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Steel plates 40 cm per side and 1 cm thick are heat treated in a static oven. Inside the oven there is a shelf where 10 separate plates are placed, in such a way that the heat treatment of one does not affect the treatment of the others. The oven is electric and emits radiation heat towards the plates. In the oven an atmosphere with nitrogen is generated to avoid the oxidation of the material, this gas acts as a convective medium on the plates. Before being placed in the oven, the plates are at room temperature of 25 ° C. The heat treatment of the plates begins with a preheating. At this stage, the combined convection and radiation heat transfer coefficient in the oven is 46 W / m2- ° C. During preheating, the oven controls the internal temperature with a quadratic compensation, therefore, the walls and the nitrogen atmosphere have a temperature Th that varies according to the expression: Th = a + bt2 where a = 750 ° C, b = 3 x 10- 5°C/ s2 and t is the time in seconds. The temperature of the plates should reach a value of 750 ° C at the end of the preheating. A) How long, in minutes, does the preheating stage last? B) How much energy in kWh does the oven consume for this purpose if the preheating process is repeated 8 times up to date? Develop, step by step, a physical - mathematical model to answer these questions. Steel properties: k = 54 W / m- °C p = 7800 kg / m3 Cp = 465 J/ kg- °C

Steel plates 40 cm per side and 1 cm thick are heat treated in a static oven. Inside the oven there is a shelf where 10 separate plates are placed, in such a way that the heat treatment of one does not affect the treatment of the others. The oven is electric and emits radiation heat towards the plates. In the oven an atmosphere with nitrogen is generated to avoid the oxidation of the material, this gas acts as a convective medium on the plates. Before being placed in the oven, the plates are at room temperature of 25 ° C. The heat treatment of the plates begins with a preheating. At this stage, the combined convection and radiation heat transfer coefficient in the oven is 46 W / m2- ° C. During preheating, the oven controls the internal temperature with a quadratic compensation, therefore, the walls and the nitrogen atmosphere have a temperature Th that varies according to the expression: Th = a + bt2 where a = 750 ° C, b = 3 x 10- 5°C/ s2 and t is the time in seconds. The temperature of the plates should reach a value of 750 ° C at the end of the preheating. A) How long, in minutes, does the preheating stage last? B) How much energy in kWh does the oven consume for this purpose if the preheating process is repeated 8 times up to date? Develop, step by step, a physical - mathematical model to answer these questions. Steel properties: k = 54 W / m- °C p = 7800 kg / m3 Cp = 465 J/ kg- °C

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter3: Transient Heat Conduction
Section: Chapter Questions
Problem 3.23P
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Heat Treatment Steel plates 40 cm per side and 1 cm thick are heat treated in a static oven. Inside the oven there is a shelf where 10 separate plates are placed, in such a way that the heat treatment of one does not affect the treatment of the others. The oven is electric and emits radiation heat towards the plates. In the oven an atmosphere with nitrogen is generated to avoid the oxidation of the material, this gas acts as a convective medium on the plates. Before being placed in the oven, the plates are at room temperature of 25 ° C. The heat treatment of the plates begins with a preheating. At this stage, the combined convection and radiation heat transfer coefficient in the oven is 46 W / m2- ° C. During preheating, the oven controls the internal temperature with a quadratic compensation, therefore, the walls and the nitrogen atmosphere have a temperature Th that varies according to the expression: Th = a + bt2 where a = 750 °C, b = 3 x 10- 5°C/ s2 and t is the time in seconds. The temperature of the plates should reach a value of 750 ° C at the end of the preheating. A) How long, in minutes, does the preheating stage last? B) How much energy in kWh does the oven consume for this purpose if the preheating process is repeated 8 times up to date? Develop, step by step, a physical - mathematical model to answer these questions. Steel properties: k = 54 W / m- °C p = 7800 kg / m3 Cp = 465 J/ kg- °C
Transcribed Image Text:Heat Treatment Steel plates 40 cm per side and 1 cm thick are heat treated in a static oven. Inside the oven there is a shelf where 10 separate plates are placed, in such a way that the heat treatment of one does not affect the treatment of the others. The oven is electric and emits radiation heat towards the plates. In the oven an atmosphere with nitrogen is generated to avoid the oxidation of the material, this gas acts as a convective medium on the plates. Before being placed in the oven, the plates are at room temperature of 25 ° C. The heat treatment of the plates begins with a preheating. At this stage, the combined convection and radiation heat transfer coefficient in the oven is 46 W / m2- ° C. During preheating, the oven controls the internal temperature with a quadratic compensation, therefore, the walls and the nitrogen atmosphere have a temperature Th that varies according to the expression: Th = a + bt2 where a = 750 °C, b = 3 x 10- 5°C/ s2 and t is the time in seconds. The temperature of the plates should reach a value of 750 ° C at the end of the preheating. A) How long, in minutes, does the preheating stage last? B) How much energy in kWh does the oven consume for this purpose if the preheating process is repeated 8 times up to date? Develop, step by step, a physical - mathematical model to answer these questions. Steel properties: k = 54 W / m- °C p = 7800 kg / m3 Cp = 465 J/ kg- °C
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