Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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### Problem 5.72: Cold Air Chamber for Quenching Steel Ball Bearings A cold air chamber is proposed for quenching steel ball bearings with a diameter of \( D = 0.2 \, \text{m} \) and an initial temperature of \( T_i = 400^\circ \text{C} \). The air in the chamber is maintained at \(-15^\circ \text{C}\) by a refrigeration system. The steel balls pass through the chamber on a conveyor belt. Optimum production of the bearings requires that 70% of the initial thermal energy content of the ball above \(-15^\circ \text{C}\) be removed. Radiation effects can be neglected, and the convection heat transfer coefficient within the chamber is \( 1000 \, \text{W/m}^2 \cdot \text{K} \). **Objectives:** - Estimate the residence time of the balls within the chamber. - Recommend a drive velocity for the conveyor. **Properties for Steel:** - Thermal conductivity (\( k \)): \( 50 \, \text{W/m} \cdot \text{K} \) - Thermal diffusivity (\( \alpha \)): \( 2 \times 10^{-5} \, \text{m}^2/\text{s} \) - Specific heat capacity (\( c \)): \( 450 \, \text{J/kg} \cdot \text{K} \) **Diagram Explanation:** The diagram illustrates the setup for cooling the steel ball bearings. The key elements are: - **Conveyor Belt**: Transports the ball bearings through the chamber. - **Ball Bearings**: Move from left to right on the conveyor. - **Cold Air**: Circulates within the chamber housing to cool the bearings. - **Chamber Length**: The chamber extends 5 meters. - **Velocity (\( v \))**: Represents the speed of the conveyor belt. This setup is designed to efficiently transfer heat from the bearings to the cold air, ensuring optimal cooling performance as required for production.
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Transcribed Image Text:### Problem 5.72: Cold Air Chamber for Quenching Steel Ball Bearings A cold air chamber is proposed for quenching steel ball bearings with a diameter of \( D = 0.2 \, \text{m} \) and an initial temperature of \( T_i = 400^\circ \text{C} \). The air in the chamber is maintained at \(-15^\circ \text{C}\) by a refrigeration system. The steel balls pass through the chamber on a conveyor belt. Optimum production of the bearings requires that 70% of the initial thermal energy content of the ball above \(-15^\circ \text{C}\) be removed. Radiation effects can be neglected, and the convection heat transfer coefficient within the chamber is \( 1000 \, \text{W/m}^2 \cdot \text{K} \). **Objectives:** - Estimate the residence time of the balls within the chamber. - Recommend a drive velocity for the conveyor. **Properties for Steel:** - Thermal conductivity (\( k \)): \( 50 \, \text{W/m} \cdot \text{K} \) - Thermal diffusivity (\( \alpha \)): \( 2 \times 10^{-5} \, \text{m}^2/\text{s} \) - Specific heat capacity (\( c \)): \( 450 \, \text{J/kg} \cdot \text{K} \) **Diagram Explanation:** The diagram illustrates the setup for cooling the steel ball bearings. The key elements are: - **Conveyor Belt**: Transports the ball bearings through the chamber. - **Ball Bearings**: Move from left to right on the conveyor. - **Cold Air**: Circulates within the chamber housing to cool the bearings. - **Chamber Length**: The chamber extends 5 meters. - **Velocity (\( v \))**: Represents the speed of the conveyor belt. This setup is designed to efficiently transfer heat from the bearings to the cold air, ensuring optimal cooling performance as required for production.
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