A copper sphere initially at a uniform temperature of 132°C is suddenly released at the bottom of a large bath of bismuth at 500°C. The sphere diameter is 1 cm and it rises through the bath at 1 m/s. How far will the sphere rise before its center temperature is 300°C? What is its surface temperature at that point? (The sphere has a thin nickel plating to protect the copper from the bismuth.)
GIVEN
• A copper sphere with a thin nickel plating rising through a bath of bismuth
• Initial copper temperature (To) = 132°C (uniform)
• Bismuth temperature (T?) = 500°C
• Ascent velocity (U?) = 1 m/s
• Sphere diameter (D) = 1 cm = 0.01 m
FIND
(a) Distance sphere will rise before its center temperature, T(o,t) = 300°C (b) The sphere surface temperature at that time, T(ro,t) ASSUMPTIONS
• Thermal resistance of the nickel plating is negligible
• Thermal properties of the copper can be considered uniform and constant
SKETCH
The Reynolds number is
Applying
(a) The Biot number for the sphere is
Therefore, internal thermal resistance is significant and the chart solutions of must be
used.
The distance (x) the sphere will rise during this time is
(b) The surface temperature can be determined
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