PRÁCTICAS Nº 4 - 5 DETERMINACIÓN DE PÉRDIDAS DE CALOR EN UN SISTEMA TÉRMICO EN FORMA UNIDIMENSIONAL Y BIDIMENSIONAL 1. OBJETIVO Determinar el flujo de calor en las zonas transciende y estacionaria Demostrar el primer principio de termodinámica para el flujo de calor Determinar las pérdidas de calor conclusión y convección 2. MODELO DE CÁLCULO.
Se modela un horno casero que resulte en forma de caja rectangular con dimensiones interiores de 46 cm x 61 cm x 76 cm y exteriores de 51 cm x 66 cm x 81 cm. Si se ignoran las pérdidas de calor a través de las esquinas y las aristas; la temperatura de la pared interior es de 204 , la temperatura de pared exterior es de 38 , y el material de las paredes es ladrillo. Estima la potencia en watts necesaria que se debe suministrar para mantener está condición de estado estacionario.
1. Forma Unidimensional:
Solución: Datos: Hay tres parejas de paredes en un horno casero a través de las cuales puede ocurrir transferencia de calor por conducción. (A) 2 paredes con dimensiones: 46cm x 61cm x 2.5cm cada una. (B) 2 paredes con dimensiones: 61cm x 76cm x 2.5cm cada una. (C) 2 paredes con dimensiones: 46cm x 76cm x 2.5cm cada una. Dónde: L: (Espesor) = 2.5cm
La temperatura en la pared interior es T 1 = 204 . La temperatura en la pared exterior es T 2 = 38 .
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De tablas se tiene: K = 0.45W/m-K. Suposiciones: (1) Existen condiciones de estado estacionario (2) El material de las paredes tiene conductividad térmica constante. (3) Se puede despreciar los efectos de pérdida de calor a través de las aristas y las esquinas. (4) Se tiene flujo de calor unidimensional en cada pared. Análisis: Para condiciones de estado estacionario el flujo de energía a través de todas las paredes es igual a la energía que suministra el elemento calentador al hornillo. El calor fluye a través de las tres parejas de paredes. Para cada pareja, la conducción de calor puede calcular según la ecuación de Fourier:
Cálculos:
Flujo calorífico en las paredes de la pareja (A):
Flujo calorífico en las paredes de la pareja (B):
Flujo calorífico en las paredes de la pareja (C):
Comentarios:
De haber un suministro de potencia igual a 6.54 KW para mantener las temperaturas para condiciones de estado estacionario. 2. Forma Bidimensional: Para el mismo modelo calcule la transferencia de calor en el sistema.
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2)
3)
4)
Transferencia o pérdida de calor:
3. PARTE EXPERIMENTAL:
1. Pérdida de calor unidimensional en el sistema térmico: 1.1. Anotar datos: Espesor de las paredes: 1.5cm Dimensiones de las paredes del sistema: Interna:
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a. 2 paredes con dimensiones: 24cm x 12cm cada una. b. 2 paredes con dimensiones: 13cm x 12cm cada una. c. 2 paredes con dimensiones: 24cm x 13cm cada una. Externa:
a. 2 paredes con dimensiones: 27cm x 15cm cada una. b. 2 paredes con dimensiones: 16cm x 15cm cada una. c. 2 paredes con dimensiones: 27cm x 16cm cada una. Tabla 1: Tiempo (min)
Temperatura Interna 0 1 2 3 4 5 6 7 8 9
26 53 75 91 102 110 115.5 119 122 124
Temperatura Externa de Temperatura en Temperatura en la Pared Bordes Esquinas 25.6 25.7 25.9 27.2 27.3 27.2 28.6 28.6 28.5 32.1 32.2 32.1 33.7 33.6 32.8 35.9 36 35.1 35 34 33.6 35.6 35 33.7 36 36.2 35.4 36.8 36.5 35.7
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1.2. Determinar la pérdida de calor total unidimensional en la caja térmica. Use la Ec. de Fourier:
4. Cálculos:
Flujo calorífico en las paredes de la pareja (A):
Flujo calorífico en las paredes de la pareja (B):
Flujo calorífico en las paredes de la pareja (C):
Comentarios:
De haber un suministro de potencia igual a condiciones de estado estacionario.
para mantener las temperaturas para
2. Pérdida de calor bidimensional en el sistema térmico: 2.1. Anotar datos: Temperatura promedio interna: 96.5
Temperatura promedio externa: 33.0
Temperatura promedio en los bordes u orillas: 32.9 Temperatura promedio en las esquinas: 32.3
2.2. Determine la pérdida de calor bidimensional total en la caja térmica. Use la Ec. de Fourier:
Propiedades del poliestireno rígido:
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Forma Bidimensional:
Para el mismo modelo calcule la transferencia de calor en el sistema. 1)
2)
3)
4)
⁄ | | |
Transferencia o pérdida de calor:
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5. CONCLUSIONES: Primero. Se vio el comportamiento de una estructura real como es que esta pierde calor en todas direcciones y se puede idealizar en sistemas unidimensionales y bidimensionales. Segundo. Conociendo este comportamiento podemos tomar mejores decisiones respecto al material que queremos usar y además la forma geométrica como debe de estar la estructura. 6. Problema Propuesto: La pared compuesta de un horno ho rno consiste de tres materiales, dos de los cuales son de conductividad térmica conocida, = 20 y = 50 y de espesor conocido = 0.30 y =0.15 El tercer material, B, que se intercala entre los materiales A y C, de espesor conocido = 0.15 pero de conductividad térmica, desconocida.
En condiciones de operación de estado estable, las condiciones revelan una temperatura de la la superficie externa =40 y una temperatura temperatura de la superficie superficie interna =800 y una temperatura del aire del horno (atmósfera (a tmósfera del horno) =1200 . Se sabe que el coeficiente de trasferencia de calos por convección interior hi=25
¿Cuál es el valor de
?
⁄
¿Cuál es el calor total perdido a través de las paredes del horno, considerado que es cúbico y
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Solución: -
Forma unidimensional: 1. Flujo de calor:
⁄ ⁄
2. Conductividad térmica K B:
⁄
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⁄
2. Pérdida de calor en los bordes de orillas:
⁄ ⁄
3. Pérdida de calor en los vértices:
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⁄
4. Pérdida de calor total en el horno:
Porcentaje de la distribución de pérdidas de calor: 84.4% en Paredes 15.1% en Bordes 0.5% en Vértices 100.0% O bien:
⁄
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PRÁCTICA Nº 6 TIPOS DE HORNOS Y DETERMINACIÓN DE LAS PÉRDIDAS DE CALOR EN UN HORNO ELÉCTRICO TIPO MUFLA 1. Objetivos. Conocer distintos tipos de hornos. Determinar la perdida de calor en un horno tipo mufla. Determinar que tipo de horno es adecuado para cada material. 2. FUNDAMENTO TEORICO. Tipos De Hornos: A. Horno Cubilote: Es un horno en posición vertical que se alimenta con carbón y el material de fundición por un costado. Tiene una tapa hermética en la base que va puesta y es sacada para la limpieza de este, la chimenea esta en la superior del horno. Con revestimiento de ladrillos y refractarios cambiables c ambiables en las compuertas.
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a) Horno Giratorio Esquematizado: (1)cubierta de acero ac ero externa (2)espesor de cubierta (3)pintura externa anticorrosiva (4)revestimiento (4 )revestimiento refractario o cemento (II)tipo de revestimiento para hornos (6)sensores de tonelaje del horno (L)soporte de sensores (9)interior del horno (10)sensor de temperatura. C. Horno a Leña: Horno cilíndrico con paredes cubiertas con ladrillo y cemento cemento de revestimiento, revestimiento, es alimentado de leña y carbón para su uso, es utilizado para fundiciones en escala menor.
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1. Pérdidas De Calor En Un Horno Eléctrico Tipo Mufla: Cuando se enciende un horno este comienza a absorber calor (paredes estructura y otros componentes) hasta mantener un equilibrio con el entorno, en este instante decimos que el horno está en un estado estacionario. Entonces las pérdidas de calor de un horno eléctrico se transportan hacia el medio ambiente pasando por las paredes del mismo y llegar finalmente al medio ambiente, es decir que cuando el horno está en estado estacionario, sólo la resistencia para compensar la pérdidas. Podemos tener el siguiente diagrama. Se pueden determinar las pérdidas de acuerdo a cuerdo a los siguientes criterios: a) Usando pérdidas por radiación y convección al medio ambiente. b) Considerando las pérdidas por conducción a través de la paredes del horno. c) Considerando todas las resistencias; es decir, las paredes del horno, la convección y la radiación al medio ambiente.
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⁄ (( ) ⁄
No se considera la placa de acero que tiene una K=48W/m .
Si consideramos la resistencia de la pared de acero, entonces tendríamos:
Es decir que la influencia de la placa de acero como resistencia térmica es despreciable, por lo tanto se puede no considerar considerar para los cálculos.
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Usando el concepto de Resistencia térmica:
Cálculo de
:
⁄
Podemos notar que las resistencias de radiación radiac ión y convección están en paralelo, entonces:
La resistencia de todo el sistema será:
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3. Determinación de las pérdidas de calor considerando radiación y convección:
⁄ ⁄ ( ) ( ) ) ⁄ ⁄ Para las pérdidas de radicación y convección se tiene:
Luego las pérdidas totales serán:
Tabla 1: Resumen de las pérdidas de calor
Q total (W)
Conducción
Radiación-Convección
Las Tres Resistencias
33.00
31.79
33.96
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PRÁCTICAS Nº 7 – 8 CALENTAMIENTO Y ENFRIAMIENTO ENFRIAMIENTO EN TRATAMIENTOS DE METALES 1. Objetivo. Determinar el comportamiento térmico de los metales cuando estos sometidos a tratamientos térmicos. Determinar la velocidad de enfriamiento de los metales. 2. FUNDAMENTO TEORICO. 1. Recocido De Regeneración, Normalizado Y Temple Normal: Los procesos que se siguen en estos tres tratamientos. Tienen entre si ciertas semejanzas que conviene destacar conjuntamente para luego estudiar los caracteres c aracteres que los diferencian. En los tres casos se calienta el acero a una temperatura ligeramente superior a la crítica, luego, después de un periodo de permanencia a esa temperatura, suficiente para conseguir el estado austenítico, se enfrían las piezas. Los enfriamientos diferentes en los tres casos. En los recocidos, se hace muy m uy lentamente dentro del horno. En los temples, se hace muy
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No es recomendable introducir las piezas frías de más de 200 mm de diámetro en hornos cuya temperatura sea superior a 350 , porque el acero relativamente frío es poco plástico, no admite deformaciones y las tensiones que se crean pueden originar grietas.
El paso de la zona crítica no es peligro cuando toda la pieza tiene la misma temperatura o la diferencia entre el centro y la l a periferia son pequeñas como ocurre en los calentamientos lentos. En cambio cuando en las piezas más gruesas la periferia alcanza esa temperatura antes que en el centro. La zona periférica sufre una contracción, mientras que el centro que no ha llegado a esa dilatación todavía y el peligro de grietas, es mayor. Para evitar que la tensiones sean peligrosas, conviene que en las secciones transversales la diferencia de temperatura entre dos puntos de un mismo radio situados a 25mm de distancia, no sea superior a 20 , y para conseguirlo, la duración del calentamiento desde la temperatura ambiente a los 850 , debe ser superior a media hora por pulgada de diámetro, y si es posible contiene que la duración del calentamiento sea de una hora por pulgada de diámetro (aprox. 2 min/mm de espesor de la pieza).
En síntesis las variables que deben tenerse en cuenta en el calentamiento son: Masa de la
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Tabla 1: Datos Experimentales Del Normalizado. PRE - CALENTAMIENTO
LECTURA TIEMPO (min)
TEMP. INICIAL (To)
TEMP. DEL HORNO (Ts,1)
1
0
20
20
2
4
20
100
3
8
20
200
4
14
20
300
5
24
20
400
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1
0.00
20
20
2
1.02
20
100
3
2.50
20
200
4
4.30
20
300
5
6.50
20
400
6
9.40
20
500
7
13.50
20
600
8
16.50
20
650
9
21.20
20
700
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En consecuencia, el modelo de las curvas experimentales será: NORMALIZADO: TEMPLE:
⁄ ⁄
t: tiempo de calentamientos en minutos. 2. Fase De Enfriamiento: Recocido De Regeneración. Se hace presente en caso después de haber terminado el ciclo de calentamiento; c alentamiento; el enfriamiento de las probetas se realiza en el interior del horno cerrado. Es importante determinar el área efectiva el horno: En hornos pequeños como los de laboratorio el área no son constantes y es necesario emplear alguna clase de promedio de área de pared interior A 1 y el área exterior A 2. Las paredes del horno son confinadas co nfinadas interior y exteriormente por paralelepípedos
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1
0
910
25
2
15
184
25
3
20
110
25
4
25
77
25
5
30
54
25
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3) Conducción y convección natural o libre comprendido desde 100
Tabla 4: Temperaturas De Enfriamiento En El Temple.
TEMPERATURA ( ) LECTURA
TIEMPO (seg)
Ts (superficial)
1
0
770
T∞ (agua) 20
a 20 .
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Calor recibido por la pieza en el horno; convección y radiación:
(Ec. 1)
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σ: constante de Boltzmann.
Ts: temperatura de la superficie. T∞: temperatura del fluido que rodea a la pieza.
Ciclo de enfriamiento: Es similar al ciclo de calentamiento.
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Ó
(Temperatura media)
6. Conclusiones:
(Ec. 7)
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Gráfico 2: Temperatura vs Tiempo De Calentamiento Y Enfriamiento.
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Gráfico 4: Temperatura vs Tiempo De Calentamiento Y Enfriamiento.
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Temperatura dela Horno en
T
= Th:
920
780
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PRÁCTICA Nº 9
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-
Solución:
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