No, he doesn't have limit. In Superman Prime, he was in Sun for million years and became our uber powerful. And he doesn't stay in Sun because he has friends and family in the mainstream universe...he cant just leave them.
One time he battled an villain (don't remember the name, I try to look it up) . He was losing, but they they got near the Sun and he kicked his ass. (Heard this from another member...not sure if it is true.)
But the basic idea is that he would never burn out in the Sun, he would never tire...just like Hulk.
On the surface of the sun?
Supes absorbs solar-energy making him stronger.
Hulk gets stronger with his anger.
In nine out of ten fights normally, Supes would win.
On thes un, where Supes is rapidly and exponentially more powerful with every passing second, Hulk would be turned into a toasted green mush.
It's not exactly a regular part of his storylines.
Whereas everyone knows that Supes gets his power from the sun.
The Superman would be pretty much unbeatable on the sun.
He normally has the speed and strength to kill Hulk - if these are even increased by a small amount, it's still enough to make his job easier.
Yes.
On the sun his power is constantly increasing.
With infinite power reserves, he'd be able to move at maximum speed, constantly, battering any Hulk with a barrage of class 250,000 ton (and increasing!) punches, hitting them multiple times a second from every direction.
With his senses being increased as well, his reaction times sharpening, his bio-field fully-charged, he could dodge - or even take - Hulks punches all day, whilst constantly unleashing tremendous salvoes of punishment.
On the sun, Superman is as good as invincible to any warrior short of Silver Surfer/Thanos level.