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Wouldn’t we be observing the outer 30% (or 1%) though? From the diagram on the page you linked it seems that the granules in the photo exist in the photosphere, where convection is the dominant mode of energy transfer. That said, none of the conduction could happen without radiation further inside.

Yeah, we’re seeing the convection from the outer 30%, bubbling up on the surface of the photosphere. All of the fusion takes place down in the core though. It’s very difficult to fuse hydrogen and so it can only occur at the extreme pressures in the middle of the sun.

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