See:
https://books.google.com/books?id=D...MItPuv_IqZxwIVgTM-Ch0SlgE8#v=onepage&q&f=true
and
https://books.google.com/books?id=s...I_unqz4uZxwIVxNCACh1YxAib#v=onepage&q&f=false
and
https://books.google.com/books?id=F...j90Yn-i5nHAhXEdT4KHS13Dg4#v=onepage&q&f=false
Laundry drying cabinets like those shown in the OP link basically worked via convection.
Air was drawn in via lower registers, heated (stove, steam or hot water pipes, etc...) then rose through the cabinet drying laundry. The steam, any smoke, fumes and so forth would exit at the top and vent out through piping either directly outdoors or to a chimney leading to same. Since hot air rises the whole system works by ventilation. Long as there is a heat source there will be a draft that brings in cold air, again it is heated, rises, and the moisture laden air exits above. This will go on just as with a fireplace, range or anything else that heats and vents out. Think some versions may have had small fans to create draft/draw air up and out, but most were very simple devices.
Benefit of not using electricity (which wasn't available everywhere) was that these units could be installed anywhere. Long as there was access to venting or a chimney. Of course today's modern safety codes and worries over carbon monoxide would probably mean anything that burned oil, coal or gas would meet stricter standards.
Common methods of extracting moisture in domestic laundries at the time (wringers, mangles, by hand) would equaled at best 400rpm spin speed. Thus laundry would have been quite wet when hung to dry in these contraptions. Heavy things like thick blankets or heavy muslin linens or clothing would have taken longer to dry than say sheer ladies blouses.
For what it is worth you can still find modern versions of these drying cabinets. Asko among others made or still makes them. IIRC even Maytag had a version. Such appliances are used for drying things that cannot or should not be tumble dried, dried flat, and or for wet/damp things like raincoats, boots, and so forth.
Modern Asko version:
http://www.asko.co.nz/laundry/drying-cabinets/dc7573
Finally we cannot let this go without a mention of Martha Stewart's Skyland estate.
http://www.themarthablog.com/2011/12/[this post was last edited: 8/8/2015-04:09]
