Praise be to Allah.
Du`a: An act of worship
It is important to note that du`a is an act of worship, and every act of worship should only be done on the basis of evidence.
Raising hands in du`a
The basic principle here is that the hands should be raised when making du`a, except when the du`a is part of another act of worship, in which case raising the hands is regarded as an additional action (and should not be done).
Examples of such acts of worship include prayer, khutbah (Friday sermon) , tawaf (circumambulation of the Ka`bah), sa`i (running between al-Safa and Marwah), etc.
Prayer includes du`a at the beginning of the prayer, in ruku’ (bowing), when standing up from ruku’, in the two sajdahs (prostrations) and in the sitting between the two prostrations – but whoever raises his hands in these places is considered to have committed an act of bid’ah (reprehensible innovation).
The same applies to raising the hands when making du`a on the pulpit, except in the case of istisqa (praying for rain). And the same applies when making du`a when doing tawaf or sa`i.
When to raise hands in du`a
When there is evidence to show that it is permissible to raise the hands in certain situations, then there is no dispute. Any du`a which has not been narrated in a report and which is not part of another act of worship is regarded as general du`a; in this case there is nothing wrong with raising the hands.
Prophet Muhammad (peace and blessings of Allah be upon him) spoke of a man who raised his hands to the sky and said, “O Lord, O Lord,” whilst his food was haram, his drink was haram, his clothing was haram, he had been nourished with haram, so how could his du`a be answered?
The Prophet (peace and blessings of Allah be upon him) also said: “Allah feels shy to let His slave raise his hands to Him and bring them back empty.”
Raising hands in du`a in nafl prayer
With regard to raising the hands after a nafl prayer, if that is not a du`a that is regularly offered, such as when a man is faced with some emergency, and he calls upon Allah at that moment, there is nothing wrong with that. But if he regularly makes du`a and raises his hands after praying an obligatory prayer, there is no clear evidence to support doing so.
And Allah knows best.