Wudu’ is a specific set of actions that purify a person from minor hadath and make them ready for prayer and other actions that require purification from hadath, such as reciting the Quran from the mus’haf for those who require it, circumambulating the Ka’bah, prostrating for recitation of verses of gratitude for those who require it.
Therefore, it is a separate act from any specific intention, as it is intended to remove hadath.
Hence, it is permissible to perform a recommended prayer with Wudu’ made for an obligatory prayer, or an obligatory prayer with Wudu’ made for a recommended prayer, or a prayer with Wudu’ made for touching the mus’haf.”
Fatwa by Dr. Khālid Naṣr