1. Before the critical radius is reached any added insulation increases heat transfer. 2. For insulated cylinders, the critical radius is given by the equation 3. For insulated cylinders, a " critical radius " must be reached. 4. This implies that adding insulation below a certain "'critical radius "'actually increases the heat transfer. 5. The planets have migration might become inefficient near the critical radius , leaving planets just outside this radius. 6. The critical radius r _ c is found by setting the derivative of G equal to zero 7. At the critical radius r = r _ c, the vector field \ partial _ \ phi becomes null. 8. This equation shows that the critical radius depends only on the heat transfer coefficient and the thermal conductivity of the insulation. 9. For our sun, that critical radius is calculated to be about three kilometers ( 1.86 miles ), " the dictionary says. 10. For our sun, that critical radius is calculated to be about three kilometers ( 1 . 86 miles ), " the dictionary says.
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