A new and non-obvious use for an existing product may be patentable.
A new use for a known device can be patented only if that use (or method of use) is new and not obvious. The Patent and Trademark Office (PTO) grants thousands of "new use" process patents every year.
Note that you should take steps to ensure that you are not infringing any pre-existing patents that cover all or part of the "known device" itself. Your use of someone else's patented device, even if your own process is patented, can pose serious legal problems.
Furthermore, a patent may not be the best way to protect your invention. Maintaining your method confidential as a "trade secret" is another option, depending on the nature of the invention such as whether it can be "reverse engineered".
A new use for an existing product is patentable, however, such claims might not cover the product itself! In other words, people still have the right to buy the existing product for its old use; you can only protect the method of using the product for its new purpose. Such method claims can be somewhat difficult to enforce. However, it is possible to argue "contributory infringement" in some situations.
For example, if a manufacturer sells the product (which is not patenable) along with a set of instructions as to its new use (which is patentable). Rather than sue all the consumers, you may be able to sue the manufacturer for contributory infringement in such situations.