Either way, you have the vent below so it can suck in from down there, but it also doesn't make a significant difference if you have it facing up. If you have it on a fluffy carpet though the bottom air vent will likely be blocked so i would put it up, but if you have it on wood either way will work.
I googled the Rosewill Challenger U3 and my answer is based on the images that I saw.
To clarify, by "up or down" I assume you mean should you place this so that the intake pulls air through the intake screen from the bottom of the case, or it pulls air from inside the case.
I would always go with placement so that the PSU's airflow does not have to compete with any other airflow.
From personal experience, a previous build that I did has the PSU pulling air from inside the case and venting out the back. There was no option for me to install it any other way. This has led to an interesting problem. If I turn the case exhaust fans up to high, they over-power the PSU fan and draw air *backwards* through the PSU. I can't imagine that is good for the PSU fan, and so I avoid it by manually controlling and balancing the speed of the case intake fans (3 of these) and the exhaust fans (two of these.)
Another practical consideration is that having it separated from the rest of the internal case air means that, hypothetically, it will be easier for your PSU to stay cool, since it will not be using the pre-heated air from inside the case.
From the images I googled, it looks like there is a screen across the bottom of your case. That's good. Just keep an eye on it and vacuum it off when it starts to get dusty.
And make sure that your PC is sitting on a hard surface where it has good airflow. Setting it on a carpeted floor is probably not what you'd want to do.