While Adobe Reader has a beautiful rendering, you might prefer a different PDF viewer for previewing. If you have a PDF viewer in a seperate window, that reloads the PDF without closing and reopening, it is easy. You can just drag it to the other monitor once and it will stay there while refreshing. I use SumatraPDF, which supports this kind of silent refresh. It also doesn't lock the PDF file and offers the possibility to jump back to the right place in source code by clicking in the PDF. I used Texmaker and its forks this way under Windows. You can refresh the pdf manually with 'r' or let your gui refresh it via command line as soon as the compilation of the PDF to review has finished.
Aditionally to SumatraPDF as an external PDF viewer, that can be called from any gui, there is at least one fork of Texmaker that offers a PDF preview window without external tools, with all the possibilities I mentioned above. Maybe it's Texstudio.
Maybe you have to deal with the focus of SumatraPDF and decide if it should stay at your TeX gui window or change to the external pdf viewer window.