Is it appropriate for an undergrad student to ask a professor to sign a non-disclosure agreement?

I don't understand most of the current answers, which mostly assume you want technical advice without paying for it, but requiring an NDA. If this is indeed what you want, I agree it's a bad idea.

However.

You write that this professor has already gone into business. This implies that he has a certain basic understanding of how business works. He probably has signed his fair share of NDAs, as well as requiring others to sign his.

It appears perfectly reasonable for you (or your friend) to set up a short meeting with this professor, say of 30 minutes or so. Quickly present your idea in a rather general manner, in an "elevator pitch" - at least outlining what problem you want to solve. Think beforehand how much you are comfortable revealing. Tell him that you'd like his advice, and be frank that you are not comfortable giving full details without protection for your intellectual property. (I'd also look for protection if I knew this professor, not only if he were unknown.)

Have a proposal ready for possible next steps, which would include him signing an NDA and his investing a little time for a discussion. Ask him explicitly what he'd expect from you in return for investing his time. Professors are busy people, and more so if they run a company on the side.

You may actually have a good chance that he'd be happy to mentor you to a limited extent pro bono - most academics are idealists at heart, otherwise they would be in industry from the very beginning. However, if you want more in-depth advice, be prepared to offer hourly rates, possibly conditional on your idea getting off the ground.

Always keep in mind that professors are busy, just as are other businesspeople. Don't come with a mindset that you are entitled to advice, but ask politely, and things may go well. If this professor is active in a similar line of business as you are, this may be a very good opportunity - he may have contacts in the industry and/or to funders that may very well be invaluable.

Let's see: you want the professor to freely give out their trade secrets on their real device, so that you can build a potentially competing device; and you want the professor to sign an NDA on your non-existent device, so that they can give you free technical advice on it?

I think that's going to get you a "ha ha ha ... no".

I also think you need to adjust your expectations.

To understand why NDAs are annoying to academics, and to find a better alternative, do check out the Professional Academic Alternative to Non-Disclosure Agreements PAANDA; here's a snippet:

... academics regularly extend and expect to receive a professional confidentiality during peer review of unpublished research and grant proposals. I am more than happy to extend the same professional confidentiality to you ...

My interpretation of the situation is this:

This is not an academic issue since you are approaching somebody who leads some business with some business-related issue.

The fact that that somebody is also a professor and that somebody who you know has a class with this professor seems unrelated. So my advice would be:

Handle this as if it were a business meeting and not an academic meeting.