Express ordinal number of hour in Chinese?
I had never head the expression 第……小时 be used to describe time. 第三个小时的第五分钟 would be more confusing, and more complex than 两点零五.

But the similar form may be used when the time is related to some certain beginning. Here are some example:


第84分钟，在VAR的判罚下，巴西队获得点球机会，由乔治扳平比分……[1]
夜幕逐渐降临，就在［救援的］第20个小时，救援现场传来喜讯……[2]