Wa 'alaykum salaam,
There are 3 situations regarding raising one's hands in du'aa:
1) Situation where the sharee'ah explicitly teaches us that it is from sunnah to raise our hands when making du'aa e.g. during the jumu'ah khutbah when the khateeb is making supplication for rain (istisqaa) or for rain to cease:
On the authority of Anas who said that a man entered the mosque on Friday while the Prophet was addressing the people. The man said: "O Messenger of Allah, our wealth has been destroyed and we have no transport to the market place. Supplicate for us for rain." The Prophet raised his hands and said: "O Allah, give us rain. O Allah, give us rain. O Allah, give us rain." [Reported by Bukhaaree & Muslim]
2) Situation in which it is been narrated by sharee'ah not to raise our hands in du'aa e.g. during jumu'ah khutbah for any du'aa other than for rain/rain to cease:
'Ammaarah ibn Ru'aybah saw Bishr bin Marwaan standing on the pulpit raising his hands. 'Ammaarah ibn Ru'aybah said: “May Allaah humiliate those two hands! I saw Allaah’s Messenger never did more with his hand than this…” and he raised his index finger. [Reported in Muslim]
3) Situation when there is no text or guidance on whether we should raise our hands or not; in this case the asl
(premise) is that it is encouraged to raise one's hands since it is one of the etiquettes of du'aa:
The Prophet mentioned, “Allah is Shy and Most Generous. He is Shy that when a man raises his hands to Him (in Du’aa), He does not allow him to put them empty in failure.” [Reported by Ahmad, Abu Dawood and At-Tirmidhee]
And Allaah knows best!!
The above is based on Sh. 'Uthaymeen's (rahimahullaah) explanation in the shar7 of hadeeth 10 of al-arba'een an-nawawiyyah.