I would like to know how heat would flow in a material being struck by sunlight in vacuum. The usual examples of Fourier heat equation always uses boundaries with fixed temperature or under convection. How do I calculate this when the surface is absorbing and emitting radiation according to Stephan-Boltzmann law? I'm considering a 1-dimensional material in vacuum, with one ending being lit, and the other being insulated. Is the analytical solution too hard to be pratically solved? If yes, do you know some source for computing this numerically? If no, do you know some source that shows this solution? This problem seems simple, but I've tried internet, teachers and books for some days, and I've still found nothing. Thanks.