You need to have the intention to make wudhu. All actions are by intention. However,  you don’t need to specify what this wudhu is for.

I saw on your post on how to make wudu that making the intention for wudu is under Mustahabb Part of making wudu. So if someone just says Bismillah and makes wudu without making the intention to purify themselves is their wudu still valid?

Purity | August 24, 2014 1:47 pm
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If in my area the water contains bacteria which is fatal when it enters through the nose. Is it permissible while making wudu that I use my fingers to wet my nose or not to take the water as up as possible as the sunnah directs us to and ? And is putting water in the nose a fardh part of wudu?