Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W/m² K on the sphere surfaces. The thermophysical properties of the sphere material are p = 3000 kg/m³, c = 850 J/kg-K, and k = 15 W/m.K. (a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?

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Chapter3: Transient Heat Conduction
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5.78 Spheres of 40-mm diameter heated to a uniform
temperature of 400°C are suddenly removed from the
oven and placed in a forced-air bath operating at 25°C
with a convection coefficient of 300 W/m².K on the
sphere surfaces. The thermophysical properties of the
sphere material are p = 3000 kg/m³, c = 850 J/kg. K,
and k = 15 W/m.K.
(a) How long must the spheres remain in the air bath
for 80% of the thermal energy to be removed?
(b) The spheres are then placed in a packing carton that
prevents further heat transfer to the environment.
What uniform temperature will the spheres eventu-
ally reach?
Transcribed Image Text:5.78 Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W/m².K on the sphere surfaces. The thermophysical properties of the sphere material are p = 3000 kg/m³, c = 850 J/kg. K, and k = 15 W/m.K. (a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed? (b) The spheres are then placed in a packing carton that prevents further heat transfer to the environment. What uniform temperature will the spheres eventu- ally reach?
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