There will be a review tonight at 7 PM in RLM 15.216B, and the course outline on the web page will be updated. This is what makes the handle of the frying pan hot. Conductivity of gases is normally quite small, so except for special circumstances, conduction is not important in stars. This is how your central heating works. Macroscopic blobs of material rise and share their heat content with their cooler surroundings.
Approximations are available, and are used in making stellar models.
The function describes the opacity of the stellar material at distance r from the center of the star. Absorption in a star arises from electron scattering and from photo ionization and from many other things as well, but the physics is well enough known so that its value can be calculated for a given composition, density and temperature. The following is a brief review of the main phases of a star's birth, life and death. For a solar mass star, this process takes a time on the order of thousands of years. Although the rapid collapse has been halted by hydrostatic equilibrium, the PMS star is already warm or hot at its surface, and loses energy by radiation.