What is conduction in stellar atmospheres?
Transfer of heat energy by physical contact of stellar materials. Current models do not assume any conduction in stellar atmospheres.
Heat transfer can take place by conduction – physical contact of solids, convection – transfer by moving molecules of gases (also usually involves conduction to the gases from the source and from the gases to the object), and radiation – direct energetic transfer by electromagnetic radiation.
Current stellar models assume all heat transfer is primarily by radiation, with negligible convection (in cooler stars) or conduction contributions. https://arxiv.org/pdf/astro-ph/9906130v1.pdf ; http://www.ifa.hawaii.edu/users/kud/teaching/4.Convection.pdf