Time dependance of temperature rise

[gilzers]

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 dependent equation that is relevant. Can anyone guide me to a relevant equation?

 

[Chestermiller]

See Heat Transmission by McAdams. He provides graphs of temperature profiles in cylinders heated from the outside by a heat transfer coefficient. But, you need to have an estimate of a reasonable value for the air-side heat transfer coefficient. Typical values are given in Transport Phenomena by Bird, Stewart, and Lightfoot.

Chet