In A Challenge for Bryan I put up a simple heat transfer problem and asked for the equations. Bryan elected not to provide these equations. So I provide the answer, but also attempt some enlightenment for people who don’t think the answer can be correct.

As DeWitt Payne noted, a post with a similar problem posted on Wattsupwiththat managed to gather some (unintentionally) hilarious comments.

Here’s the problem again:

Case 1

Spherical body, A, of radius ra, with an emissivity, εa =1. The sphere is in the vacuum of space.

It is internally heated by a mystery power source (let’s say nuclear, but it doesn’t matter), with power input = P.

The sphere radiates into deep space, let’s say the temperature of deep space = 0K to make the maths simpler.

1. What is the equation for the equilibrium surface temperature of the sphere, Ta?

Case 2

The condition of case A…