A dry cough by definition is nonproductive. It is caused by increased sensitivity of airway nerves, and is often the result of irritation (cough = more cough).
How to Treat Dry Coughs:
Treat dry coughs with cough suppressants, such as dextromethorphan, to reduce frequency/intensity.
Understanding Types of Illness
The Tale Of Two Coughs - Dry Coughs And Chesty Coughs
When it comes to cold and flu symptoms, there are two main types of coughs—chesty coughs and dry coughs.