Do you know of, or recommend, a power supply that would fit within the 1U case? Most power supplies I’ve found are significantly larger than your case in their height dimensions.
A power supply to supply what? If you give us a little more information such as output voltage(s) and current(s) and the input voltage, we may be able to help.
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Need to know wattage, inputs (115V or 115V/230V), Outputs. Do you want a switching supply (most likely to find in a low profile) or a linear regulated?
Designed a 3-output linear regulated 1U once. Used a torroid xfmr, and some real short electrolytics.
A 1U height is not an easy task. Many small switchers are not enclosed, so you have to consider clearance to the top, and how to insulate.
I recently designed a 1U enclosure and selected the power supply. The application was a 180-200W supply for Pentium4 motherboard, drives, fans, etc. Of course, your application may be different, but here's a list of some sources I found:
We chose a supply from Sparkle, the smallest of the small, and have been happy with it. It's tightly packed, so make sure you don't restrict the airflow to/from it.