Calculation of time to replace a volume of extracted air by heating it...

Can someone check my calculation...
Time to replace 15m^3 of air extracted at 20oC, with air heated by a 650 Watt heater from 0oC to 20oC.
Air-Volume = 15 m^3 Temp-Change = 20oC less 0oC = 20oC Heater-Watts = 650W where 1W = 1J/Sec Air SPH = 716 J/Kg K Air Density = 1.3kg / m^3
Time (secs) = Temp-Change * Air-Density * Air SPH / Heater-Watts * Air- Volume Time (secs) = 20 * 1.3 * 716 / 650 * 15 = 430 secs or just over 7 mins
Repeated 3x a day is 0.37hr @ 0.65kW @ 11p/kWhr = 2.65p or bugger all. That is running a fan 3x a day for 10mins assuming it removes 100% of free flow (which is not likely, so the running time could be as much as 20min to achieve 15m^3 of air). Whatever it costs very little indeed yet enforces a near 40% air change 3x a day.
Is my calculation correct?
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Yes (assuming a typo), but you've made things unnecessarily difficult. All that matter are:
The total mass of air to be heated = # of times x vol x density The specific heat of air The raise in temperature The conversion ratio between Joules and kWHr = 1/3.6M The cost of 1kWHr
Thus: 3 x 15 x 1.3 x 716 x 20 x 0.11/ 3600000 = 0.0256 or 2.56p
This of course assumes that no heat is being lost via convection coupled with conduction through the walls, radiation, etc, which will not actually be true. Note that, all other things being equal, the more powerful the heater, the MORE EFFICIENT it will be, because there will be less time for heat to escape via these methods while the air is being heated. If this seems counter-intuitive, it is nevertheless true - for a fuller discussion of this principle, see the discussion about kettles which began with my post #10 of the following thread, particularly my subsequent 'thought experiment' post #15: http://groups.google.com/group/uk.tech.digital-tv/browse_frm/thread/439f82b970d243c3/d0345b5bd506925d
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:-)
Noted.
It is indeed true. The fan heater is 650-1300-2000W unit so would be used on 2000W, a fan heater given very rapid warm up of the bulk body of air also.

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Will do, thanks.
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