Presuming "tumble dryer" refers to the household appliance commonly used to dry wet clothing, "drying machine" is a possible alternative, but it is not a common alternative here in the US; we typically say "clothes dryer" or just "dryer".
Of course, all of these words may have other meanings in different contexts. In particular, at home a "dryer" could be a "hair dryer" as well as a "clothes dryer", but "put it in the dryer" would refer only to the clothes dryer as a hair dryer has no place that one could put something into. (or "into which one could put something" if one chooses to be pedantic/prescriptivist).
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