Bachelor of Technology in Metallurgical Engineering is a four-year undergraduate program offered by universities/institutes in the field of metallurgy. B.Tech in metallurgical engineering is basically the study of metals. Employment opportunities for metallurgical engineers are available in various areas such as chemical and metallurgical labs, iron and steel companies etc.

NIT Trichy is better in ranking as well as in terms of faculty as compared to NIT Rourkela. So you should go for BTech in Metallurgy in NIT Trichy.