## Refrigerators: Part#1

A month ago our refrigerator stopped working. A repair didn’t seem possible, so we headed to the shops to search for something as similar as possible to what we had just lost.

Thankfully, the snappily-named Bosch KGN33NW3AG fridge-freezer has proved to be entirely adequate.

Of course a new refrigerator requires testing (obviously) and an assessment of how close to specification it is performing. So…

How much energy should a fridge use?

I made a ‘guess-timate’ by estimating the rate at which heat which would flow into the fridge. My thought was that this should be similar to rate at which the fridge would use energy.

[Aside: the actual calculation is tricky, but I’ll come back to it in a later post]

To estimate the heat flow into the fridge I measured the size of fridge and freezer compartments and the thickness of the insulation.

Then I calculated the area of each compartment that faced the room which I assumed to be at a nominal 20 °C.

Heat will constantly flow from the room, through the insulation, into the cold compartments and a simple rule (called Fourier’s Law) allows me to calculate the rate at which energy flows (watts).

I assumed that a perfect ‘heat pump’ – the scientific name for a refrigerator – would pump all this heat back out again, but would (unrealistically) not require any energy to operate.

By multiplying the rate of energy flowing into the refrigerator (in watts) by an amount of time (in seconds) I could work out how much energy (in joules) even a perfect refrigerator of this size must use.

I could then convert the energy used (in joules) into kilowatt-hours – the charging unit used by electricity companies – by dividing by 3.6 million (the product of 3600 seconds in an hour and 1000 watts in a kilowatt).

My calculations indicated that heat flows would be:

• About 16.4 W into the refrigerator, amounting to around 144 kW-h over a year.
• About 14.8 W into the freezer, amount to around 130 kW-h over a year.

So if the device were perfect, I calculated it would use 274 kW-h per year.

The specification for the fridge says that it will use 290 kW-h per year, just 6% more energy than I estimated a perfect fridge would use. This indicates a fridge performing surprisingly well.

I assume that Bosch’s estimated consumption is realistic. So how wrong could my estimate be?

Well I assumed that the thermal insulation around the fridge had a thermal conductivity of 0.03 W/K/m – just three time greater than that of still air. This is exceptionally good insulation. But my estimate could easily be wrong by 10% or so if improved insulation had been used.

Opening the door.

Many people think that opening the door of the fridge will affect its energy consumption, but my calculations indicate that it is not really a very big problem.

I assumed that at worst, opening the door could replaces all the air in the fridge with room temperature air. If this were the case then:

• opening the fridge door 10 times a day every day would use an additional 3.7 kW-h of energy per year which is just over 1% of the annual expected usage.
• opening the freezer door once a day would use an additional 0.4 kW-h of energy per year which is much less than 1% of the annual consumption.

So my calculations indicate that as long as door is not left open for many minutes at time, perhaps by careless children tired of their parents nagging, then it will have relatively little effect on the energy consumption of the fridge.

Data

I logged data at four locations in the fridge/freezer over a day or so last weekend.

The figure below shows a composite view of the data from the top of the fridge and the freezer over a period from 7 p.m. on Saturday to 4:30 p.m. on Sunday.

I’ll analyse this data more in the next article, but here I will just note that the data show:

• The basic cycle of the heat pump which switches on around once every 45 minutes.
• The more rapid cycling of the air within the fridge – every 10 minutes or so.
• The effect of leaving the door open.

It is pretty clear that when my son and his friend arrived home at approximately 5 a.m. on Sunday morning (!) they contrived to leave the door open for the best part of an hour!

I thought this was impressive detective work on my part and it could well be the start of a new mode of behaviour analysis: Forensic Thermometry.

Perhaps I should propose °CSI Teddington. 😉

Anyway. More on the temperature and humidity data in the next article.

### 10 Responses to “Refrigerators: Part#1”

1. Disorientata Says:

“careless children tired of their parents nagging” ahaahahaah brilliant 🙂

2. doug1943 Says:

Probably a dumb question but … does it matter if the fridge is ’empty’ (ie there is only air inside), or whether there is something in it? I seem to recall a piece of folk wisdom that said that a fridge that was relatively sparse required more energy to keep cool, as opposed to one that was, for example, filled with bottles of water. Something about the SHC of water?

• protonsforbreakfast Says:

I’m not sure in practice. Cooling stuff down takes a lot of energy, but once it is cold it slows the rate at which the fridge will warm.

3. Ed Davies Says:

Why would a “perfect” fridge use as much electrical energy as the amount of heat leaking in? Surely it ought to be a lot less due to the CoP of the heat pump? A perfect fridge would be running up against Carnot’s limit.

• protonsforbreakfast Says:

Ed

Yes indeed, and I may come to that in part 3. I have made calculations of the achievable COPs for the fridge and freezer and the amount of work done could plausibly be a significant factor smaller than this. But I just wanted to avoid introducing a law of thermodynamics and COPs in this first article. This seemed like a good vague concept. Sorry.

M

4. Ross Mason Says:

When you get into humidity in a fridge, could you please monitor the temperature of the cold tubing in the fridge. I have an ongoing discussion with local manufacturers who insist on keeping things light ( read cheap) which means to transfer coolth the pipes have to be colder than if a large(er) tube is used. I suspect it is the major issue in keeping high humidity (RH) in the fridge .

• protonsforbreakfast Says:

I don’t have a direct measurement of that temperature, but I do have a measurement of the dewpoint of the air just after it has been chilled. My guess is that this is the actual temperature of the element with which the air has been in contact. More in a couple of days – this whole ‘working-5-days-a-week-thing’ really gets in the way of blogging!

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