"First, I would ask what requirements the exhaust manifold must meet in terms of temperature, vibration, thermal cycling, upstream and downstream attachment methods, packaging, manufacturing process and target cost.
I would find out what materials had been used for this application before and analyze how the new manifold requirements differ from the existing applications. Perhaps the materials used for current applications could be used for the new one. I would be asking a lot of questions.
I would make a preliminary selection based on everything I was able to determine about the requirements, and then take advantage of Finite Element Analysis modeling, using the material characteristics, to see if we were on the right track. Maybe this would require a few iterations. Then, we would be in a position to make an initial recommendation. Of course, careful testing of prototype hardware might result in further adjustments, but this is how I would get started."