My first thoughts were:
- Oh god, another free energy / perpetual motion machine idea
- Hmm: this guy seems to understand basic energy (given his observation that the computer contributed to the room heat budget)
- He works for a boating magazine (those guys tend to know their basic science/math).
So looked I at the figures.
It seems he's taking about these tea lights: http://www.ikea.com/ie/en/catalog/products/50097995/
They're actually €2 here in Ireland (about 1.70 GBP).
Measuring some tea lights I have here (they can't be too different to those IKEA candles), the diameter is 39mm x 11mm high. That's a total volume of 1.314 litres of wax for all 100 tea lights. It's most likely parafin wax in those candles. The density of parafin wax is 900kg/m3 so that's 1.183kg of parafin wax.
Looking at the heat of combustion per unit mass parafin wax and kerosene / heating oil are pretty much identical energy wise at 46MJ/kg [1]. So the tea lights represent 54MJ of energy [2].
Looking at the latest prices for heating oil (kerosene) in Ireland (December 2013) is €0.83/litre. The density of kerosene is slightly less than parafin wax at about 800kg/m3. So to get 54MJ of energy I'll need 1.479 litres of kerosene. That's €1.22 at current prices.
Which is almost identical to 1 GBP at the time of writing. So fuel wise, this is on par with home heating oil (at the time of writing).
So what's with the flower pots? From a basic physics point of view there is no energy advantage here that I can see. But what it does do is contain the flame and make the apparatus safer than naked flame.
Conclusion:
Tea light candles are handy, store well and don't spill. They are also (probably) safer than liquid kerosene. At 1 GBP it's on parity with home heating oil for energy/cost. At the €2 price it's not quite as efficient as heating oil, but still in the same ball park. There might be a CO risk for small poorly ventilated spaces... but I guess no different to that of candles. Ok.. there might be something to this after all.. but it's no energy miracle.
[1] http://en.wikipedia.org/wiki/Heat_of_combustion
[2] Burning stuff is a rather efficient way of releasing energy. You'll get pretty much every scrap of that in heat.