Mushy Ball is the new fictitious planet in solar orbit. Since Mushy is new to the neighborhood, no one is sure what will happen with Mushy now that the light of day is shining on the planet. Professor Joseph R. Genius believes that the planet will turn into a frozen rock. Professor Uri F. Kidding thinks J.R. is smoking something and that Mushy will turn into an Earth like planet.
The green curve is sub surface "Mushy" energy. Whatever energy is absorbed at the equator, a portion of that energy will travel towards the poles. The curve shows the potential difference between 10 degree "walls" Since the "surface" of Mushy is less dense than the sub-surface, the rate of transfer through these walls would be slower below the "surface" than above the "surface".
What Uri is trying to explain to Junior is that there is no "surface" but a series of surfaces. Each surface, because of different density of composition would have different internal and external rates of energy transfer.
Surface 1 would have wall transfer 1. Each progressive surface in the chart above absorbs half the energy of the surface before. The wings of the first wall are taller, so it would be easier to transfer energy to the surface than to the poles. The deeper the absorption penetrates the easier the energy trans fer to the pole is with respect to the surface. Since surface 1 absorbs 25% of the incident radiation, surface 2 is 12.5%, surface 3 is 6.75% and surface 3 is 3.375% of the full radiant energy at the equatorial surface. If the "surface" is frozen away from the equator, the transfer of energy becomes more difficult and the "surfaces" below the frozen surface retain more energy. For Mushy to not gain energy, the equatorial surface would have to be impenetrable. With the sub-surfaces retaining more energy, even if is only a fraction of a Watt per day, Mushy will approach Earth like stored energy conditions.