Can Previous Results Estimate Box Response When Plate Cools Faster?

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drewbagel423
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Let's say I have a box, mounted to a plate in a vacuum (pure conduction). The system is initially at a steady state at temperature Ti. The plate then begins cooling at a rate of 3 C/min. The box is going to cool at some rate, and with some time constant. For this test, I have place a thermocouple on the box, so I can measure its response.

Now I want to run it again such that the plate cools at a rate of 4 C/min. Is it possible to use the previous results to estimate the box's response for this new profile? If so, how could I go about doing it?

TIA
 

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vacuum does not necessarily mean conduction since there is also radiation. Your problem is rather ill defined. What are the dimensions, assumptions, why does the plate begins cooling?
I cannot make up from you description if heat is going from the plate to the box or vise-versa