How is energy transported from the core to the surface of the sun by radiation and by convection?

It happens through a whole lot of collisions .Extremely high energy photos form from the nuclear processes in the core . The high density means those photons are immediately absorbed by other nuclei and icons . The energy then remitted as another high energy photon and goes on and on until finally that energy is close enough to the sun's outer limits for the photon to escape . From each collision the photons lose a little energy . From the time it is formed from nuclear fusion until it reaches the photon may bounced around 170000 years

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White dwarf is very hot, but also very small and that is why it may appear dim.