4 36-7 35-2 35-0 35-0 35-0 35-0 4-5 36-1 34-4 34-2 34-2 34-2 34-2
5 35-7 33-7 33-4 33-4 33-4 33-4 5-5 35-2 33-1 32-7 32-7 32-7 32-7
6 34- 32-5 32-1 32-1 32-1 32-1 6-5 31- 31-5 31-5 31-5 31-5
7 31-4 31-0 31-0 31-0 31-0 7-5 31-0 30-5 30-5 30-5 30-5
8 30-6 30-0 30-0 30-0 30-0 8-5 30-2 2-6 2-6 2-6 2-6 2- 2-2 2-2 2-2 2-2
-5 2-6 28- 28- 28- 28- 10 2-4 28-6 28-5 28-5 28-5
10-5 2-2 28-3 28-2 28-2 28-2 11 2-0 28-0 28-0 28-0 28-0
11-5 28-8 27-8 27-7 27-7 27-7 12 28-7 27-5 27-5 27-5 27-5
12-5 27-3 27-3 27-3 27-3 13 27-1 27-1 27-1 27-1
13-5 27-0 26- 26- 26- 14 26-8 26-8 26-8 26-8
14-5 26-7 26-6 26-6 26-6 15 26-5 26-5 26-5 26-5
15-5 26-4 26-4 26-4 26-4 16 26-3 26-3 26-3 26-3
16-5 26-2 26-2 26-1 26-1 17 26-1 26-1 26-1 26-1
17-5 26-0 26-0 26-0 26-0 18 26-0 25- 25- 25-
18-5 25- 25-8 25-8 25-8 1 25-8 25-8 25-7 25-7
1-5 25-8 25-7 25-7 25-7 20 25-7 25-6 25-6 25-6
20-5 25-7 25-6 25-6 25-6 21 25-7 25-5 25-5 25-5
60
21-5 25-6 25-5 25-5 25-5 22 25-6 25-5 25-4 25-4
22-5 25-6 25-4 25-4 25-4 23 25-6 25-4 25-4 25-4
23-5 25-4 25-3 25-3 24 25-3 25-3 25-3
24-5 25-3 25-3 25-3 25 25-3 25-3 25-3
25-5 25-3 25-2 25-2 26 25-2 25-2 25-2
26-5 25-2 25-2 25-2 27 25-2 25-2 25-2
27-5 25-2 25-2 25-2 28 25-2 25-2 25-2
28-5 25-2 25-2 25-1 2 25-2 25-1 25-1
2-5 25-2 25-1 25-1 30 25-2 25-1 25-1
30-5 25-1 25-1 31 25-1 25-1
31-5 25-1 25-1 32 25-1 25-1
32-5 25-1 25-1 33 25-1 25-1
33-5 25-1 25-1 34 25-1 25-1
34-5 25-1 25-1 35 25-1 25-1
35-5 25-0 36 25-0
36-5 25-0 37 25-0
37-5 25-0 38 25-0
38-5 25-0 3 25-0
3-5 25-0 40 25-0
Ao* &e )*o,ede* '*,* ,oo %*n "& *e",ione& LD de ,(e*do. Coo D &e nt(%o ,on&te " o* en (e LD + %*ido e& ,#indo " "on'it(d. e o#tiene " &i'(iente '*,;
61
0 5 10 15 20 25 30 35 40 45 23
28
33
38
43
48
L6 L12 L23 L30 L35 L40
%K 7&&
Coo &e )(ede o#&e*%* en e&t '*,- edid (e (ent " "on'it(d L de " "et ,on *e&)e,to " n,o D- " te)e*t(* en e" #o*de de " "et di&in(+e + &e )*o9i & " de" #iente. E&to &e de#e (e " ene*' (e ?(+e t*%& de e"" de#e *e,o**e* & di&tn,i " ,iendo (e &e &ii"e ,&i tod " n" de e&t.
Po* e$e)"o ,(ndo LD0-25 " %*i,i/n de te)e*t(* %* de 45 &t 43C- ient& (e LD8 " te)e*t(* de,*e,e de 45 32 C " ,(" e& & ,e*,n " de" #iente =25YC> (e en e" e$e)"o nte*io*.
P* )ode* n"i* e$o* "o& e**o*e& ,oetido& " ,#i* "& dien&ione& de " "et + &(i* (e e" ,"o* e& (nidien&ion" &e (&*on "& ,ondi,ione& )*o)(e&to& )o* e" "ite*" , nteniendo ,on&tnte e" e&)e&o* D + e" *e&to de %*i#"e& de" )*o#"e.
e o#t(%o " &i'(iente t#" de *e&("tdo&;
L7&& LF Ca#$! 1% 7
Ca#$! 2% 7
@?? 1-50 122-8 120-8 1-70 @+? 2-35 133-77 132-11 1-24
12@<? 3-20 137-26 136-40 0-63 1@2? 4-05 138-35 138-46 0-07 1@? 4-0 138-6 13-1 0-88 2(@?? 5-75 138-7 141-2 1-80 2@+? 6-60 138-83 142-75 2-82 2@<? 7-45 138-84 144-34 3-6 ((@2? 8-30 138-84 146-08 5-22
62
1.00 3.00 5.00 7.00 .00 0.00
2.00
4.00
6.00
8.00
10.00
e o#t(%o " &i'(iente '*,;
e )(ede o#&e*%*- (e e" e**o* (e &e ,oete " &(i* (e e" ,"o* (e ?(+e de&de " #&e de " ,o&ti"" e& (nidien&ion"- % (entndo ,ono*e (ent e" %"o* de L. e ""e'/ e&t ,on,"(&i/n- de#ido (e e" *e&to de )*o)iedde& + ,ondi,ione& de" )*o#"e- &e nt(%ie*on ,on&tnte& e& de,i*- no %*i*on. En ot*& )"#*&- (e " &(i* (e "o& '*diente& de te)e*t(* t*n&%e*&"e& &on (+ )e(eo&- o en ot*& )"#*&- (e " te)e*t(* &o"o de)end de " di*e,,i/n en U9V &e %n ,oete* eno& e**o*e& &i &e (ent L &t ,ie*to )(nto- "(e'o- e" e**o* e)ie (ent*- " '*, indi, (e e" ,"o* en *e"idd e&t ?(+endo en do& di*e,,ione&. P* inte*%"o de LD ddo )o* e" "ite*" , &e o#&e*% (e "o& e**o*e& ,oetido& &()e*n "
63
8Q- " &(n,i/n de ,"o* (nidien&ion" no e& ,e)t#"e. e )(ede o#&e*%*- (e &i &e tiene (n L (+ '*nde- e" e**o* ,oetido " &(i* (e e" ,"o* ?(+e en (n di*e,,i/n- e& '*nde.
Ao* &e % ,o)** "& ,(*%& o#tenid& t*n&e*en,i de ,"o* &(iendo ,"o* (nidien&ion" + #idien&ion"ente %& e" ,#io de "on'it(d L.
0.00 50.00
@nidien&ion"
Bidien&ion"
T!ans3!n)ia % Ca#$! 7
e o#&e*% (e " to* e" ?($o de ,"o* de ne* #idien&ion"- " t*n&e*en,i de e&t (ent de +o* ne* (e en e" ,&o (nidien&ion". E& de,i* &i &e &(e (e e&te ?(+e en (n &o" di*e,,i/n )* "et& & "*'& &e ,oeten (,o& e**o*e& de ,",("o de t*n&e*en,i de ,"o*. <e e,o& &e )(ede die*en,i* (,o e$o* #& ,(*%& (e " %*i* "o& ,&o& nte*io*e&. En ,on,"(&i/n en *e"idd ,(ndo &e tienen "et& (+ '*nde& " ene*' en o* de ,"o* &e di&i) &t t" )(nto (e " te)e*t(* en 9L &e "o & ,e*,n " de" #iente- + de#ido (e *e,o**e & di&tn,i e&t &e )ie*de en +o* )*o)o*,i/n.
64
CONCLUSIONES
En e" "ite*" &e o#&e*% (e "o& %"o*e& o#tenido& dent*o de (n i& ,o"(n de nodo& &e )*o9in "& te)e*t(*&- ient*& (e "& te)e*t(*& de "& ,o"(n& )* "& di&tint& )o&i,ione& "o "*'o de " "et %*n. R/n )o* " ,(" e" %"o* o#tenido de " t*n&e*en,i de ,"o* de o* #idien&ion" )(do o#tene*&e ,oo &i &e *e&o"%ie* de o* (nidien&ion".
P* " &o"(,i/n de" "ite*" # &e 'ene* +o* ,ntidd de nodo& + ,on e""o& +o* nWe*o de e,(,ione&- "o (e 'ene* (n +o* e9,tit(d de " te)e*t(* en dete*indo& )(nto& de " "et.
!in"ente en e" "ite*" , &e o#&e*% (e " %*i* " */n LD- " ,(" &e en,(ent* en (n *n'o de 1.5 + 10- &e %* " dien&i/n ) " i'(" (e e" %"o* de " t*n&e*en,i de ,"o* + (e &t t#in de)ende de " "et. Ade& &e 'ene*/ " '*, de" porcenta*e de error vs L+), donde ient*& " */n LD &e )e(e &e 'ene* (n " )*o9i,i/n e& de,i*- +o* ) =n,o> e9i&ti* (n " )*o9i,i/n.
clc
h=input('Ingresar coeficiente de coneccion [W!m"#$]:');
$=input('Ingresar coeficiente de conduccion [W!m#$]:');
%=input('Ingresar ingresar temperatura en la %ase [&]:');
a=input('Ingresar ingresar temperatura del am%iente [&]:');
n=L!x; m=(W!y);
(-")=.(($+y)!("+x));
(-n,)=.(($+x)!(y));
/=*eros(((n+m),n)-);
for i=":n.
(n-n.)=.(($+y)!("+x));
(((n+0),)-((((0.)+n),)))=.(($+x)!y);
(((n+0),)-((0+n),"))=.(($+y)!x);
(((n+0),)-((((0,)+n),)))=.(($+x)!y);
(((n+f),g,)-((n+(f.)),g,))=.(($+x)!y);
(((n+f),g,)-((n+f),g,"))=.(($+y)!x);
(((n+f),g,)-((n+(f,)),g,))=.(($+x)!y);
(((n+f),g,)-((n+f),g))=.(($+y)!x);
((n+p)-((n+p).n))=.(($+x)!("+y));
((n+p)-((n+p),n))=.(($+x)!("+y));
((n+p)-((n+p).))=.(($+y)!x);
(((n+m),)-(((n+m).n),))=.(($+x)!y);
(((n+m),)-((n+m),"))=.(($+y)!(x+"));
for 1=(m+n),":(n+m),n.
(1-1)=((h+x),(($+y)!x),(($+x)!y));
((n+m),n-n+m)=.(($+x)!("+y));
((n+m),n-(n+m),n.)=.(($+y)!("+x));
/((n+m),n-)=(((h+x)!"),((h+y)!"))+a;
&=in()+/;
end
6.2 ANÁLII GRÁ!ICO
Ot* o* de )*e,i* " %*i,i/n de te)e*t(* e& ,on (n di&t*i#(,i/n de ,o"o*e& (e *e)*e&enten " te)e*t(* "o "*'o de " ,o&ti""- )o* "o (e )*e&ento& ,ontin(,i/n )* "o& die*ente& %"o*e& de J;
67
m!
68
Figura #. <i&t*i#(,i/n '*, de te)e*t(* &iendo x= y=! mm
m!
Con e&te n"i&i& '*,o &e o#&e*% ,oo +o* ,ntidd de nodo&- " te)e*t(* "o "*'o de " ,o&ti"" &e di&t*i#(+e de o* & &(%id e& de,i*- no &e o*n tnt& *e,t& ,o)*d& ,on " di&t*i#(,i/n en "& '(*&
)* (n x= y=!mm ,oo en " '(* 1 o&t*d nte*io*ente.
P* J317 W
m!
72
m!
73
74
2.2.1. En un instant t................................................................................2
2.(. GENERACIÓN DE ENERGÍA.................................................................3
2.(.1 C$n%u))i*n..........................................................................................4
2.. ALETAS DE /REA DE SECCIÓN TRANSVERSAL UNI,ORME............8
(. PLANTEAMIENTO DEL PROBLEMA.........................................................10
(.1. LITERAL A...........................................................................................11
(.2. LITERAL B...........................................................................................18
(.(. LITERAL C...........................................................................................37
CONCLUSIONES........................................................................................43
ANE-OS.....................................................................................................44
1.OBJETIVOS
E" o#$eti%o de" &i'(iente )*o+e,to- e& o*ient* ,e*, de (n int*od(,,i/n "o& odo& de t*n&e*en,i de ,"o*- ,on n&i& en "o& (ndento& de ,ond(,,i/n + ,on%e,,i/n- + de&)*e,indo " t*n&e*en,i de ,"o* )o* *di,i/n. e n"i*n )*o#"e& de t*n&e*en,i de ,"o* )o* ,ond(,,i/n (nidien&ion" + ("tidien&ion"- en e&tdo e&t#"e- t*%& de todo& n"ti,o& + n(*i,o&.
E" o#$eti%o )*in,i)" de e&te )*o+e,to e& )"i,* e" todo de die*en,i& nit& en " *e&o"(,i/n de )*o#"e& de ,ond(,,i/n (nidien&ion" + #idien&ion" en e&tdo e&t#"e.
2.MARCO TEÓRICO
2.1. REQUERIMIENTO DE CONSERVACIÓN DE LA ENERGÍA
L te*odini,- + " t*n&e*en,i de ,"o*- &on do& ,ien,i& (e e&tn ntiente *e",iond& + (e " te*odini,- t*t &o#*e " velocidad " (e &e t*n&e*e ,"o*- ient*& (e " t*n&e*en,i de ,"o*- &e ,on&ide* (n e9ten&i/n de " te*odini,. E" (&o de " )*ie* "e+ de " te*odini,- e& de,i*- " ley de la conservación de la energía, $(e' (n ))e" i)o*tnt&io- en e" de&**o""o de "o& )*o#"e& de t*n&e*en,i de ,"o*.
2.2. CONSERVACIÓN DE LA ENERGÍA PARA UN VOLUMEN DE CONTROL
P* )"i,* " )*ie* "e+ de " te*odini,- &e de#e identi,* )*ie*o- e" %o"(en de ,ont*o"- e" ,(" *e)*e&ent (n *e'i/n t*idien&ion" en e" e&),io- "iitd )o* (n &()e*,ie de ,ont*o"- t*%& de " ,("- )(eden in'*e&* " ene*' + " te*i. L )*ie* "e+ de#e &ti&,e*&e &o#*e ,("(ie* inte*%"o
de tie)o t )* e&te inte*%"o- de#e e9i&ti* (n #"n,e ene*'ti,o- ent*e
"& ,ntidde& de todo& "o& ,#io& de ene*'- edido& en :o("e&.
2.2.1. En un instant t L %e"o,idd " (e " ene*' t*i, + e,ni, in'*e& en (n %o"(en de ,ont*o"- & " %e"o,idd " (e &e 'ene* ene*' t*i, dent*o de" %o"(en de ,ont*o"- eno& " %e"o,idd " (e &"e ene*' t*i, + e,ni, de" %o"(en de ,ont*o" de#e &e* i'(" " %e"o,idd de in,*eento de " ene*' ",end dent*o de" %o"(en de ,ont*o".
2
2.2.2. En un int!"a#$ % ti&'$ t
L ,ntidd de ene*' t*i, + e,ni, (e in'*e& en (n %o"(en de ,ont*o"- & " ,ntidd de ene*' t*i, (e &e 'ene* dent*o de" %o"(en de ,ont*o"- eno& " ,ntidd de ene*' t*i, + e,ni, (e &"e de" %o"(en de ,ont*o" de#e &e* i'(" " in,*eento en " ,ntidd de ene*' ",end en e" %o"(en de ,ont*o".
E" )*ie* )&o en e&t *e&o"(,i/n- ,on&i&te en identi,* " &()e*,ie de ,ont*o"- t*ndo (n "ne )(nted. E" &i'(iente )&o- ,on&i&te en identi,* "o& t*ino& de ene*'- e&to& t*ino& in,"(+en; L ene*' t*i, + e,ni, (e ent* + &"e de" %o"(en de ,ont*o" de& de e&to- e& )o&i#"e 'ene** ene*' t*i, dent*o de" %o"(en de ,ont*o"- de#ido " ,on%e*&i/n de ot*& o*& de ene*'- e&te )*o,e&o- e& ,ono,ido ,oo 'ene*,i/n de ene*'. L e,(,i/n- de" #"n,e ene*'ti,o- (ed &;
´ Eent + ´ Eg− Esale= dEalm
dt ≡ ´ Ealm
<e donde;
´ Eent = Energía térmica y mecánica que entraal volumen de control[W ]
´ Esale= Energíatérmica y mecánica que sale del volumen de control[W ]
´ E g=Cantidad de energía térmicaque se genera dentro del volu mende control[W ]
dEalm
dt =Velocidadde cambiodela energíaalmacenadadentrodelvolumende control[W ]
Conservación de la energía para un volumen de control. Aplicación en un instante.
2.(. GENERACIÓN DE ENERGÍA E" t*ino 'ene*,i/n de ene*'- &e &o,i ,on " ,on%e*&i/n de ot* o* de ene*' =(i,- e",t*i,- e"e,t*o'nti, o n(,"e*> ene*' t*i,. E& (n fenómeno volumétrico.
E9i&ten t*e& odo& de t*n&e*en,i de ,"o*;
3
2.(.1 C$n%u))i*n
e ,on&ide* ,oo " t*n&e*en,i de ene*' de "& )*t,("& & ene*'ti,& "& eno& ene*'ti,& de (n &(&tn,i- de#ido "& inte*,,ione& ent*e "& i&&. P* e&te todo de t*n&e*en,i de ,"o*- " e,(,i/n o ode"o- &e ,ono,e ,oo " Ley de Fourier:
q } rsub {x} =-k {dT} over {dx} ¿
<e donde;
q } rsub {x} =Flujo de calor o transferencia de calor por unidad de área [W/ {m} {!} " ¿
dT
! =Conductividad térmica[W /m " # ]
E" &i'no eno&- e indi,- (e &e t*n&e*e ,"o* en " di*e,,i/n de " te)e*t(* de,*e,iente.
E&t e,(,i/n- &e ode" en " &i'(iente '(*;
4
2.(.2. C$n"))i*n
E" odo de t*n&e*en,i de ,"o* )o* ,on%e,,i/n &e &(&tent tnto en e" o%iiento o"e,("* "eto*io ,oo en e" o%iiento %o"(t*i,o de" ?(ido en " ,) "ite. L ,ont*i#(,i/n de#id " o%iiento o"e,("* "eto*io =di(&i/n> doin ,e*, de " &()e*,ie donde " %e"o,idd de" ?(ido e& #$.
E&te odo de t*n&e*en,i de ,"o*- &e ,"&i, de ,(e*do ,on " nt(*"e de" ?(ido e9i&ten do& ti)o& de ,on%e,,i/n;
1 C$n"))i*n 3$!4a%a5 C(ndo e" ?($o e& ,(&do )o* edio& e9te*no&- ,oo (n %enti"do*- #o#& o %iento& to&*i,o&.
2 C$n"))i*n #i6! 7natu!a#5 E" ?($o e& ind(,ido )o* (e*& de e)($e- (e &(*'en )*ti* de die*en,i& de den&idd o,&iond& )o* %*i,ione& de te)e*t(* en e" ?(ido.
in i)o*t* " nt(*"e )*ti,("* de" )*o,e&o de t*n&e*en,i de ,"o* )o* ,on%e,,i/n- " e,(,i/n o ode"o )*o)ido e& de " o*;
q =#$ {T} rsub {s} - {T} rsub {%} &
<e donde;
T s=Temperaturadela super$icie[ # ]
" # ]
C#e *e,",* (e e" ,oe,iente de t*n&e*en,i de ,"o* )o* ,on%e,,i/n- de)ende de "& ,ondi,ione& en " ,) "ite- en "& (e in?(+en " 'eoet* de " &()e*,ie- " nt(*"e de" o%iiento de" ?(ido + (n &e*ie de )*o)iedde& te*odini,& de" ?(ido + de t*n&)o*te.
Dsa!!$##$ % #a )a'a #8&it n #a t!ans3!n)ia % )a#$! '$! )$n"))i*n
En e" de&**o""o de e&te )*o+e,to- e" todo de " t*n&e*en,i de ,"o* )o* *di,i/n- &e ,on&ide*/ de&)*e,i#"e.
2.+. TRANS,ERENCIA DE CALOR EN SUPER,ICIES E-TENDIDAS
@n %e- (e &e t(%ie*on ,"*o& todo& "o& ,on,e)to& e9)"i,do& )*e%iente. e de#e ,ono,e* (e e" de&**o""o de n(e&t*o )*o+e,to- ,on&i&ti/ en " t*n&e*en,i de ,"o* )o* ,ond(,,i/n + ,on%e,,i/n- )e*o t*%& de supercies extendidas. E&t *&e- ,e *ee*en,i (n &/"ido (e e9)e*ient t*n&e*en,i de ene*' )o* ,ond(,,i/n + ,on%e,,i/n dent*o de &(& "ite& + "o& "*ededo*e&. E9i&ten (,& &it(,ione& (e i)"i,n ee,to& ,o#indo& de ,ond(,,i/n + ,on%e,,i/n- " )"i,,i/n & *e,(ente- e& (e"" en " (e &e (& (n &()e*,ie e9tendid de ne* e&)e,, )* aumentar " *)ide de t*n&e*en,i de ,"o* ent*e (n &/"ido + (n ?(ido ,onti'(o e&t &()e*,ie e9tendid- &e denoin aleta.
6
Us$ % a#tas 'a!a au&nta! #a t!ans3!n)ia % )a#$! %s% una 'a!% '#ana. Su'!9)i )$n a#tas.
A" e9in* " '(* nte*io*- &e )(ede )*e,i* (e " t*n&e*en,i de ,"o*- &e in,*eent (entndo e" *e de " &()e*,ie t*%& de " ,(" o,(**e " ,on%e,,i/n. E&to &e "o'* ,on e" e)"eo de aletas (e &e extienden de&de " )*ed " ?(ido ,i*,(ndnte.
Di3!nts )$n90u!a)i$ns % a#tas5
1 A#ta !)ta % s))i*n t!ans"!sa# uni3$!&5 E& ,("(ie* &()e*,ie )*o"on'd (e &e (ne (n pared plana ,on *e t*n&%e*&" ,on&tnte. =E&te e& e" ode"o de e$e)"o de n(e&t*o )*o+e,to>.
A#ta !)ta % s))i*n t!ans"!sa# uni3$!&
7
2 A#ta !)ta % s))i*n t!ans"!sa# n$ uni3$!&5 E& ,("(ie* &()e*,ie )*o"on'd (e &e (ne (n pared plana ,on *e t*&%e*&" %*i#"e.
A#ta !)ta % s))i*n t!ans"!sa# n$ uni3$!&
( A#ta anu#a!5 A(e"" (e &e (ne de o* ,i*,(ne*en,i" (n ,i"ind*o- + &( &e,,i/n t*n&%e*&" %* ,on e" *dio de&de " "ne ,ent*" de" ,i"ind*o
A#ta anu#a!
+ A#ta % a0u:a5 ()e*,ie )*o"on'd de &e,,i/n t*n&%e*&" ,i*,("*
A#ta % a0u:a
2.. ALETAS DE /REA DE SECCIÓN TRANSVERSAL UNI,ORME
Cd "et &e (ne (n &()e*,ie #&e de te)e*t(* T (( )=T b + &e
e9tiende (n ?(ido de te)e*t(* T %' P* "& "et& (e &e e&t#"e,en-
A, e& (n ,on&tnte + A& P9- donde A& e& e" *e de " &()e*,ie edid de " #&e 9 + P e& e" )e*et*o de " "et.
e denen "& &i'(iente& e,(,ione&;
( ( x )=T ( x )−T %
m !=
! *c
(
cos# m++( &m! )sen& m+
Ade& de e&to- e&to& inte*e&do& en e" ,"o* tot" t*n&e*ido )o* " "et- ddo )o* " &i'(iente e,(,i/n;
q$ =√ &)! *c "(b
(.PLANTEAMIENTO DEL PROBLEMA
e end(*e,e (n )", edinte (n &e*ie de ,o&ti""& "on'it(din"e& (e tienen (n &e,,i/n t*n&%e*&" *e,tn'("* ,on (n "on'it(d L 8 + n,o D 4 . L #&e de " )", &e ntiene (n te)e*t(* (nio*e T # 45 C- ient*& (e "& &()e*,ie& de "& ,o&ti""& de e9)onen " i*e (n
te)e*t(* de T % 25 C + (n ,oe,iente de ,on%e,,i/n de 600 F
2. H.
a @&ndo e" todo de die*en,i& nit& ,on 9 + 2 + (n
tot" de 5 9 3 )(nto& nod"e& + *e'ione&- e&ti* " di&t*i#(,i/n de " te)e*t(* + " t*n&e*en,i de ,"o* de " #&e. Co)*e e&to& *e&("tdo& ,on "o& (e &e o#t(%ie*on " &()one* (e " t*n&e*en,i de ,"o* en " ,o&ti"" e& (nidien&ion" + )o* e""o &ee$nte " ,o)o*tiento de (n "et.
6 E" e&),ido de " "" (e &e (& en " &o"(,i/n nte*io* de die*en,i& nit& e& #(*d- "o (e tiene ,oo *e&("tdo (n )*e,i&i/n )o#*e )* "& e&ti,ione& de te)e*t(*& + de " t*n&e*en,i de ,"o*. In%e&ti'(e e"
ee,to de *eniento de " "" " *ed(,i* e" e&),ido nod" 9
>.
) In%e&ti'(e " nt(*"e de " ,ond(,,i/n #idien&ion" en " ,o&ti"" + dete*ine (n ,*ite*io )* e" (e &e *on#"e " )*o9i,i/n (nidien&ion". ' e&to e9tendiendo &( n"i&i& de die*en,i& nit& )* dete*in* " t& de ,"o* de " #&e ,oo (n (n,i/n de " "on'it(d de "
,o&ti"" )* e" inte*%"o de 1.5 , LD , 10- nteniendo " n,(* D
,on&tnte. Co)*e &(& *e&("tdo& ,on "o& dete*indo& edinte " )*o9i,i/n de " ,o&ti"" ,oo (n "et.
(.1. LITERAL A
L8 D 4 T b=)* 0C J 10 W
m!
m ! !
x= y=!mm - Co)*e e&te ,"o* ,on e" o#tenido &i &e &(e
(n "et
Su'ust$s
• Condi,ione& de E&tdo E&t#"e • P*o)iedde& ,on&tnte& • ,oe,iente de ,on%e,,i/n • Coe,iente de ,on%e,,i/n (nio*e &o#*e "& &()e*,ie& de "& ,o&ti""
N$ta5 )* "o& ,",("o& )o&te*io*e& , e& e" ,"o* )o* ,on%e,,i/n (e &e en,(ent*
T %=!* (
C.
Ade& T b e& " te)e*t(* en " #&e - + T b=)* 0C
N$%$ 1
9 = T %−T + > K J y
!
y
(T *−T +) y 0
9 = T %−T + > K !
! (T b−T +) K
! (T !−T +) K J (T *−T +) 0
=600> =29 103> =25 T1> K 5 = )*−T + > K 5 = T !−T + > K 10 = T *−T + > 0
30 1.2T1 K22.5 5T1 K 5T2 5T1 K 10T5 10T1 0
21.2 T1 5 T2 10T5 255
N$%$ 2
9 = T %−T ! > K J y
!
y
(T -−T !) y 0
9 = T %−T ! > K !
! = T ,−T ! >K ! = T −T ! > 0
=600> =29 103> =25 T2> K 5 = T +−T ! > K 5 = T ,−T ! > K 10 = T −T ! > 0
30 1.2T2 K 5T1 5T2 K 5T3 5T2 K 10T6 10T2 0
21.2 T2 5 T1 5T3 10 T6 30
N$%$ (
13
9 = T %−T , > K J y
!
y
(T .−T ,) y 0
=600> =29 103> =25 T3> K 5 = T !−T , > K 5 = T )−T , > K 10 = T .−T , > 0
30 1.2T3 K 5T2 5T3 K 5T4 5T3 K 10T7 10T3 0
21.2 T3 5 T2 5T4 10 T7 30
N$%$ +
x
x
T −T ) > 0
15 0.6T4 K 15 0.6T4 K 5T3 5T4 K 5T8 5T4 0
11.2 T4 5 T3 5T8 30
N$%$
14
J x (T +−T *)
y K J y
y
2T5 T1 0.5T6 22.5
J x (T !−T )
y K J y
y
2T6 T2 0.5T5 0.5T7 0
N$%$ ;
2T7 T3 0.5T6 0.5T8 0
N$%$ <
15
x
5 (T .−T /) K 5 (T )−T /) K 600 (! x+(−,)
! =25 T >
10.6T8 5T7 5T4 15
( !+0! −*
−* !+0!
qC + y
m
q!
W
m
16
W
m
Coo (n "et
P 2=1> K 2D 2 K =2>=4 9 103> 2.008
*c " D 4 9 10 3
T=0> T# 450C
K C ! e −mx
e'(nd ,ondi,i/n - 9 L
E" ,&o en e" (e no& en,ont*o& e& t*n&e*en,i de ,"o* )o* ,on%e,,i/n en e" e9t*eo
A, T=L> T % J * c
/T
e &(e T=L> 1 32.320C
-
7.32 =20 C ! > e (+.,0**)( x +(
−,) K C ! e
3.76 C !=.!0*
( =9> 0.625 C ! e +.,0** x
K 1.375> e −+.,0** x
√ &)! *c (b sen& ( m+)+(&/m! ) cos# (m+) cos# (m+ )+(& /m! )sen&(m+)
√ -(((!0(()(+()() x +( −,) =20>
Qe**o* |+,(0-1−+,(0
+,(0-1 | 100Q 0.0842Q de e**o*
on %"o*e& (+ )*o9ido&- e" todo de die*en,i& nit& en e&tdo e&t#"e e& (n )*o9i,i/n (+ #(en.
P* &e* ,o)*o#* (e "o& *e&("tdo& o#tenido& ,on e" ,"o* de (n "et &e io (n e&t(dio (nidien&ion" de " t*n&e*en,i de ,"o*.
1
! y (T ,−T ) )
21
Ca#$! %s% #a 6as
qbase=¿ 132.126
e o#&e*% (e e" ,"o* de " /*(" de " "et (nidien&ion" &e )*e,e (,o " ,"o* o#tenido ,iendo (n n"i&i& (nidien&ion" de ,"o*e& en e&tdo e&t#"e.
P* ne& did,ti,o&- &e * (n n"i&i& de die*ente& te*i"e& de " ,o&ti"" e& de,i*- %o& to* %"o*e& die*ente& de J. Tondo (n #(en ,ond(,to*
,oo e" o*o =J317 W
m! > + (n " ,ond(,to* ,oo e" )ino =J0-12 W
m! >.
A ,ontin(,i/n &e )*e&entn "o& %"o*e& de te)e*t(*& en "o& die*ente& nodo& )* )ode* &e* ,o)*do&- *e,o*dndo (e )* e" n"i&i& (e ,on&ide*d " &iet* + "& te)e*t(*& o#tenid& '*,i& " )*o'* de Mt"# )*e&entdo en " &e,,i/n de ne9o&.
Tabla . Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- &iendo x= y=! mm
N$%$ =>1? =>(1; =>?@12 1 3-32 44-656 26-351 2 35-73 44-38 25-204 ( 33-45 44-217 25-048 + 32-17 44-108 25-004
22
45.00 00
40 44-686 31-113 36-36 44-434 26-748 ; 33-7 44-253 25-471 < 32-61 44-144 25-040 3-32 44-656 26-351 1? 35-73 44-38 25-204 11 33-45 44-217 25-048 12 32-17 44-108 25-004
1 2 3 4 5 6 7 8 10 11 12 0 5
10 15 20 25 30 35 40 45 50
Co)*,i/n de Te)e*t(*&
H10 H317 H0-12
Nodo
Te)e*t(* =C>
!r"ca . Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- (ti"indo '*,o de #**&.
Coo &e o#&e*% en " t#" 1- "o& %"o*e& de te)e*t(* )* (n #(en ,ond(,to* )e*ne,en ,e*,no& "o "*'o de " ,o&ti"" ient*& (e )* (n " ,ond(,to*- " te)e*t(* die*e de&de " te)e*t(* de " )*ed =45C> &t e" e9t*eo de " ,o&ti""- donde &( te)e*t(* e& ,e*,n " de" #iente =25C>.
(.2. LITERAL B (.2.1 P!i&!a 'a!t
x= y=+mm
!(0-T +−*T !−+(T 1=!)(
!(0-T !−*T +−*T ,−+(T +(=+*
24
N$%$
N$%$ ;
+(0- T −*T .−* T +-=+*
! (T +−T 1 )+! (T +(−T 1)+! ()*−T 1)+! (T +.−T 1)=(
T ++T +(+)*+T +.−) T 1=(
)T 1−T +−T +(−T +.=)*
N$%$ 1?
)T +(−T !−T ++−T 1−T +=(
N$%$ 11
N$%$ 12
N$%$ 1(
N$%$ 1+
N$%$ 1
N$%$ 1
!(0-T +-−+(T +*−*T /−*T !)=+*
!(T +.−+(T 1−* T +=!!*
!(T +−* T +.−* T +1−+(T +(=(
N$%$ 1
N$%$ 2?
27
+(0,T !)−*T +-−*T !,=.0*
m
m
Ao* ,o)*o#*eo& e" ,"o* de "et ,on (n n"i&i& (nidien&ion" de ,"o*e& + " ,e* "o& #"n,e& de ene*'& ,o**e,t& en ,d nodo + &(iendo T1 ,oo " te)e*t(* de " #&e- &e o#t(%ie*on "o& &i'(iente& *e&("tdo&;
Ca#$! %s% #a 6as
qbase=+,(0,()
T + T ! T , T ) T * T - T . T T 1
45.00 00
42.02 2
A ,ontin(,i/n &e )*e&entn "o& %"o*e& de te)e*t(*& en "o& die*ente& nodo& )* )ode* &e* ,o)*do&- *e,o*dndo (e )* e" n"i&i& (e ,on&ide*d " &iet* + "& te)e*t(*& o#tenid& '*,i& " )*o'* de Mt"# )*e&entdo en " &e,,i/n de ne9o&. Tondo (n #(en ,ond(,to* ,oo
e" o*o =J317 W
m! > + (n " ,ond(,to* ,oo e" )ino =J0-12 W
m! >.
Tabla #. Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- &iendo x= y=+mm
N$%$ =>1? =>(1; =>?@12 1 41-6 44-80 27-887 2 3-2 44-64 25-14 ( 37-2 44-512 25-415 + 35-6 44-33 25-203 34-4 44-23 25-101 33-4 44-212 25-04 ; 32-6 44-14 25-021 < 32-1 44-104 25-003 42-2 44-830 34-751 1? 3-8 44-675 2-747 11 37-8 44-53 27-345 12 36-1 44-421 26-166 1( 34-8 44-321 25-578 1+ 33-8 44-23 25-27 1 33-0 44-176 25-120 1 32-4 44-131 25-01 1; 42-3 44-836 36-370 1< 40-0 44-684 30-7 1 37- 44-548 28-052 2? 36-3 44-430 26-537 21 34- 44-330 25-766 22 33- 44-248 25-371 2( 33-1 44-185 25-15 2+ 32-5 44-140 25-025
31
1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 1 20 21 22 23 24 0.0 5.0
10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
Co)*,i/n de Te)e*t(*&
H10 H317 H0-12
Nodo
Te)e*t(* =C>
Coo &e o#&e*% en " t#" 2- "o& %"o*e& de te)e*t(* )* (n #(en ,ond(,to* )e*ne,en ,e*,n& "o "*'o de " ,o&ti"" ient*& (e )* (n " ,ond(,to*- " te)e*t(* die*e de&de " te)e*t(* de " )*ed =45C> &t e" e9t*eo de " ,o&ti""- donde &( te)e*t(* e& ,e*,n " de" #iente =25C>.
32
(.2.1 S0un%a Pa!t x= y=(0*mm
P* e" n"i&i& &(io& (e )* ,d nodo e" ,"o* in'*e&.
N$%$ 1 )
33
−*T ++!(0,T !−*T ,−+(T +=.0*
N$%$ (
! ( y
−*T !+!(0,T ,−*T )−+(T +1=.0*
S $6s!"a un 'at!*n n #as )ua)i$ns@ '$! #$ u s si&'#i9)a asta # n$%$ 1
N$%$ +
N$%$
N$%$
N$%$ ;
34
N$%$
N$%$ 1?
N$%$ 11
N$%$ 12
N$%$ 1(
N$%$ 1+
N$%$ 1
N$%$ 1
35
N$%$ 1;
11;
−T ++)T +.−T +/−T ,,=)*
N$%$ 1
N$%$ 2?
N$%$ 21
N$%$ 22
N$%$ 2(
N$%$ 2+
N$%$ 2
N$%$ 2
N$%$ 2;
N$%$ 2<
N$%$ 2
N$%$ (?
N$%$ (1
N$%$ (2
1(2
(1(2 )
37
N$%$ ((
N$%$ (+
N$%$ (
N$%$ (
N$%$ (;
N$%$ (<
N$%$ (
N$%$ +?
N$%$ +1
N$%$ +2
N$%$ +(
N$%$ ++
38
N$%$ +
N$%$ +
N$%$ +;
N$%$ +<
N$%$ +
N$%$ ?
N$%$ 1
N$%$ 2
N$%$ (
N$%$ +
N$%$
N$%$
3
N$%$ ;
N$%$ <
N$%$
N$%$ ?
N$%$ 1
N$%$ 2
N$%$ (
N$%$ +
N$%$
40
N$%$
N$%$ ;
N$%$ <
N$%$
N$%$ ;?
N$%$ ;1
N$%$ ;2
N$%$ ;(
N$%$ ;+
N$%$ ;
N$%$ ;
N$%$ ;;
41
N$%$ ;<
N$%$ ;
N$%$ <?
/()+,0.*−(0+*T /(=(
O#teniendo n"ente "& te)e*t(*&;
T1 +(@? T2 41-550 T( 40-263 T+ 3-124 T 38-104 T 37-185 T; 36-358 T< 35-613 T 34-46 T1? 34-352 T11 33-824 T12 33-361 T1( 32-58
42
T1+ 32-612 T1 32-321 T1 32-083 T1; 43-384 T1< 41-37 T1 40-646 T2? 3-48 T21 38-446 T22 37-505 T2( 36-657 T2+ 35-83 T2 35-20 T2 34-58 T2; 34-057 T2< 33-582 T2 33-168 T(? 32-813 T(1 32-514 T(2 32-270 T(( 43-541 T(+ 42-165 T( 40-87 T( 3-73 T(; 38-687 T(< 37-733 T( 36-870 T+? 36-04 T+1 35-37 T+2 34-776 T+( 34-225 T++ 33-740 T+ 33-31 T+ 32-57 T+; 32-653 T+< 32-404 T+ 43-616 T? 42-285 T1 41-037 T2 3-884 T( 38-82 T+ 37-868 T 36- T 36-215
43
T; 35-511 T< 34-883 T 34-326 T? 33-836 T1 33-410 T2 33-044 T( 32-737 T+ 32-486 T 43-63 T 42-323 T; 41-082 T< 3-32 T 38-876 T;? 37-13 T;1 37-041 T;2 36-255 T;( 35-54 T;+ 34-18 T; 34-35 T; 33-868 T;; 33-440 T;< 33-074 T; 32-765 T<? 32-513
qaleta$rmula=+,(0-1 W
m
Ao* ,o)*o#*eo& e" ,"o* de "et ,on (n n"i&i& (nidien&ion" de ,"o*e& + " ,e* "o& #"n,e& de ene*'& ,o**e,t& en ,d nodo + &(iendo T1 ,oo " te)e*t(* de " #&e- &e o#t(%ie*on "o& &i'(iente& *e&("tdo&;
con x=(0* mm y y=) mm
qbase=¿ 130.5028
T +, 33.536
T +) 33.1183
T +* 32.7605
T +- 32.4610
T +. 32.2174
A ,ontin(,i/n &e )*e&entn "o& %"o*e& de te)e*t(*& en "o& die*ente& nodo& )* )ode* &e* ,o)*do&- *e,o*dndo (e )* e" n"i&i& (e ,on&ide*d " &iet* + "& te)e*t(*& o#tenid& '*,i& " )*o'* de Mt"# )*e&entdo en " &e,,i/n de ne9o&. Tondo (n #(en ,ond(,to* ,oo
e" o*o =J317 W
m! > + (n " ,ond(,to* ,oo e" )ino =J0-12 W
m! >.
Tabla $. . Co)*,i/n de te)e*t(*& )* die*ente& te*i"e&- &iendo x= y=(2*mm
N$%$ =>1? =>(1; =>?@12 N$%$ =>1? =>(1; =>?@12 1 43-05 44-86 30-03 41 35-37 44-367 25-778
45
2 41-550 44-806 27-271 42 34-776 44-320 25-543 ( 40-263 44-723 26-35 43 34-225 44-277 25-376 + 3-124 44-647 25-85 44 33-740 44-238 25-258 38-104 44-576 25-610 45 33-31 44-204 25-173 37-185 44-510 25-422 46 32-57 44-175 25-10 ; 36-358 44-44 25-24 47 32-653 44-150 25-05 < 35-613 44-32 25-205 48 32-404 44-130 25-017 34-46 44-340 25-143 4 43-616 44-16 40-15 1? 34-352 44-22 25-100 50 42-285 44-834 36-077 11 33-824 44-24 25-06 51 41-037 44-755 32-37 12 33-361 44-211 25-048 52 3-884 44-681 30-630 1( 32-58 44-177 25-032 53 38-82 44-610 28-72 1+ 32-612 44-148 25-020 54 37-868 44-545 27-75 1 32-321 44-123 25-011 55 36- 44-483 26-63 1 32-083 44-102 25-003 56 36-215 44-426 26-377 1; 43-384 44-07 36-541 57 35-511 44-374 25-64 1< 41-37 44-820 32-01 58 34-883 44-327 25-673 1 40-646 44-73 2-534 5 34-326 44-283 25-467 2? 3-48 44-663 28-044 60 33-836 44-245 25-320 21 38-446 44-52 27-087 61 33-410 44-211 25-214 22 37-505 44-526 26-446 62 33-044 44-182 25-135 2( 36-657 44-465 26-008 63 32-737 44-157 25-073 2+ 35-83 44-408 25-704 64 32-486 44-136 25-021 2 35-20 44-356 25-42 65 43-63 44-17 40-450 2 34-58 44-308 25-343 66 42-323 44-836 36-483 2; 34-057 44-265 25-238 67 41-082 44-757 33-327 2< 33-582 44-227 25-163 68 3-32 44-683 30-51 2 33-168 44-13 25-10 6 38-876 44-613 2-218 (? 32-813 44-163 25-06 70 37-13 44-547 27-75 (1 32-514 44-13 25-037 71 37-041 44-485 27-02 (2 32-270 44-118 25-011 72 36-255 44-42 26-46 (( 43-541 44-13 3-107 73 35-54 44-376 26-02 (+ 42-165 44-82 34-730 74 34-18 44-32 25-718 ( 40-87 44-750 31-715 75 34-35 44-286 25-4 ( 3-73 44-674 2-65 76 33-868 44-247 25-342 (; 38-687 44-604 28-247 77 33-440 44-213 25-22 (< 37-733 44-538 27-26 78 33-074 44-184 25-144 ( 36-870 44-476 26-588 7 32-765 44-15 25-078 +? 36-04 44-420 26-112 80 32-513 44-13 25-022
46
(.(. LITERAL C Lo (e &e )idi/ en e" "ite*" , e& %*i* e" %"o* de D )* die*ente& inte*%"o&- e in%e&ti'* "o& ee,to& (e e&to& )*od(,en en " t*n&e*en,i de ,"o* de&de " #&e de " ,o&ti"". @ti"indo e" inte*%"o de LD )*o)(e&to en e" en(n,ido &e o#t(%o " &i'(iente '*,;
Tabla %. S*i,i/n de" e&)e&o* D- nteniendo L $o- ,on J10 W
m! .
D => LD C"o* 1< =F> C"o* 2< =F> Q e**o* ?@<? 10-00 61-81 62-77 1-55 1@2 6-40 76-78 77-2 0-67 1@ 4-83 87-77 87-2 0-17 2@?; 3-87 7-1 6- 0-21 2@+; 3-23 105-50 104-4 0-53 2@<< 2-78 112- 112-08 0-81 (@2 2-43 11-86 118-58 1-07 (@;? 2-16 126-23 124-5 1-30 +@11 1-5 132-20 130-21 1-51 +@1 1-77 137-86 135-50 1-71 +@2 1-63 143-25 140-54 1-0 @(( 1-50 148-42 145-35 2-07
1.00 3.00 5.00 7.00 .00 0.00
1.00
2.00
3.00
LF
P$!)nta: % !!$! 7
!r"ca $. Po*,ent$e de e**o* %& LD- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
e (ti"i*on %"o*e& de D de&de 0.8 &t 5.33. e )(ede o#&e*%*- (e e" e**o* (e &e ,oete " &(i* (e e" ,"o* (e ?(+e de&de " #&e de " ,o&ti"" e& (nidien&ion"- % (entndo ,ono*e (ent e" %"o* de D. e ""e'/ e&t ,on,"(&i/n- de#ido (e e" *e&to de )*o)iedde& + ,ondi,ione& de" )*o#"e- &e nt(%ie*on ,on&tnte& e& de,i*- no %*i*on. En ot*& )"#*&- (e " &(i* (e "o& '*diente& de te)e*t(* t*n&%e*&"e& &on (+ )e(eo&- o en ot*& )"#*&- (e " te)e*t(* &o"o de)end de " di*e,,i/n en U9V &e %n ,oete* eno& e**o*e& &i &e di&in(+e D &t ,ie*to- "(e'o- e" e**o* e)ie (ent*- " '*, indi, (e e" ,"o* en *e"idd e&t ?(+endo en do& di*e,,ione&. Po* &(e*te )* e" inte*%"o de LD ddo- e"
47
e**o* ,oetido- no e& '*nde- )o* "o tnto- " &(n,i/n de ,"o* (nidien&ion" e& (+ ,e)t#"e. e )(ede o#&e*%*- (e &i &e tiene (n e&)e&o* (+ )e(eo- (n(e e" ,"o* &e t*n&it en do& di*e,,ione&- e" e**o* ,oetido " &(i* (e ?(+e en (n di*e,,i/n- e& i**e"e%nte.
+ AN/LISIS DE VARIACIÓN DE LAS PROPIEDADES
@no de "o& o#$eti%o& )*in,i)"e& e* e&t(di* e" ee,to ,(&do " ,#i* (n de "& )*o)iedde& de" )*o#"e ient*& "& de& no %*n.
m!
Tabla &. S*i,i/n de" e&)e&o* D- nteniendo L $o- ,on J0-12 W
m! .
Ca#$! 2D 7
!!$!
?@<? 10-00 6-7 13-72 102-06 1@2 6-40 8-4 14-50 70-80 1@ 4-83 -78 15-11 54-48 2@?; 3-87 10-2 15-64 43-24 2@+; 3-23 11-5 16-12 34-83 2@<< 2-78 12-0 16-54 28-21 (@2 2-43 13-7 16-3 22-81 (@;? 2-16 14-62 17-30 18-2 +@11 1-5 15-41 17-63 14-44 +@1 1-77 16-16 17-5 11-0 +@2 1-63 16-88 18-26 8-16 @(( 1-50 17-57 18-55 5-56
48
50.00
100.00
150.00
LF
P$!)nta: % !!$! 7
!r"ca %. Po*,ent$e de e**o* %& LD- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
m!
Tabla '. S*i,i/n de" e&)e&o* D- nteniendo L $o- ,on J317 W
m!
Ca#$! 2D 7
!!$!
?@<? 10-00 181-3 181-85 0-05 1@2 6-40 12-5 12-74 0-11 1@ 4-83 200-45 200-13 0-16 2@?; 3-87 206-7 206-54 0-21 2@+; 3-23 212-8 212-45 0-25 2@<< 2-78 218-68 218-05 0-2 (@2 2-43 224-1 223-46 0-33 (@;? 2-16 22-57 228-74 0-36 +@11 1-5 234-85 233-2 0-40 +@1 1-77 240-07 23-04 0-43 +@2 1-63 245-24 244-11 0-46 @(( 1-50 250-36 24-14 0-4
4
1.00 3.00 5.00 7.00 .00 0.00 0.10 0.20 0.30 0.40 0.50 0.60
% E!!$! "s. LF >?? >(1; 7O!$
LF
P$!)nta: % !!$! 7
!r"ca &. Po*,ent$e de e**o* %& LD- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
e o#&e*% (e e" e**o* (e &e ,oete " )*o9i* "o& %"o*e& de ,"o* de ne* (nidien&ion"- di&in(+en " oento (e &e tiene (n #(en ,ond(,to*.
Con e&te n"i&i& &e )(ede ,on,"(i* (e e" 9io e**o* en )o*,ent$e- " &(i* (e e" ,"o* ?(+e en (n dien&i/n- e& +o* en e" )ino (e en e" o*o. E&t& '*,&- &e "& *e"i*on nteniendo- e" *e&to de )*o)iedde& ,on&tnte& + (ti"indo e" i&o inte*%"o LD de" "ite*" ,. i e" te*i"- )o&ee e$o*e& )*o)iedde& de ,ond(,to*- "o& '*diente& de te)e*t(*- en ,d &e,,i/n t*n&%e*&" de " ,o&ti""- %n &e* & )e(eo& + " o* ,oo ?(+e e" ,"o*- % &ee$*&e e$o* (n ,o)o*tiento (nidien&ion" + e" e&t(dio de" ,"o* en do& dien&ione&- &e* eno& ne,e&*io- e&to o*** e&(e*o en ,",("o& de & nodo&.
P* )o+* Wn & n(e&t*& ,on,"(&ione& (e "o& '*diente& de te)e*t(* &on (+ )e(eo& &i e" te*i" e& (n e$o* ,ond(,to* o )o&ee (n '*n %"o* de ,ond(,ti%idd t*i, &e *e"i/ " '*, de '*diente de te)e*t(*&- tondo en ,(ent "& te)e*t(*& o#tenid& en (n n"i&i& (nidien&ion".
50
O*o =TC >
1 2-3 42-0 44-8 1-5 27-0 40-7 44-7
2 25- 3-6 44-7 2-5 25-4 38-5 44-6
3 25-2 37-5 44-5 3-5 25-1 36-7 44-5
4 25-0 35- 44-4 4-5 25-0 35-2 44-4
5 25-0 34-6 44-3 5-5 25-0 34-0 44-3
6 25-0 33-5 44-2 6-5 25-0 33-1 44-2
7 25-0 32-8 44-2 7-5 25-0 32-5 44-1
8 25-0 32-2 44-1
0 1 2 3 4 5 6 7 8 20
25
30
35
40
45
50
H &()(e&to
T&'!atu!as 7C
En " '*, o#tenid- not#"e (e " ,ond(,ti%idd *e'(" " U(nio*iddV de " te)e*t(* en " "et. C(ndo e&t )*o)iedd e& (+ "t =,oo e& e" ,&o de" o*o> e" '*diente e& ,&i n("o. A(e""o no o,(**e en "o& no ,ond(,to*e& ,oo e" )ino o en e" te*i" &()(e&to ,(+o '*diente e& )*on(n,ido. e de#e *e,o*d* (e e" te*i" &()(e&to ten (n %"o* de H i'(" 10 FH. e %e (e edinte (ent e" %"o* de H- " oento (e &e ,#i )o&i,i/n nod"- ,d nodo tiene (n eno* die*en,i de te)e*t(* ,on e" nodo %e,ino.
Ao*- &e %e* e" ee,to di*e,to de ,#i* "o& %"o*e& de H nteniendo "o& %"o*e& de "& de& )*o)iedde& ,on&tnte& de "o& "ite*"e& + #. e de#e en,ion* (e )* )ode* ,",("* e" ,o)o*tiento #idien&ion" de "o& ,"o*e& en ,d (no de "o& n"i&i& )*e%io& + en e" )*e&ente &e (ti"i/ (n &e)*,i/n de *endi$ de %K>%>?@&& + (e " )*o9i,i/n #idien&ion" &e* & )*e,i&. En *e&(en &e o#t(%ie*on e&to& %"o*e&;
Tabla (. S*i,i/n de " ,ond(,ti%idd- nteniendo $o- ,on d9d+0-5.
7F&= Ca#$! 1% 7
Ca#$! 2% 7
!!$!
1?@?? 130-6 128-78 1-46 2?@?? 165-51 163-78 1-05 (?@?? 183-54 181-6 0-86
52
+?@?? 14-5 13-12 0-76 ?@?? 202-06 200-68 0-68 ?@?? 207-45 206-14 0-63 ;?@?? 211-52 210-27 0-5 <?@?? 214-71 213-50 0-56 ?@?? 217-26 216-0 0-54 1??@?? 21-37 218-23 0-52 1?@?? 225-8 224-4 0-46 2??@?? 22-47 228-4 0-42 2?@?? 231-63 230-6 0-40 (??@?? 233-0 232-18 0-3 (?@?? 234-15 233-26 0-38 +??@?? 234-5 234-08 0-37
0.00 200.00 400.00 600.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
% E!!$! "s. L>< >+ >??
7C$NDUCTIVIDAD TRMICA
P$!)nta: % !!$! 7
!r"ca '. Po*,ent$e de e**o* %& J- tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
E&to& *e&("tdo&- )o+n #&tnte " ,on,"(&i/n nte*io*- de (e &i (n te*i" e& e$o* ,ond(,to*- "o& '*diente& de te)e*t(* ent*e nodo + nodo- &on de&ido )e(eo&- + (e e" e**o* de &(i* (e e" ,"o* ?(+e en (n dien&i/n di&in(i*. <e e,o- &e )(do (ti"i* en " '*,- te*i"e& ,on e$o* ,ond(,ti%idd t*i,- )e*o "o& te*i"e& ,on ,ond(,ti%idd t*i, +o*e& 300 FH &on ,ono,ido& ,oo te*i"e& &()e*,ond(,to*e&. Lo&
53
te*i"e& &()e*,ond(,to*e&- )e&* de tene* #(en& )*o)iedde& de ,ond(,to*- &/"o (n,ionn ,oo ,ond(,to*e& ,ie*t& te)e*t(*& ,*ti,&- "& ,("e& &on (+ #$&- ="*ededo* de 1 H 20 H>. Ot*o dee,to de e&to& te*i"e&- e& (e &on (+ di,i"e& de ,on&e'(i*- + )o* "o tnto- &( )*e,io e& (+ "to. i &e % t*#$* (n e)*e& ,on e&to& te*i"e&- e" ,o&to de o)e** ,on e""o&- &e* t#in (+ "to- + (e &e de#e ,()"i* e&t*i,t& ,ondi,ione& de t*#$o. Po* e&o no &e &(ti"in ,ond(,ti%idde& & "t& en " t#" + en " '*, "o& )(nto& (ti"ido&- (e*on & (e &(,iente& )* ,o)*o#* n(e&t*& ,on,"(&ione& ,e*, de" ,#io de te*i"- en "o& "ite*"e& + #.
A" ,o)** "& t*n&e*en,i& de ,"o* o#tenid& ,iendo (n n"i&i& #idien&ion" ,on (no (nidien&ion" &e o#tiene "o& &i'(iente& *e&("tdo&;
110.00
160.00
210.00
@nidien&ion"
Bidien&ion"
T!ans3!n)ia % )a#$! 7
L )o, die*en,i ent*e & ,(*%& )o+ " ,on,"(&i/n de (e (n n"i&i& #idien&ion" no e& ne,e&*io )* die*ente& %"o*e& de J- de e,o e" te*i" " tene* e$o*e& )*o)iedde& de ,ond(,to* &e di&tin'(e eno& "& do& '*,&.
54
Ao* " )*o)iedd (e &e (ie*e %*i* e& e" ,oe,iente ,on%e,ti%o de" edio en e" (e &e en,(ent* " ,o&ti"" o en ot*& )"#*& e" edio en e" (e e&t &e (#i,.
e &,*on "o& &i'(iente& *e&("tdo&;
T#" 8. S*i,i/n de" ,oe,iente de ,on%e,,i/n- nteniendo J $o- ,on d9d+0-5.
7F&2=
Ca#$! 1% 7
Ca#$! 2% 7
P$!)nta: % !!$! 7
!r"ca (. Po*,ent$e de e**o* %& - tondo ,oo %"o* te/*i,o e" ,"o* en 1<.
55
<e e&t '*, &e ""e' " ,on,"(&i/n (e e" e**o* ,oetido ,(ndo &e (ti"i (n edio ,on +o* ,oe,iente ,on%e,ti%o e)ie ,*e,e*. A(n(e &e o#&e*% (e e"
e**o* ,oetido " &(i* (e e" ,"o* ?(+e en (n dien&i/n e& (+ )e(eo )* de&)*e,i* " )o&i#i"idd de (e e" ,"o* ?(+ en (n &o" di*e,,i/n- &e * (n n"i&i& & )*o(ndo de" ,&o. e n"i* "o& '*,o& de '*diente de te)e*t(* de ,"o*e& (nidien&ion"e&- e&to& (e*on "o& *e&("tdo& o#tenido&;
56
<9= >
2J =TC
0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 45-0 0-5 44-6 44-3 44-0 43-8 43-6 43-4 43-3 43-2 43-0 42-
1 44-2 43-6 43-1 42-7 42-3 42-0 41-8 41-5 41-3 41-1 1-5 43-8 42- 42-2 41-6 41-2 40-7 40-4 40-0 3-7 3-4
2 43-5 42-3 41-4 40-7 40-1 3-6 3-1 38-7 38-3 38-0 2-5 43-1 41-8 40-7 3-8 3-1 38-5 38-0 37-5 37-1 36-7
3 42-8 41-3 40-0 3-0 38-2 37-5 36- 36-4 36-0 35-5 3-5 42-6 40-8 3-4 38-3 37-4 36-7 36-0 35-5 35-0 34-5
4 42-3 40-4 38- 37-7 36-7 35- 35-2 34-6 34-1 33-6 4-5 42-1 40-0 38-4 37-1 36-0 35-2 34-5 33-8 33-3 32-8
5 41- 3-6 37- 36-6 35-5 34-6 33-8 33-2 32-6 32-1 5-5 41-7 3-3 37-5 36-1 34- 34-0 33-2 32-6 32-0 31-5
6 41-5 3-0 37-1 35-7 34-5 33-5 32-7 32-1 31-5 31-0 6-5 41-3 38-7 36-8 35-3 34-1 33-1 32-3 31-6 31-0 30-5
7 41-2 38-5 36-5 35-0 33-8 32-8 31- 31-2 30-7 30-2 7-5 41-1 38-4 36-3 34-7 33-5 32-5 31-6 30- 30-3 2-8
Con &( *e&)e,ti% '*, de '*diente& de te)e*t(*;
0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 2
34
3
44
4
%K 7&&
T&'!atu!a 7C#sius
E&te '*,o (e&t* ,oo %* " di&t*i#(,i/n de te)e*t(* ,on *e&)e,to " ,oe,iente ,on%e,ti%o. i &e tiene (n ,oe,iente =100 )o* e$e)"o> " di&t*i#(,i/n e& ,&i n(" en ,#io )* %"o*e& "to& de =,oo 1000 )o* e$e)"o> " ,(*% )*e&ent (n )endiente & )*on(n,id + )o* ende (n ,#io & ,e"e*do de " te)e*t(* ,on *e&)e,to " )o&i,i/n nod". Po* e""o &e )(ede de,i* (e e" (ento de" ,oe,iente ,on%e,ti%o =(e de)ende de" ?(ido> ,e (e e" '*diente de te)e*t(* ,#ie ,on&ide*#"eente )e*o " %e (ent e" ,"o* e9)("&do )o* " "et.
Ao* &e )*o,ede* n"i* " ,(*% X %& ,oe,iente ,on%e,ti%o )* "o& do& n"i&i& *e"ido&.
57
@nidien&ion"
Bidien&ion"
7F&2=
T!asn3!n)ia % )a#$! 7
E&t '*, " ini,io (e&t* (n "ne (+ ,(*%. E" ,#io de" ,"o* )* %"o*e& de UV eno*e& 300 e& )*on(n,ido. C#io& "i'e*o& en e" ,oe,iente ,on%e,ti%o en e&t *e'i/n )*od(,i* ee,to& (+ ,on&ide*#"e& en e" ?($o de ,"o*. Pe*o de&)(& de e&te %"o* e" ,*e,iiento de " ,(*% &e ,o)o*t ,&i "ine"ente )o* "o (e &e )od* &(i* (e e" )*o,e&o &e Ue&t#i"iV + e" (ento de" ,oe,iente ,on%e,ti%o no e$o* de&ido " t*n&e*en,i de ,"o*. En e&t '*, &e )(ede die*en,i* e$o* #& '*,& ,ono*e &e (ent e" ,oe,iente ,on%e,ti%o- &e )(ede ,on,"(i* (e e" ,oe,iente ,on%e,ti%o tiene (n +o* in?(en,i en ,#i* "o& '*diente& de te)e*t(* ent*e "o& nodo& %e,ino&.
Ao* " %*i#"e ,#i* &e* " "on'it(d L de " ,o&ti""- ,on e&to &e )od* )*ede,i* " i)o*tn,i de " 'eoet* de e&t en " t*n&e*en,i de ,"o*.
e o#t(%ie*on "& &i'(iente& t#"& de *e&("tdo&;
58
L12
=TC>
L23
=TC>
L30
=TC>
L35
=TC>
L40
=TC>
0 45-0 45-0 45-0 45-0 45-0 45-0 0-5 43-5 43-4 43-3 43-3 43-3 43-3
1 42-2 41- 41-8 41-8 41-8 41-8 1-5 41-0 40-5 40-4 40-4 40-4 40-4
2 40-0 3-3 3-1 3-1 3-1 3-1 2-5 3-0 38-1 38-0 38-0 38-0 38-0
3 38-1 37-1 36- 36- 36- 36- 3-5 37-4 36-1 35- 35- 35- 35-
4 36-7 35-2 35-0 35-0 35-0 35-0 4-5 36-1 34-4 34-2 34-2 34-2 34-2
5 35-7 33-7 33-4 33-4 33-4 33-4 5-5 35-2 33-1 32-7 32-7 32-7 32-7
6 34- 32-5 32-1 32-1 32-1 32-1 6-5 31- 31-5 31-5 31-5 31-5
7 31-4 31-0 31-0 31-0 31-0 7-5 31-0 30-5 30-5 30-5 30-5
8 30-6 30-0 30-0 30-0 30-0 8-5 30-2 2-6 2-6 2-6 2-6 2- 2-2 2-2 2-2 2-2
-5 2-6 28- 28- 28- 28- 10 2-4 28-6 28-5 28-5 28-5
10-5 2-2 28-3 28-2 28-2 28-2 11 2-0 28-0 28-0 28-0 28-0
11-5 28-8 27-8 27-7 27-7 27-7 12 28-7 27-5 27-5 27-5 27-5
12-5 27-3 27-3 27-3 27-3 13 27-1 27-1 27-1 27-1
13-5 27-0 26- 26- 26- 14 26-8 26-8 26-8 26-8
14-5 26-7 26-6 26-6 26-6 15 26-5 26-5 26-5 26-5
15-5 26-4 26-4 26-4 26-4 16 26-3 26-3 26-3 26-3
16-5 26-2 26-2 26-1 26-1 17 26-1 26-1 26-1 26-1
17-5 26-0 26-0 26-0 26-0 18 26-0 25- 25- 25-
18-5 25- 25-8 25-8 25-8 1 25-8 25-8 25-7 25-7
1-5 25-8 25-7 25-7 25-7 20 25-7 25-6 25-6 25-6
20-5 25-7 25-6 25-6 25-6 21 25-7 25-5 25-5 25-5
60
21-5 25-6 25-5 25-5 25-5 22 25-6 25-5 25-4 25-4
22-5 25-6 25-4 25-4 25-4 23 25-6 25-4 25-4 25-4
23-5 25-4 25-3 25-3 24 25-3 25-3 25-3
24-5 25-3 25-3 25-3 25 25-3 25-3 25-3
25-5 25-3 25-2 25-2 26 25-2 25-2 25-2
26-5 25-2 25-2 25-2 27 25-2 25-2 25-2
27-5 25-2 25-2 25-2 28 25-2 25-2 25-2
28-5 25-2 25-2 25-1 2 25-2 25-1 25-1
2-5 25-2 25-1 25-1 30 25-2 25-1 25-1
30-5 25-1 25-1 31 25-1 25-1
31-5 25-1 25-1 32 25-1 25-1
32-5 25-1 25-1 33 25-1 25-1
33-5 25-1 25-1 34 25-1 25-1
34-5 25-1 25-1 35 25-1 25-1
35-5 25-0 36 25-0
36-5 25-0 37 25-0
37-5 25-0 38 25-0
38-5 25-0 3 25-0
3-5 25-0 40 25-0
Ao* &e )*o,ede* '*,* ,oo %*n "& *e",ione& LD de ,(e*do. Coo D &e nt(%o ,on&te " o* en (e LD + %*ido e& ,#indo " "on'it(d. e o#tiene " &i'(iente '*,;
61
0 5 10 15 20 25 30 35 40 45 23
28
33
38
43
48
L6 L12 L23 L30 L35 L40
%K 7&&
Coo &e )(ede o#&e*%* en e&t '*,- edid (e (ent " "on'it(d L de " "et ,on *e&)e,to " n,o D- " te)e*t(* en e" #o*de de " "et di&in(+e + &e )*o9i & " de" #iente. E&to &e de#e (e " ene*' (e ?(+e t*%& de e"" de#e *e,o**e* & di&tn,i " ,iendo (e &e &ii"e ,&i tod " n" de e&t.
Po* e$e)"o ,(ndo LD0-25 " %*i,i/n de te)e*t(* %* de 45 &t 43C- ient& (e LD8 " te)e*t(* de,*e,e de 45 32 C " ,(" e& & ,e*,n " de" #iente =25YC> (e en e" e$e)"o nte*io*.
P* )ode* n"i* e$o* "o& e**o*e& ,oetido& " ,#i* "& dien&ione& de " "et + &(i* (e e" ,"o* e& (nidien&ion" &e (&*on "& ,ondi,ione& )*o)(e&to& )o* e" "ite*" , nteniendo ,on&tnte e" e&)e&o* D + e" *e&to de %*i#"e& de" )*o#"e.
e o#t(%o " &i'(iente t#" de *e&("tdo&;
L7&& LF Ca#$! 1% 7
Ca#$! 2% 7
@?? 1-50 122-8 120-8 1-70 @+? 2-35 133-77 132-11 1-24
12@<? 3-20 137-26 136-40 0-63 1@2? 4-05 138-35 138-46 0-07 1@? 4-0 138-6 13-1 0-88 2(@?? 5-75 138-7 141-2 1-80 2@+? 6-60 138-83 142-75 2-82 2@<? 7-45 138-84 144-34 3-6 ((@2? 8-30 138-84 146-08 5-22
62
1.00 3.00 5.00 7.00 .00 0.00
2.00
4.00
6.00
8.00
10.00
e o#t(%o " &i'(iente '*,;
e )(ede o#&e*%*- (e e" e**o* (e &e ,oete " &(i* (e e" ,"o* (e ?(+e de&de " #&e de " ,o&ti"" e& (nidien&ion"- % (entndo ,ono*e (ent e" %"o* de L. e ""e'/ e&t ,on,"(&i/n- de#ido (e e" *e&to de )*o)iedde& + ,ondi,ione& de" )*o#"e- &e nt(%ie*on ,on&tnte& e& de,i*- no %*i*on. En ot*& )"#*&- (e " &(i* (e "o& '*diente& de te)e*t(* t*n&%e*&"e& &on (+ )e(eo&- o en ot*& )"#*&- (e " te)e*t(* &o"o de)end de " di*e,,i/n en U9V &e %n ,oete* eno& e**o*e& &i &e (ent L &t ,ie*to )(nto- "(e'o- e" e**o* e)ie (ent*- " '*, indi, (e e" ,"o* en *e"idd e&t ?(+endo en do& di*e,,ione&. P* inte*%"o de LD ddo )o* e" "ite*" , &e o#&e*% (e "o& e**o*e& ,oetido& &()e*n "
63
8Q- " &(n,i/n de ,"o* (nidien&ion" no e& ,e)t#"e. e )(ede o#&e*%*- (e &i &e tiene (n L (+ '*nde- e" e**o* ,oetido " &(i* (e e" ,"o* ?(+e en (n di*e,,i/n- e& '*nde.
Ao* &e % ,o)** "& ,(*%& o#tenid& t*n&e*en,i de ,"o* &(iendo ,"o* (nidien&ion" + #idien&ion"ente %& e" ,#io de "on'it(d L.
0.00 50.00
@nidien&ion"
Bidien&ion"
T!ans3!n)ia % Ca#$! 7
e o#&e*% (e " to* e" ?($o de ,"o* de ne* #idien&ion"- " t*n&e*en,i de e&t (ent de +o* ne* (e en e" ,&o (nidien&ion". E& de,i* &i &e &(e (e e&te ?(+e en (n &o" di*e,,i/n )* "et& & "*'& &e ,oeten (,o& e**o*e& de ,",("o de t*n&e*en,i de ,"o*. <e e,o& &e )(ede die*en,i* (,o e$o* #& ,(*%& (e " %*i* "o& ,&o& nte*io*e&. En ,on,"(&i/n en *e"idd ,(ndo &e tienen "et& (+ '*nde& " ene*' en o* de ,"o* &e di&i) &t t" )(nto (e " te)e*t(* en 9L &e "o & ,e*,n " de" #iente- + de#ido (e *e,o**e & di&tn,i e&t &e )ie*de en +o* )*o)o*,i/n.
64
CONCLUSIONES
En e" "ite*" &e o#&e*% (e "o& %"o*e& o#tenido& dent*o de (n i& ,o"(n de nodo& &e )*o9in "& te)e*t(*&- ient*& (e "& te)e*t(*& de "& ,o"(n& )* "& di&tint& )o&i,ione& "o "*'o de " "et %*n. R/n )o* " ,(" e" %"o* o#tenido de " t*n&e*en,i de ,"o* de o* #idien&ion" )(do o#tene*&e ,oo &i &e *e&o"%ie* de o* (nidien&ion".
P* " &o"(,i/n de" "ite*" # &e 'ene* +o* ,ntidd de nodo& + ,on e""o& +o* nWe*o de e,(,ione&- "o (e 'ene* (n +o* e9,tit(d de " te)e*t(* en dete*indo& )(nto& de " "et.
!in"ente en e" "ite*" , &e o#&e*% (e " %*i* " */n LD- " ,(" &e en,(ent* en (n *n'o de 1.5 + 10- &e %* " dien&i/n ) " i'(" (e e" %"o* de " t*n&e*en,i de ,"o* + (e &t t#in de)ende de " "et. Ade& &e 'ene*/ " '*, de" porcenta*e de error vs L+), donde ient*& " */n LD &e )e(e &e 'ene* (n " )*o9i,i/n e& de,i*- +o* ) =n,o> e9i&ti* (n " )*o9i,i/n.
clc
h=input('Ingresar coeficiente de coneccion [W!m"#$]:');
$=input('Ingresar coeficiente de conduccion [W!m#$]:');
%=input('Ingresar ingresar temperatura en la %ase [&]:');
a=input('Ingresar ingresar temperatura del am%iente [&]:');
n=L!x; m=(W!y);
(-")=.(($+y)!("+x));
(-n,)=.(($+x)!(y));
/=*eros(((n+m),n)-);
for i=":n.
(n-n.)=.(($+y)!("+x));
(((n+0),)-((((0.)+n),)))=.(($+x)!y);
(((n+0),)-((0+n),"))=.(($+y)!x);
(((n+0),)-((((0,)+n),)))=.(($+x)!y);
(((n+f),g,)-((n+(f.)),g,))=.(($+x)!y);
(((n+f),g,)-((n+f),g,"))=.(($+y)!x);
(((n+f),g,)-((n+(f,)),g,))=.(($+x)!y);
(((n+f),g,)-((n+f),g))=.(($+y)!x);
((n+p)-((n+p).n))=.(($+x)!("+y));
((n+p)-((n+p),n))=.(($+x)!("+y));
((n+p)-((n+p).))=.(($+y)!x);
(((n+m),)-(((n+m).n),))=.(($+x)!y);
(((n+m),)-((n+m),"))=.(($+y)!(x+"));
for 1=(m+n),":(n+m),n.
(1-1)=((h+x),(($+y)!x),(($+x)!y));
((n+m),n-n+m)=.(($+x)!("+y));
((n+m),n-(n+m),n.)=.(($+y)!("+x));
/((n+m),n-)=(((h+x)!"),((h+y)!"))+a;
&=in()+/;
end
6.2 ANÁLII GRÁ!ICO
Ot* o* de )*e,i* " %*i,i/n de te)e*t(* e& ,on (n di&t*i#(,i/n de ,o"o*e& (e *e)*e&enten " te)e*t(* "o "*'o de " ,o&ti""- )o* "o (e )*e&ento& ,ontin(,i/n )* "o& die*ente& %"o*e& de J;
67
m!
68
Figura #. <i&t*i#(,i/n '*, de te)e*t(* &iendo x= y=! mm
m!
Con e&te n"i&i& '*,o &e o#&e*% ,oo +o* ,ntidd de nodo&- " te)e*t(* "o "*'o de " ,o&ti"" &e di&t*i#(+e de o* & &(%id e& de,i*- no &e o*n tnt& *e,t& ,o)*d& ,on " di&t*i#(,i/n en "& '(*&
)* (n x= y=!mm ,oo en " '(* 1 o&t*d nte*io*ente.
P* J317 W
m!
72
m!
73
74
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