When you arrive at Beijing Airport, please take the shuttle bus Line 3 to get to Beijing Railway Station, where you could catch an express or a fast train to reach Shenyang. The fastest train only takes about 4 hours on the way.

It is suggested that you search out the train schedule and ticket fare on this page: https://www.travelchinaguide.com/china-trains/

How do I get from beigjing airport on domestic flight to shenyang? What is the cost and flying time?