Is the mere intention for ablution or prayer sufficient, or must the intention be specified for the removal of ritual impurity and the permissibility of prayer, or for performing the current obligatory prayer?

The person performing ablution (wudu') must intend to remove ritual impurity (hadath (definition)), or to perform the obligatory ablution, or to make permissible that which is not permissible without it, such as prayer (salat), circumambulation (tawaf (definition)), and touching the Qur'an. As for prayer, it suffices for the worshiper to intend the specific prayer in their heart, such as the Dhuhr or Asr prayer. It is not a condition to recall the intention of performing it on time (ada') or making it up (qada'), and it is not legislated to utter the intention aloud in ablution or prayer, because its place is the heart.