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The tubes of yogurt have a shell of thin plastic, with a single lengthwise seam and sealed at each end symmetrically apart from a small cut to initiate tearing at one end. They are of internal length 15 cm (diameter ~2cm). I assume that the microwaves used by the oven are of frequency 2.45 GHz, or 12.25 cm in wavelength.

I have noticed standing-wave heating effects in food containing structures with linear dimension of the order of 5–20 cm; but that has always been in a complex mass. In this case, the configuration is simple: a single horizontal, roughly elliptical, cylinder filled with a homogeneous product. As usual, the sample sits on a rotating plate to receive even radiation.

The tube gets too hot to hold at one end while the other end remains frozen, consistently after several trials with near-identical tubes.

I would not be too bothered if the heating were in the middle, or at each end, or even at two symmetrically placed nodes. What puzzles me is this: Why just one end? How do the microwaves tell one end from the other?

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    $\begingroup$ Off topic, but a practical solution to the problem: heat the tube for 1/2 of the total time. Then, open the oven door, rotate the tube by 180 degrees, and finish heating it. $\endgroup$ – David White Feb 13 at 17:23
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The distribution of microwave power inside the oven cavity is uneven. Oven manufacturers combat this by putting turntables and waveguide mode-mixers in their designs and it sounds like the ones in your oven (if it has them) are not very effective.

You can map the anisotropy of the radiation inside the oven by populating the floor of the oven with marshmallows and then turning the oven on for a brief time. The hot spots in the microwave field will melt the marshmallows near them first.

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  • $\begingroup$ The turntable is effective. This explanation would work if, say, the hot spot were at the centre of the turntable and the tube lay along a radius of the turntable. But I put the tube (roughly) concentrically on the turntable. $\endgroup$ – John Bentin Feb 13 at 21:36
  • $\begingroup$ as an experiment, try removing the frozen yogurt from its plastic tube and then microwave it. Some black inks used on plastic can get hot by absorbing microwaves, meaning that the heat source is the wrapper on the yogurt. $\endgroup$ – niels nielsen Feb 13 at 22:08

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