Sony E series laptop power supply uncomfortably hot?

Hi I have a new Sony Viao E series 15.5inch laptop. So its an i 5 with intel hd graphics. 4gb ram and such. So anyway today my laptop battery was low so I pluggeed it in to the charger. While it was charging I did multiple browser task and one download and an install. My CPU usage wasb't high but my power supply got uncomfortably hot This is snot normal, I was using it for like almost 2 hrs and like it isn't normai. Like when i first brought it, I was connected to a power supply for almost 5 hrs and nothing like that happened. I wasn't doing anything intense and i need to do intense stuff for uni. This laptop is for engineering/scinces. SO like is it normal to have a hot power supply or do i have to return it?

 

I am having E series myself, and yes my power adapter.power supply unit, gets damn hot after 1 or 2 hrs, sometimes it looks like it will blast if i dont put it in front of AC.

 

I got scared, either way I think its poor thermal mangement in part of this model, because in turn sometimes battery pack is hot, so really my model came with integrated intel hd graphics and I don't think it can run CAD, CFD and stuff like that. I know it can run Matlab but other extensive programming. I mean I don't even know if it can run image analysis (Matlab package). Though the E series in Sony site has a dedicated GPU im switching it. Unless u guys can convince me other wise?