I've read several things about covering the tefilin shel yad :
- covering it with the tallit while fixing it
- covering it with the tallit for the entire tefila
- covering it with the shirt sleeve for the entire tefila
- covering it with the jacket sleeve for the entire tefila
It seems that different sources are linked to kabbalah and the fact that it is not proper to pray with a bare arm or with a jacket sleeve hanging down
Do you have some details about those points ? Also I have noticed some rabbanim don't seem to pay attention to those things for example Rav Ovadia Yossef shlita. Thanks.