Nuclear Fusion Makes Most Stars Shine

Nuclear fusion is the primary energy source for most stars' shining. There is another energy source, called the Kelvin-Helmholtz mechanism: As stars form from collapsing clouds of gas, they release gravitational potential energy. This binding energy gets converted into heat, up to 1/2 of which can then been converted into light radiating off of the star. The Kelvin-Helmholtz mechanism is important during star formation, but it can't power stars for anywhere near as long as they actually shine.

Given the Sun's mass and radius, how long could the Sun radiate light at its current luminosity if it were powered entirely by the Kelvin-Helmholtz mechanism? You may approximate the Sun as having uniform density.

Give your answer in years.