Burning sensation from drainage pipes after abdominoplasty. PS said sensation is normal. thoughts?

Drainage may indeed cause discomfort and pain, but it is most likely temporary. Pain is usually due to severed nerves during surgery and should resolve as you heal through the coming months. Pain medication may be prescribed if the pain becomes intolerable and restricts your daily activities. 

Patients will experience various levels of discomfort whilst drains are still in position. When they are removed they will be pulled along the exit wound which can be uncomfortable for some, but of course it is temporary. The drains are there to drain excess blood so are necessary in a big operation where there is a chance of leakage from a  large raw area. This settles in a few days usually.If you have any concerns return to your PS for advice and guidance.