I Wonder How Much That Costs ... Not Much!

Well if you don't know yet, I've been trying to answer the question: "How much does opening and closing my refrigerator door cost?" You can read my first blog about this topic here: I Wonder How Much That Costs ...

Firstly, thanks to Element14 and EnOcean for letting me road-test this product. I cannot stress enough how well this product performed, and it far exceeded my expectations. You can read the road test review for more information. As for the question of how much it costs, it turns out, the answer is a lot less than I thought. When you open a refrigerator door there is a thermal gradient between the ambient air and the refrigerator air. This thermal gradient will cause natural convection to occur, and warm air will move into the refrigerator. When you open the door there will also be a quick flow of air that causes forced convection, but I’m only considering the natural convection for now. Natural convection can be calculated using

where Q is the heat (Watts),

h_C is the heat transfer coefficient (Watts/(m²·Kelvin),

A is the cross-sectional area (m²),

and ΔT is the temperature difference (Kelvin).

I wanted to get an estimated solution for what it was costing me, since an exact solution could be quite a rigorous mathematical endeavor. I will assume the major heat movement method is natural convection, and that the heat transfer coefficient for natural convection in air is 25 (W/m²K). The actual heat transfer coefficient is somewhere between 5 and 25 (W/m²K). To balance the heat transfer coefficient, I assumed the efficiency of my refrigerator for converting electrical power into cooling was 100%. I realize this isn’t even close to what it probably is, but it will likely balance with the heat transfer coefficient uncertainty.

In my apartment the ambient temperature is about 25°C and my refrigerator maintains an air temperature of 5°C. My refrigerator is actually a two door model with the freezer on the left and the fridge on the right. The cross-sectional area of the door is 1.41 m x 0.46 m or 0.6486 m². So, suppose the fridge door is left open for 60 seconds (that’s quite a long time). The resulting heat loss is

So, the heat is 324 Watts, but we need kilowatt hours to calculate the cost, so

Note, 60/3600 is the fraction of an hour that is 60 seconds; that is, 60 seconds is 1/60^th of an hour. Note also we divide by 1000 to convert Watts to kilowatts. If your electricity costs 20 cents per kWh, then this would cost:

Now think about that, it’s not even one cent! In fact, if there was 1 kilowatt of heat when I opened the fridge and left it open for an hour it would only cost $0.2. Mind you, the fridge may not like this and the cooling system may fail, but it would still only cost about 20 cents of heat loss.

To analyze my data I took the worst day for opening the refrigerator door, which happened to be a Sunday. I did the analysis on it, and I got a grand total of about $0.02 or 2 cents spent opening the door. Even at 365 days a year that’s just over $7 spent. Maybe if I include the forced convection portion this number would increase, but that will have to wait for another day.

I have attached the excel spreadsheet of my data for June 22. I have included the data from my sensor log files in two sheets; the magnetic contact switch and the temperature sensor. I made each opening and closing of the fridge door an event, and took the temperature reading closest to the time of the opening door event.

Conclusions:

Although the results were not what I expected, I gained a lot of experience with EnOcean’s Wireless Gateway for the Raspberry Pi and their energy harvesting sensors. This product is top rate, and I am overly impressed with their performance. Thanks to Element14 and EnOcean for letting me test a theory I had, even though the results were not as insightful as I had hoped.