Vacuum furnaces are used in manufacturing for metal heating in brazing and sintering processes, as well as for heat treatment of steel alloys. The vacuum, and absence of air/oxygen, facilitates a low contamination process and prevents detrimental surface oxidisation. Heat is often provided in these furnaces by electrical heating elements, and their thermal design is critical to the effective operation of the furnace. In one such case, this element is modelled as a long, cylindrical electrically heated rod, 20 mm in diameter installed in a vacuum furnace as shown. The surface of the heating rod has an emissivity of 0.9 and is maintained at 1000 K, while the interior walls of the furnace are black and are at 800 K. Calculate the net rate at which heat is lost from the rod per unit length

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
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Chapter9: Heat Transfer With Phase Change
Section: Chapter Questions
Problem 9.2DP
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Vacuum furnaces are used in manufacturing for metal heating in brazing and sintering
processes, as well as for heat treatment of steel alloys. The vacuum, and absence of
air/oxygen, facilitates a low contamination process and prevents detrimental surface
oxidisation. Heat is often provided in these furnaces by electrical heating elements, and their
thermal design is critical to the effective operation of the furnace. In one such case, this
element is modelled as a long, cylindrical electrically heated rod, 20 mm in diameter
installed in a vacuum furnace as shown. The surface of the heating rod has an emissivity of
0.9 and is maintained at 1000 K, while the interior walls of the furnace are black and are at
800 K. Calculate the net rate at which heat is lost from the rod per unit length.

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