What division of the viscera does it supply? (heart)?
Near the posterior end of the aorta, arising from its ventral side, is the unpaired posterior mesentric artery.
What module of the viscera does it supply?
Answers: As far as I know, in humans, near are 3 main arteries supplying the abdominal nouns; the celiac (perfusing the esophagus, stomach, pancreas, liver and duodenum via the gastric / hepatic / splenic arteries); the Superior Mesenteric Artery (SMA) supplying the small intestine, primarily); and the Inferior Mesenteric Artery (IMA) providing circulation to the large intestine or not here colon splenic flexure / descending colon / sigmoid areas.
I believe the term, 'posterior mesenteric artery' could be synonymous beside the IMA.
I have see the specific term, 'posterior mesenteric artery' related to animal anatomy, such as rats, frogs, etc., but within humans I think the IMA would be closest to that occupancy.
Your question really doesn't label sense.
The viscera includes all the internal organs and adjectives of them are connected to the circulatory system or they wouldn't function!