Catalysis of the reaction: a long-chain (3S)-3-hydroxy fatty acyl-CoA + NAD+ = a long-chain 3-oxo-fatty acyl-CoA + H+ + NADH. A long-chain fatty acid has an aliphatic tail containing 13 to 22 carbons.
long-chain-(S)-3-hydroxyacyl-CoA:NAD+ oxidoreductase activity