# Can a fan cool objects better in a less dense atmosphere?

Assuming constant fan power, how would atmospheric pressure/density affect the cooling rate of objects being cooled by a fan? Like in a lower pressure atmosphere, would a fan be able to cool objects more quickly because it could blow less dense air at a faster speed, would it cancel out and be the same or would the cooling rate be lower under less atmospheric pressure/density?

• Ask yourself this question: What would happen if the air density were zero? – Chet Miller May 30 '17 at 0:40
• I'll add to Chester Miller's comment. Please provide more information. Is the object outdoors or indoors? Regarding heat transfer, you will normally find that convection, conduction, and radiation, are ALL happening at the same time. If you don't specify more constraints on the problem, you will not get a reasonable answer. – David White May 30 '17 at 1:31
• Well I'm thinking of an object that's inside an air tight container. – Tom May 30 '17 at 1:44
• If the air tight container has vacuum in it (zero density), the fan blades will just spin, but will not push any air around, so the fan won't contribute to any cooling whatsoever. – Chet Miller May 30 '17 at 12:36
• Right, and I can imagine that the cooling ability of a fan approaches zero as the density of air does, but what I was wondering was as the density of air approaches zero, at what rate does the cooling decrease? Would it just be a linear decrease, or is it otherwise? Like if the mass of air being blown is lower by a certain proportion, but the velocity is higher by the square root (because power of the fan is constant), and the cooling rate would decrease by the square root of the air density decrease. – Tom May 30 '17 at 13:26

This can be understood using heat transfer formulae $$dQ=h \cdot A \cdot (T_{air}-T_{solid})$$ where heat transfer coefficient is an empirical function of velocity and density. So to remove heat, one need to either increase velocity or increase density. In your question, you increase velocity and reduce density, so the trend is uncertain.