"upper part of" is correct and usable in written English.
You can use it to refer to a specific location above a certain point. For example, "The upper part of the tree was filled with brightly-colored fruit."
The upper part of her building was on fire.
Reinhardt laughed, the upper part of his body bouncing energetically.
The face and upper part of the chest were 'livid'livid
The school closed down the upper part of the campus on Thursday, Sept.19.
And who's that pudgy bespectacled face that intermittently skids through the upper part of the screen?
"I felt a very strong pain in the upper part of my thigh.
The upper part of the woman's body was intact, unlike in most suicide bombings.
Rahlves tried to pass on an upper part of the course.
"The first one is on the upper part of the left-hand page".
"There are some much earlier things," she said, waving toward the upper part of the painting.
Mitch suggested I try the upper part of the Middle Loup, which has fewer obstructions.
