Yes a heat pump tumble dryer is feasible and in fact AEG made some about 10 years ago. They were very expensive (around £1000) and only available in Germany, but were beautifully built.
I actually did quite a lot of development work on one about 10 years ago, when I was working for a large appliance manufacturer.
The heat pump dryer would work like a condenser dryer i.e. a closed loop. The air from the drum is passed over the cold coil at about 10C. This condenses out the water in the air stream. This cool air, which is pretty damp like cold foggy day, is then passed over the hot coil at about 50C, picking up the heat it gave up earlier plus any heat from the pumping energy. The air is now warm (about 45C) and very dry, like a hot desert breeze. This is passed over the clothes where it picks up more moisture and cools. The cycle then repeats. The water that is condensed out is collected and then drained away, but the air is in a sealed system, so no external vent pipe is required. Any heat leaking from the system simply contributes to the house heating.
Research showed that, excluding heating, a standard tumble dryer accounts for about 15% of the electricity usage of an "average" household. So a reduction in the energy usage would have been really beneficial.
Unfortunately the prototype were were tasked with developing was focused on outright speed. It's energy consumption per kg was about 5 times standard. However, because of the way it operated (in essence, it stored energy up and used it on one big burst to dry quickly) the extra energy consumption wasn't taken into account in the energy rating system so it appeared as an "A" grade.
I was told to stop development of the heat pump concept as it wasn't novel (as AEG had one, thought the patents were lapsed) ad speed was the way forward.
My counter argument was that all we needed to do was develop a cheaper, mass market, one rather than the expensive AEG, after all Ford didn't invent the motor car, he just produced the first affordable ones.
Alas my pleas fell on deaf ears and the tumble dryer project was refocused on gas (hummm, really novel) then quietly taken out the back and put out of it's misery.
