Coil heat exchanger for tub

Hey all!

I'd like to build a coil heat exchanger for a tub that would work on wood. All of the designs I see online are open from the sides and not isolated and I wonder won't it be better to insulate it from the sides?
I thought also to make the dimensions for hight over width because it looks to me that it would be more efficient because heat goes up. Last thought is that I' thinking of making it from corrugated stainless steel for more surface area. What do you think?