Ventilation of an insulated case

I came across to an interesting problem when I was having difficulty implement a computing cluster in my small office. Although my attempt was unsuccessful, at least I had the chance to observe a situation described graphically below.

As seen in the figure, there is an insulated case. In the case there is a heat source. The objective is fixing the ambient temperature of the case by selecting a fan having an appropriate power at the outlet (blue rectangle at the upper right corner).

Assumptions are:

  • case is fully insulated
  • indoor temperature remains fixed
  • case ambient temperature has no temperature gradient (it instantly adapts to average temperature)
  • efficiency of the elements are assumed to be 100%

Question is what factors affect the fan selection process?

Factor suggestions:

  • initial case ambient air temp
  • target case ambient air temp
  • indoor temp
  • outdoor temp
  • heat source power
  • case interior volume

My answer is only “the difference between target case ambient temperature and indoor temperature” and “heat source power”. Interesting isn’t it?

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