Heat transfer within edible objects

The veggie-juicer in our kitchen will happily take fruit, such as apples and oranges. Apparently, in the case of the orange, it works best if the fruit is cold (but not frozen) throughout. So here’s the question my wife asked me last week: If I have an orange at room temperature, and want to cool it to fridge temperature throughout as quickly as possible, how should I do it?

Putting it in the fridge for several hours will do the trick. But it’s quite slow. Putting it in the freezer would cool it quicker, but we don’t want the outside frozen while the inside remains warm. So what about a combination of the above – putting it in the freezer for a while, then transferring it to the fridge.

Now, I have to say I don’t know the answer to this. The combination freezer-fridge method seems on the face of it to have some merit – get the outside really cold as quickly as possible, then let that cold help bring down the temperature of the inside, while, at the same time, letting the outside rise a bit.

But a second thought says that the distance heat (and cold) penetrates into a substance in a given time depends very much on the thermal diffusivity of that substance.   To penetrate a few centimetres of orange is going to take a given time (approximately the distance squared divided by the thermal diffusivity), no matter what you do to it (except drilling holes in it and pouring liquid nitrogen inside).

So I don’t have an answer. (It sounds like a nice investigation for a science fair project to me – get a nice big orange and stick thermometers into different parts of it – N.B. please don’t ram mercury thermometers into anything – you DON’T want mercury all over your kitchen bench).  But I do know that the question isn’t as trivial as it might sound.  I remember several years ago reading a research article looking at the mathematical modelling of the penetration of burns/scalds into the skin.  What matters here is things like the temperature of the hot object, how long it was in contact with the skin, the area of contact, and how long it was before the patient got the burn under running cold water (and how long they held it there for).  I think the idea of the article was that knowledge of these things would help medical staff make decisions on treatment options.

I could, I suppose, do some mathematical modelling of heat transfer in spherical volumes of water (i.e. oranges), which isn’t going to be too taxing for a theoretical physicist.  But I’ll leave it to those who like experimenting to give it a shot and tell me the answer…

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