Yes that's called the Kapalbhati Pranayama. You will find a lot of videos on Youtube.com where the Pranayama is being demonstrated by the Yoga Guru Swami Ramadev. Like this one.
The Yogic treatise Hatha Yoga Pradipika's 2nd Chapter describes it as follows:
Bhastrāvallohakārasya rechapūrau sasambhramau
When inhalation and exhalation are performed very quickly, like a pair
of bellows of a blacksmith, it dries up all the disorders from the
excess of phlegm, and is known as Kapâla Bhâti.
So, as you can see it is a little bit more than just exhaling rapidly with some force. But still Kapalabhati is the answer to your question.
Also, the purpose of this Pranayama is obviously not just clearing the nose. It's the most preliminary breathing exercise that helps in awakening the Kundalini Shakti - the primary goal of Yoga. Besides, it also has other health related benefits. More advanced forms of Pranayama, that involve Kumbhaka (retaining the breath inside), are practiced thereafter.