Métodos de
Métodos de
Transferencia de Calor
Transferencia de Calor
en Flujo Bidireccional
en Flujo Bidireccional
por Conducción
por Conducción
Pro"esor#
Pro"esor#
Realizado
Realizado por#
por#
Luis
Luis Castillo Castillo Ninoska Ninoska JiménezJiménez
$ctubre %&'(
$ctubre %&'(
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Conducción de Calor
Conducción de Calor Bidireccional
Bidireccional
Es la forma que transmite el calor en cuerpos sólidos, se calienta un
Es la forma que transmite el calor en cuerpos sólidos, se calienta un
cuerpo, las moléculas que reciben directamente el calor aumenta su
cuerpo, las moléculas que reciben directamente el calor aumenta su
vibración y chocan con las que rodean; estas a su vez hacen lo mismo con
vibración y chocan con las que rodean; estas a su vez hacen lo mismo con
sus vecinas hasta que todas las moléculas del cuerpo se agitan, por esta
sus vecinas hasta que todas las moléculas del cuerpo se agitan, por esta
razón, si el extremo de una varilla metálica se calienta una ama, transcurre
razón, si el extremo de una varilla metálica se calienta una ama, transcurre
cierto tiempo para
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Transferencia de Calor por Conducción
Transferencia de Calor por Conducción
en Cerramientos Heterogéneos
en Cerramientos Heterogéneos
En el supuesto de un cerramiento heterogéneo, que combine
En el supuesto de un cerramiento heterogéneo, que combine
transmisión de calor por capas en serie y por secciones en paralelo, podrá
transmisión de calor por capas en serie y por secciones en paralelo, podrá
ocurrir que las temperatura interiores de las diferentes secciones a cierta
ocurrir que las temperatura interiores de las diferentes secciones a cierta
profundidad di!eran, generando transmisiones de calor bidireccionales que
profundidad di!eran, generando transmisiones de calor bidireccionales que
complican enormemente su cálculo, siendo preciso recurrir a métodos
complican enormemente su cálculo, siendo preciso recurrir a métodos
numéricos de gran comple"idad, como los de elementos !nitos, que exceden
numéricos de gran comple"idad, como los de elementos !nitos, que exceden
a este traba"o #e llama especialmente la atención al caso que se considere
a este traba"o #e llama especialmente la atención al caso que se considere
la capa l$mite de la convección como una capa en serie que aporta su
la capa l$mite de la convección como una capa en serie que aporta su
resistencia super!cial a la resistencia total del cerramiento, originando en las
resistencia super!cial a la resistencia total del cerramiento, originando en las
áreas del cerramiento con diferentes conductancias, también llamadas
áreas del cerramiento con diferentes conductancias, también llamadas
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Métodos de Transferencia de Calor por
Métodos de Transferencia de Calor por
Conducción
Conducción
%nal$tico& 'mplica obtener una solución
%nal$tico& 'mplica obtener una solución exacta de la ecuación()*
exacta de la ecuación()*
+rá!co& roporciona solo resultados aproximados en puntos
+rá!co& roporciona solo resultados aproximados en puntos
discretos
discretos
-umérico (de diferencias !nitas, de elemento !nito o de elemento
-umérico (de diferencias !nitas, de elemento !nito o de elemento
de
de frontera*
frontera* #e
#e utili
utiliza
za para
para obtener
obtener resultados
resultados extremadamente
extremadamente
precisos en cuanto a geometr$as comple"as
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Método Analítico
Método Analítico
Este
Este método
método permitirá
permitirá encontrar
encontrar la
la distribución
distribución de
de temperatura
temperatura
resolviendo
resolviendo la
la
ecuación
ecuación de
de conducción
conducción de
de calor
calor en
en los
los dos
dos e"es
e"es
coordenados
coordenados
Esta es una ecuación de tipo lineal homogénea
Esta es una ecuación de tipo lineal homogénea
parcial
parcial
#i la ecuación es valida para
#i la ecuación es valida para
T
T
, también los es para
, también los es para
una
una
C•T
C•T
.onde a, b, c, d, son condiciones de
.onde a, b, c, d, son condiciones de
frontera
frontera
%l solucionar esta ecuación se encuentran
%l solucionar esta ecuación se encuentran
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El
El método
método anal$tico
anal$tico que
que se
se aplica
aplica a
a la
la solución
solución se
se llama
llama
#E%0
#E%0%1'2-
%1'2- .E
.E 3
3%0'%
%0'%45E#
45E#
#olución
#olución queda
queda acotada
acotada entre
entre cero(6*
cero(6* y
y uno()*
uno()*
E7E859&
E7E859&
#e tiene un sólido con las siguientes condiciones de frontera&
#e tiene un sólido con las siguientes condiciones de frontera&
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Método Gráco
Método Gráco
El
El principio
principio básico
básico de
de la
la solución
solución por
por este
este método
método es
es que
que las
las
l$neas isotermas son perpendiculares a las l$neas de u"o de calor
l$neas isotermas son perpendiculares a las l$neas de u"o de calor
en un punto espec$!co .e esta manera, se toma el elemento de
en un punto espec$!co .e esta manera, se toma el elemento de
análisis y se trata de dibu"ar sobre él un sistema de cuadrados
análisis y se trata de dibu"ar sobre él un sistema de cuadrados
curvil$neos compuesta por l$neas de u"o de calor y l$neas
curvil$neos compuesta por l$neas de u"o de calor y l$neas
isotermas
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Metodología
Metodología
)
) 'denti!car l$nea
'denti!car l$neas de sime
s de simetr$a en la
tr$a en la ransfer
ransferencia de
encia de 1alor
1alor
<
< 5as l$n
5as l$neas d
eas de sim
e simetr$a
etr$a se co
se compor
mportan c
tan como s
omo super
uper!cies
!cies
adiabáticas (l$neas q=6* 5as l$neas isotérmicas son
adiabáticas (l$neas q=6* 5as l$neas isotérmicas son
perpendiculares a las l$neas de simetr$a
perpendiculares a las l$neas de simetr$a
>
> 'nten
'ntentar dibu
tar dibu"ar las l$ne
"ar las l$neas de temp
as de temperat
eratura cons
ura constante de
tante dentr
ntro
o
del sistema, buscando que sean perpendiculares a las l$neas
del sistema, buscando que sean perpendiculares a las l$neas
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%eterminación de la Transferencia de
%eterminación de la Transferencia de
Calor
Calor
5a
5a manera
manera en
en que
que se
se aprovecha
aprovecha una
una grá!ca
grá!ca de
de u"o
u"o para
para
obtener la transferencia en un sistema bidimensional es
obtener la transferencia en un sistema bidimensional es
evidente seg?n se muestra en la ecuación&
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&ecomendaciones prácticas para el
&ecomendaciones prácticas para el
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F
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&ecomendaciones para el uso de la
&ecomendaciones para el uso de la
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Método (umérico
Método (umérico
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