How much time the brown or black cough last after quitting smoking? and after how much time i should consult a doctor?

Can go on for weeks: There are tiny little hair cells on the respiratory epithelium whose job it is to push any accumulated mucus up the tract to where it is coughed out on a regular basis. Tobacco smoke stops these cells from working, so a lot of junk just accumulates lower down. When you stop smoking, they begin to work again, and cough can last several weeks or even a month or more. If cough goes on 2 m., see MD.