How to sell tutoring?

You could setup a website and target keywords based on thermodynamisc keywords and get the keywords ranked. You could also setup a facebook page and buy ads based on those who have interest in thermodynamisc. You could also find forums that talk about thermodynamisc and that a coaching offer in your signature and make posts frequently.

Well I've never seen an ad on Facebook for thermodynamics myself, but I think your best results would be flyers in colleges or any other way you can directly advertise to students of thermodynamics, university websites where you can post tutoring offers, or tutoring websites.

Shoenickel gave great suggestions.

Are you wanting to do this online or locally?

If online I would encourage you to follow what Shoenickel said and consider putting a course on Udemy as well... you could even host your classes there and advertise in other places.

Ultimately, you'll need to determine who your target market is... college students, working rocket scientists(i have no idea about science folk ) and then work towards targeting them where they're at.

What pages on Facebook do thermo engineers like, what groups are they in, what websites do they read and what forums do they lurk in the wee hours of the night?

There was a need in my niche so I put out a post on the forum where the users hung out stating I was willing to do a 30-day course (1 hour each day). The title was

"Learn X in 30 Days" and I charged $100. I got 10 users within a week.

I then established the class' schedule and my first 5 days of lessons before the first class started.

I then communicated the time to all students and I used Skype (I ended up upgrading to the paid version due to conferencing a group).

When I started the class I also started my Camtasia recording.

I started the lesson and afterwards I let the students ask questions. I even went so far to create programs on the fly along with debugging them.

At the end of the class I would save my recording (after of course closing my Skype).

I edited my recording, packaged my source code and sent out the necessary links to my students for reviewing the class via Video as well as having the source code.

Once the entire 30-Day course was done I had over 45 videos and a bunch of source code files.

I then setup a new website with a WP membership plugin (WishList).

Then I went back to the forum and posted an official ad in their marketing area for new students.

My site has grown to well over 160 video plus a butt load of source code files which I use as incentive for joining.

I am still getting new students and tons of compliments after 2 years of work.

That is the best thing that I have done in my niche. Best decision that I have ever made.

Good luck!