What is the entire reaction mechanism for 1-butanol with ammonium bromide in the presence of sulfuric acid?

The mechanism is SN2. As -OH is a very poor leaving group, concentrated H₂SO₄ is used to protonated the -OH group to become -OH₂⁺ which is a much better leaving group. Then, Br⁻ ion in ammonium bromide acts as a nucleophile to substitute water.

The mechanism is shown below.