I feel very dumb that I cannot figure this one out despite a PhD in fiber optics, so looking for some bigger brains to help.... I'm passing an oven over an optical fiber and I'm trying to figure out what temperature the fiber will see in the center. I know the ambient temperature of the oven 600C, the size of the fiber which is 80 microns diameter and the material silica. So I can pull up the thermal conductivity and various other constants. I also know the speed and length of the oven. First order approximations are fine, I don't need to simulate the oven shape. What I can't figure out is a time dependant equation that is relevant. Can anyone guide me to a relevant equation?