how many years does it take for heat generated in the sun's core to reach its outer layer,the photosphere?

Answer 1

Excellent Question!

There is no exact figure, but some sources say as much as a million years.

During the proton-proton chain, the name of the process of nuclear fusion in our sun (there are other processes such as the triple alpha process or the CNO cycle) photons of gamma radiation are generated during fusion.

Those photons travel outward from one atom to another being absorbed and then re-radiated back out again to be picked up by the next atom outwards.

It takes a long time for that photon of energy to reach the photosphere, and by that time a goodly number of them have lost some of their energy and the wavelengths have changed to x-rays, UV, visible light, IR, microwave or radio light.
What happened to the energy that was lost by the photons on thier way out of the star? The star uses it to sustain its temperature and fusion process. After all, it has to fight gravity trying to collapse it all its life.

There is a good article on how the sun operates at this website and it is a fascinating subject.

http://www.stellar-database.com/intro.html

Answer 2

I've seen calculations that put it at around 10,000 years.