UNIVERSIDAD NACIONAL DE INGENIERÍA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURALY PETROQUIMICA
A
2
LABORATORIO DE OPERACIONES UNITARIAS I
TEMA
:
INTERCAMBIADORES DE CALOR
PROFESOR
:
ING. UBALDO APAZA
Feijoo Ruiz Carlos David Tafur Lopez Heine Enrique ESTUDIANTES
:
Frias Rivera Raul Gaudencio Huaylinos Vargas Jose Luis
2009-II
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
INTRODUCCIÓN Los intercambiadores de calor son uno de los equipos mas frecuentes, prácticamente no existe industria en la que no se encuentre un intercambiador de calor, debido a que la operación de calentamiento y enfriamiento es inherente a todo proceso. Siem Siempre pre que que exis existe te una una dife difere renc ncia ia de temp temper erat atur ura a en el univ univer erso so,, la ener energí gía a se tran transf sfie iere re de la regi región ón de may mayor temp temper erat atur ura a a la de meno menor r temperatura. De acuerdo con los conceptos de la termodinámica, esta energía transmitida se denomina calor. La ciencia llamada transmisión o transferencia de calor complementa los principios primero y segundo de la termodinámica clásica, proporcionando los méto método doss de anál anális isis is que que pued pueden en util utiliz izar arse se para para pred predec ecir ir la velo veloci cida dad d de la transmisión del calor, además de los parámetros variables durante el proceso en función del tiempo. Las leyes de la termodinámica tratan de la transferencia de energía, pero siempre se refieren a sistemas que están en equilibrio, y solo pueden utilizarse para predecir la cantidad de energía requerida para cambiar un sistema de un estado de equilibrio a otro, por lo que no sirven para predecir la rapidez con que puedan producirse estos cambios. Para Para un anál anális isis is comp comple leto to de la tran transf sfer eren enci cia a del del calo calorr es nece necesa sario rio considerar mecanismos fundamentales de transmisión: conducción, convección y radiación, además del mecanismo de acumulación. El análisis de los sistemas y modelos de intercambio de calor requieren familiaridad con cada uno de estos mecanismos y sus fundamentos, así como de sus interacciones. i nteracciones.
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
INTERCAMBIADORES DE CALOR OBJETIVOS Evaluar los coeficientes de transferencia de calor para un intercambiador tipo tubos concéntricos en disposición paralela y contracorriente. Comprobar las correlaciones recomendadas por los textos para determinar el coeficiente de película del agua circulando dentro de los tubos y el coeficiente de pelícu película la del vapor vapor conde condensá nsándo ndose se.. Asimis Asimismo, mo, comproba comprobarr los rangos rangos de los coeficientes individuales para el lado del agua (enfriamiento o calentamiento) y del lado del vapor (condensación en película) dado en los textos. Uso de las correlaciones apropiadas y de los números adimensionales los cuales caracterizan esta operación unitaria.
ll. RESUMEN DE LA PRACTICA DEL LABORATORIO LABORATORIO Los intercambiadores de calor son equipos donde se lleva a cabo la transferencia de calor entre una corriente fluida fría y una corriente fluida caliente. En la siguiente práctica de laboratorio vamos a observar cómo se puede aprovechar la energía que se encuentra almacenada en un fluido en fase gaseosa (fluido caliente) para poder calentar otro fluido que se encuentra en fase líquida (fluido frío). El equipo empleado para tal propósito se denomina intercambiador de calor de tubos concéntricos, el cual consta de un tubo interno de acero inoxidable a través de cual circulará el fluido frío, y un tubo anular de longitud efectiva de intercambiador de 3.28 metros, por donde circulará el fluido caliente. Asimismo, seremos capaces de determinar experimentalmente los coeficientes de calor peliculares del agua y del condensado, así como también el coeficiente global de transferencia de calor, a partir de la toma de data sobre las condiciones de operación durante el proceso. El análisis de la transferencia de calor por convección se complica por el hech hecho o de que que el movi movimi mien ento to del del flui fluido do jueg juega a un pape papell impo import rtan ante te en la transferencia de calor. En consecuencia, es esencial conocer la distribución de velo veloci cida dad d del del flui fluido do en movi movimi mien ento to para para pode poderr dete determ rmin inar ar el camp campo o de temp temper erat atur ura a en dich dicho o flui fluido do.. Es por por esta esta razó razón n que que al fina finall del del labo labora rato tori rio o debemos ser capaces de evaluar la influencia de la velocidad en la transferencia de calor. El flujo de calor desde un fluido a través de una pared sólida hasta un fluido
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
lll. FUNDAMENTO TEORICO CLASES DE INTERCAMBIADORES DE CALOR El intercambiador de calor es uno de los equipos mas frecuentes, prácticamente no existe industria en la que no se encuentre un intercambiador de calor, debido a que la operación de calentamiento y enfriamiento es inherente a todo proceso.
,La Fig. XVII.1 muestra el intercambiador de calor mas sencillo se compone de un tubo dentro de otro; este montaje de corrientes paralelas funciona, tanto en contracorriente como en cocorriente, circulando el fluido caliente o el frío a través del espacio anular, mientras que el otro fluido circula por la tubería interior.
INTERCAMBIADOR DE PASO SIMPLE (1-1).- (1-1).- El intercambiador más sencillo que consta de dos tubos concéntricos, no es adecuado cuando el gasto másico es elevado. Si se utilizan varios tubos concéntricos en paralelo, el peso del material de los tubos que se necesita se haría tan grande, que es mucho más económico el construirlos formando un conjunto de carcasa y tubos, de forma que se utiliza una carcasa común para muchos tubos; éste intercambiador, debido a que funciona con un solo paso de fluido en el lado de la carcasa y un solo paso de fluido en el lado de los tubos se denomina intercambiador 1-1, Fig XVII.2.
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En este tipo de intercambiador, uno de los fluidos circula por el interior de los tubos, mientras que el otro fluido se ve forzado a circular entre la carcasa y la parte exterior de los tubos, normalmente a ellos. Cuando las temperaturas TC del fluido del lado caliente y TF del fluido del lado frío son variables de un punto a otro, a medida que el calor va pasando del fluido más caliente al más frío, la velocidad de intercambio térmico entre los fluidos también también variará a lo largo del intercambiado intercambiador, r, porque su valor depende, depende, en cada sección, de la diferencia de temperaturas entre los fluidos caliente y frío. En un flujo paralelo en equicorriente, la temperatura final del fluido más frío nunca puede llegar a ser igual a la temperatura de salida del fluido más caliente. Sin embargo, en un flujo en contracorriente, la temperatura final del fluido más frío (que es el que se calienta) puede superar la temperatura de salida del fluido más caliente (que se enfría), puesto que existe un gradiente de temperaturas favorable a todo lo largo del intercambiador de calor. En un intercambiador en contracorriente, los coeficientes de transmisión de calor del lado de la carcasa y del lado de los tubos deben ser del mismo orden de magnit magnitud ud y ser grande grandess para para obtene obtenerr un coefi coeficie ciente nte globa globall satisf satisfact actorio orio.. La velocidad y turbulencia del líquido del lado de la carcasa son tan importantes como las del líquido del lado de los tubos. Para evitar el debilitamiento de las placas tubulares es preciso mantener una distancia mínima entre los tubos, por lo que no resulta práctico colocar los tubos tan juntos que la sección libre para el flujo del fluido por el exterior de los tubos sea tan pequeña, como la del interior de los mismos.
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Si las dos corrientes son del mismo orden de magnitud, la velocidad del lado de la carcasa es menor que la del lado de los tubos; por esta razón se instalan placas deflectoras con el fin de disminuir la sección de flujo del líquido del lado de la carcasa y obligarlo a circular en dirección cruzada a la bancada de tubos en vez de hacerlo paralelamente a ellos; de esta forma se consigue un coeficiente de transferencia de calor más elevado en flujo cruzado, que en circulación paralela a los tubos. El flujo pasa perpendicularmente a los tubos, circulando hacia abajo en la primera sección, hacia arriba en la segunda, y así sucesivamente; la turbulencia adicional que se crea mediante mediante este tipo de flujo aumenta el coeficient coeficiente e de transmisión transmisión de calor del lado de la carcasa. Las pantallas , (placas deflectoras), son discos circulares de una plancha metálica a los que se ha cortado, para estos intercambiadores, un cierto segmento circular, de forma que la altura de este segmento sea igual a la cuarta parte del diámetro inte interi rior or de la carc carcas asa, a, por por lo que que las las plac placas as defl deflec ecto tora rass así así obte obteni nida dass se denominan placas del 25%, viniendo perforadas para recibir los tubos; para evitar fugas, o hacer que estas sean mínimas, las holguras entre las placas y la carcasa, y entre las placas y los tubos deben ser pequeñas. Este tipo de construcción resulta práctico solamente para carcasas pequeñas.
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La carcasa carcasa tiene un diámetro normalizado; la distancia o espaciado entre placas no debe ser menor de 1/5 del diámetro de la carcasa ni mayor que el diámetro interior de la misma. Los tubos se unen a la placa tubular acanalando los orificios y acampanando en su interior los extremos de los tubos mediante un mandril cónico rotatorio que fuerza al metal del tubo más allá de su límite elástico, de forma que el metal se introduce en las acanaladuras; en los intercambiadores que van a trabajar a presiones elevadas, los tubos se sueldan a la placa tubular. En general, el intercambiador de calor de carcasa y tubos tiene unas placas (cabezales) en donde se fijan los tubos por ambos extremos, mediante soldadura u otro tipo de fijación; este tipo de construcción tiene un bajo costo inicial, pero sólo se puede utilizar para diferencias pequeñas de temperatura entre el fluido caliente y el frío, puesto que no se ha hecho ninguna previsión para evitar las tensiones mecánicas de origen térmico debidas a la dilatación entre los tubos y la carcasa. Otra desventaja consiste en que el montaje del haz de tubos no se puede desmon desmontar tar para para su limpie limpieza za;; estos estos inconv inconveni enient entes es se soluci soluciona onan n fácilme fácilmente nte haciendo que una de las placas de tubos esté fija, mientras que la otra se sujeta mediante pernos a un cabezal flotante que permite el movimiento relativo entre el haz de tubos y la carcasa; la placa de tubos flotante está sujeta con mordazas entre la cabeza flotante y unas bridas, de modo que es posible retirar el haz de tubos para su limpieza.
Coeficiente global de transmisión de calor (U) Es razonable esperar que la densidad de flujo de calor sea proporcional a una fuerza impulsora. Para el flujo de calor la fuerza fuerza impulsora se toma como (Th (Th - Tc), siendo Th la temperatura media del del fluido caliente y Tc Tc la del fluido frío. El término (Th - Tc) es la diferencia global de temperatura local ∆T. Es evidente que ∆T puede variar considerablemente de un punto a otro a lo largo del tubo y, por lo tanto, puesto que la densidad de flujo de calor es proporcional a ∆T, la densidad de flujo de calor calor variará variará también también con la longit longitud. ud. Es necesar necesario io partir partir de una ecuación diferencial, localizando la atención en un área diferencial dA a través de la cual se transmite un flujo diferencial de calor dq bajo la acción de una fuerza
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Análogamente, si se elige el área interna Ai, el coeficiente está también basado sobre dicha área y se se representa por por Ui. Puesto que ∆T y dq son independientes de la elección del área, se deduce que: (Uo/Ui) = (dAi/dAo) = (Di/Do)
Cálculo de coeficientes globales a partir de coeficientes individuales El coeficiente global se obtiene a partir de los coeficientes individuales y de la resistencia de la pared del tubo en la forma que se indica seguidamente. La velocidad de transmisión de calor a través de la pared del tubo viene dada por la siguiente ecuación diferencial: (dq/dAml) = (Km*(Twh-Twc))/Xw donde: del tubo.
(Twh-Twc) = diferencia de de te temperatura a través de de la la pa pared Km = conductiv conductividad idad calorífica calorífica de la pared. pared. Xw = espesor espesor de la pared del tubo. (dq/dAml) = dens densid idad ad de fluj flujo o loca locall de calor calor,, basa basada da en la media media logarítmica de las áreas interior y exterior del tubo.
Se tiene además que:
∆T = Th – Tc = (Th – Twh) Twh) + (Twh – Twc) Twc) + (Twc – Tc) Tc) = dq/(dAi * hi) + dq * Xw/(dAml * Km) + dq/(dAo * ho) Supóngase que la velocidad de transmisión de calor esta arbitrariamente basada en el área exterior. exterior. Si se despeja despeja dq de la ecuación anterior anterior y ambos miembros miembros de la ecuación que resulta se dividen entre dAo, se tiene: (dq/dAo) = (Th – Tc)/((1/hi)*(dAo/dAi) + (Xw/Km)*(dAo/dAml) (Xw/Km)*(dAo/dAml) + 1/ho) Ahora: (dAo/dAi) = (Do/Di)
y
(dAo/dAml) = (Do / Dml)
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
Si como área base se toma el área interior Ai, se obtiene el coeficiente global
Ui = 1/((1/ho)*(Di/Do) + (Xw/Km)*(Di/Dml) + 1/hi)
Coeficiente global en forma de resistencia El inverso de un coeficiente global puede considerarse como una resistencia global compuesta de tres resistencias en serie. La resistencia total o global viene viene dada por la ecuación 1/Uo = (1/hi)*(Do/Di) + (Xw/Km)*(Do/Dml) + 1/ho equivalente a: Ro = ri*(Do/Di) + rw*(Do/Dml) + ro Los términos individuales del segundo miembro de la ecuación de la resistencia global representan las resistencias individuales de los dos fluidos y de la pared metálica. metálica. La caída global global de temperatura temperatura es proporcion proporcional al a 1/U, y las caídas caídas de temperatura en los dos fluidos y en la pared son proporcionales a las resistencias individuales, o bien:
∆T/(1/Uo) = ∆Ti/((1/hi)*(Do/Di)) = ∆To/(1/ho) Donde:
∆T = Caída global global de temperatur temperatura. a. ∆Ti = Caída de tempera temperatura tura a través través del fluido fluido interior. interior. ∆Tw =Caída de temperatura a través de la pared metálica. ∆To =Caída de temperatura a través del del fluido exterior
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Esquema del equipo en arreglo Contracorriente
Donde: V1,V2,V3,V4,V5,V6,V7 son válvulas. P1,P2,P3 son las presiones en los manómetros. MF es el medidor de Flujo de agua en GPM/LPM. El flujo de vapor se mide con el vortex en flujo masico m asico en lb/h. Los puntos del 1 al 7 indican donde se toman las medidas de temperatura.
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
Esquema del equipo en arreglo Paralelo
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
La medición de los Temperaturas se realizara con el panel digital que se indica en la figura en los cuales los puntos indicados en el diagrama del equipo de Intercambiador de doble tubo se pueden medir cambiando el selector circular al número deseado respectivo según indican los arreglos anteriores.
Vapo
r H2O
∆T 1
∆T 2 1
2 PARALELO
Vl. CUESTIONA CUESTIONARIO RIO
Vapor H2O
∆T 1 1 2 CONTRACORRIENTE
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
δ: Vector Unitario V: Velocidad Media Φv*: Función de disipación expresada en función de v*, x*, y*, z* To: Temperatura Ambiente
∂ D ∂ ⇒ = ∂t * V ∂t ρ Cp (T 1 − T 0 )
(T 1
V ∂T * D
∂t *
− T 0 )
= K
∂T * D ∂T = ∂t * V ∂t
∀ *2 D
2
= V 2φ v * ∇* = D∇ ∇ *2 = D 2∇2
φv
⇒
[T 0 + T * (T 1 − T 0 )] + µ V 2φ v *
∂T * ∀ *2 D D = K µ V 2φ v [T 0 + T * (T 1 − T 0 )] + 2 2 ∂t * V ρ Cp (T 1 − T 0 ) D V ρ Cp (T 1 − T 0 ) D ∂T * 1 Br φ v * = ∇ *2 T *+ ∂t Re Pr Re Pr Donde: VD ρ VD Re = µ
Pr =
Cp µ
Br =
K
µ V 2 K (T 1
Entonces: Q
= hA∆T ⇒
h=
Q A∆T
⇒
h=
− T 0 )
Cpm ∆T A∆T
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
2.
Por análisis dimensional deducir la ecuación (18) para una convección forzada. Ver referencias 2, 3, 7, 10, 12, 14.
Sabemos:
= aN Re
Nu Nu
b
N Pr
c
n
Pr Pr
b
w
……(1)
Como: Pr b
=
Cpb µ b K b
y
Pr w
=
Cpb µ w K w
Reemplazando en (1):
Cpb µ b K b b c Nu = aN Re N Pr Cpb µ w K w
n
Como: Cp b
= Cp w
y
K b
b
= K w
µ
n
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
reposo. A corta distancia de la entrada se forma una capa limite laminar a lo largo de la pared del tubo. Si la turbulencia en la corriente de entrada del fluido es alta, la capa limite se vuelve turbulenta rápidamente, independiente de si la capa delimitadora permanece laminar o se vuelve turbulenta, su espesor se incrementa hasta que llena todo el ducto. De este punto en adelante el perfil de velocidad y de temperatura permanece sin cambios significativos. Estos perfiles de velocidad y temperatura nos indican como varían dichas propiedades a lo largo del diámetro de la tubería y se dicen que están en desarrollo porque conforme avanzan los perfiles se van estabilizando conforme se va desplazando en el medio de este caso en el interior de la tubería, hasta que estos perfiles se mantengan constantes. Estos perfiles varían de acuerdo al tipo de flujo que se tiene.
¿Qué en ¿Qué entie tiend ndee us uste ted d po porr fl fluj ujos os la lamin minar ares es co comp mple leta tame ment ntee desarrolladas con una temperatura superficial constante y flujo de calor constante?, explique.
4.
El desarrollo de la capa limite en un fluido que se calienta o enfría en un ducto es cual cualititat ativ ivam amen ente te simi simila larr al de la capa capa hidr hidrod odin inám ámic ica. a. A la entr entrad ada a la temperatura suele ser uniforme transversalmente, pero a medida que el fluido corre a lo largo del ducto el espesor de la capa caliente o fría se incrementa hasta que se transfiere calor hacia o desde el fluido que se encuentra en el centro del ducto ucto.. Desp espués de este ste punto, nto, el perf perfilil de la temp temper erat atur ura a per perman manece esencialmente constante si el perfil de velocidad es totalmente estable.
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
Para gases a presiones ordinarias y temperaturas basadas en µ = 1.76 x10 −5 Pa. s 0.0426 lb
ft .h h = bc ρ 0.8ν 0.8 / D 0.2
Donde: b = 3.04x10-3 (S.I) y 1.44x10 -2 (U.S. usual) Para aire a presión atmosférica h = b(ν 0.8 / D 0.2 )
Donde:
µ C p k
= 0.78 y
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
Al ser: π dLτ 0
π d 2
= P
4
⇒ P =
4 Lτ 0 d
L ρ u F 2
= λ q0*
2d
; τ 0 =
λρ u F 2 8
= C W =
λ 4
=
C W ρ u F 2
= hc (T pF − T F )
Resultando finalmente: u F
=
C W λρ u F 2 8 Pr hc (T pF
− T F )
St =
(T pF − T F ) =
Nu Re Pr
=
hC C pF ρ u F
Que concuerda bastante con la ecuación:
C W λρ u F 2 8 Pr
=
λ 8 Pr
=
; hC = Cw 2 Pr
C W λρ u F 8 Pr
2
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
Ecuación que se puede integrar entre las condiciones de: T = T pF , u = uF y las condiciones medias del flujo principal, T = T F, u = uF, obteniéndose: T F
q*
u F
∫ dT = − τ C ∫ du ⇒ T T pF
T
pF
0
− T F =
q *u F
τ C F
⇒ q = hC (T pF − T F ) = hC * 0
Deduciéndose: hC
=
τ 0 C F u F
El número de Stanton es: St =
= τ 0 = λ
Nu Re Pr
=
u F 2 8
hC
ρ u F C F
ρ =
=
λ 8
λρ u F C F 8
=
C W 2
q 0*u F
τ 0 C F
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA 0.14
n factor factor adimension adimensional. al. F que se utiliza únicamente cuando la viscosidad n pF
varia marcadamente con la temperatura, tomando que determina el valor de h C la forma: hC
= 0.023
k F d
0.14
n Re 0.8 Pr 1 / 3 F n pF
La analogía de Colburn define un factor adimensional ψ, función de número de Reynolds, de la forma: 2/3
−0.2
C F n = 0.023 d i G Ψ= C F G k n hC
Que se utiliza en gran número de ecuaciones empíricas con carácter aproximado
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
Porcentaje de pérdidas al ambiente
Q vapor - Q agua x100% Q vapor
%perdidas perdidas = Ecuaciones para el calculo de:
C1 = C2 = C3 = C4 =
Densidad :
ρ agua T °K
C
=
C 1 T 1+ 1− Kmol ρ C 2 3 C m
C 4
3
5.459 0.305 .3054 42 647.13 0.081
M = 18.015
+ C × T + C × T 2 + C × T 3 + C × T 4
C1 = 276370
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
FLUJO DE CONDENSADO
CAUDAL LPM 0.73 0.8782
T5 (°C) in 130.40 130.20
T1 (°C) out 130.90 129.60
T prom. °K 403.65 402.90
Densidad Kmol/m3 53.47 53.48
W agua Kmol/s 0.000651 0.000783
λ
J/Kmol 39279976.47 39319649.87
Q cond. J/s 25560.41 30780.55
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
Determinación experimental experimental del coeficiente de película del agua hi y del lado del vapor ho, utilizando las ecuaciones 9 y 10 respectivamente. Calculo para el lado delQAgua
hi =
agua
Ai × LMTDi LMTDi
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
PRESIÓN = 15 psi Q agua J/s 13881.36 17758.87 19165.71
TW4 °C 131.00 130.50 129.60
TW3 °C 130.10 128.80 128.70
TW2 °C 130.30 129.00 128.70
Tprom °C 130.467 129.433 129.000
Ti °C 130.466 129.433 128.999
Q agua J/
T 6 ( ° C) i
T7 (°C) t
Ti °C
LMTDi °K
hi W/
2
.°K
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
0.73 0.88 1.01
2.178E-02 2.620E-02 3.013E-02
595.738 728.890 761.785
Aplicando una Regresion Lineal
A= Rw °K/W
21.354 18.423 16.473
r = 0.98
1.272E-02 Ro °K/W
ho W/m^2 °K
ho =
1 Ro Ro × Ao
1.679E-03 1.372E-03 1.313E-03
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UNIVERSIDAD NACIONAL DE INGENIERIA FACULTAD DE INGENIERIA DE PETROLEO, GAS NATURAL Y PETROQUIMICA
COEFICIENTE PELICULAR PELICULAR DE VAPOR V APOR CONDENSADO EN LA SUPERFICIE EXTERNA Ec. 25 1
ARREGLO EN PARALELO h
PRESIÓN =15 psi PROPIEDADES FISICAS
k f × ρ f × g × λ 4 × µ To Do D o ∆ × × f 3
= 0.725
∆To = Tv − Tw
2
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