When is it recommended to raise one's hands when supplicating, and is it permissible to raise them after the supererogatory prayer?

The basic ruling regarding raising the hands in supplication (Du'a) is permissibility, unless the supplication is part of another act of worship like prayer, sermon, circumambulation (Tawaf), or striving (Sa'y). In such cases, raising the hands is considered an innovation (Bid'ah), unless there is specific textual evidence allowing it. As for absolute supplication, raising the hands is permissible. There are narrations indicating the desirability of raising the hands in supplication, such as the Hadith of the man who extends his hands to the sky, and the Hadith about Allah feeling shy towards His servant when he raises his hands. As for raising the hands after supererogatory (Nafl) prayers, there is no harm in it if it is for a contingent reason. However, if it becomes a regular habit after obligatory (Fard) prayers, there is no clear evidence to support it.