I guess it depends how much buildup you have. Vinegar did the job perfectly for me. While brick cleaner/hydrochloric acid is stronger, it also reacts with aluminum and may aggravate already corroded parts.
On the other hand, your picture shows cleaning of exhaust elbow, which has a combination of carbon residue (acidic) and calcium deposits. Exhaust components are regularly cleaned with high PH alkalis (carbon remover solutions), not strong acids.