Does Insulation Increase a Sphere's Surface Temperature During Cooling?

[JWS]

A solid steel sphere is heated to 150 deg F and allowed to cool in a room at 60 deg F. During cooling, the sphere is wrapped in insulation which is at room temperature before used. Will the surface of the metal sphere warm or will only the rate of cooling change?

Don't laugh, I've seen conflicting answers amongst even pHd physicists.

 

[cjl]

If the sphere is insulated when at an isothermal state (I.E. before it's had a chance to cool at all yet), then only the rate of cooling will change. If the sphere is allowed to cool somewhat, and the sphere has a fairly low thermal conductivity relative to the convective heat transfer at the surface (such that there is a significant temperature gradient from the center of the sphere to the surface), the surface could indeed warm up immediately after insulation, as the slowed rate of cooling would allow the sphere's temperature to equalize somewhat. On the whole, though, the sphere will still be losing energy.

 

[berkeman]

A solid steel sphere is heated to 150 deg F and allowed to cool in a room at 60 deg F. During cooling, the sphere is wrapped in insulation which is at room temperature before used. Will the surface of the metal sphere warm or will only the rate of cooling change?

Don't laugh, I've seen conflicting answers amongst even pHd physicists.

Welcome to the PF.

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