Forced/Thermal Convection

[SalvoR]

Hello everyone,
I am trying to figure out a heat transfer problem.
I am dealing with a 250-micron fiber optic strand that needs to heat to 300 degrees before entering an extruder. The strand goes into a preheater at 72 degrees, gets multi-wrapped (10 wraps) around sheaves, and then exits the preheater into the extruder. The preheater uses two Leister 61S heaters for heat and they both get their air blown by Leister's own airpak blower. We can assume 13 meter per second air speed out of each heater.
The fiber optic strand itself is moving 400 meters per minute. The height of the heating zone is 25 inches (.635 meters). This translates to roughly 250 inches (6.5 meters) of fiber strand in the active heat zone. At 400 meters per minute, 6.5 meters of strand is exposed to heat for about 1 second.

If I set the preheater temp to 500 degrees, what would the product's temperature be exiting the preheater?
Can anyone help me figure this out?
TIA!

 

[EdStainless]

I presume that you know the heat capacity and TC of hte fiber strand.
You could start by assuming that the outside surface reaches 500 instantly and then seeing what the average bulk temp is after 1 sec.
You could try estimating some forced convection coefficients, but more important may be if you can keep the sheaves heated above 300.
I used to heat treat metal wire, 1950F for 2-5sec. It really just took testing to see if it worked because the numbers are so rough.

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P.E. Metallurgy, consulting work welcomed

 

[SalvoR]

@Edstainless
Thanks for the reply. I'm still waiting for material property of the product. My guess is that the fiber will be similar to plastic. Next week we'll be running some tests using payoffs and takeups to stimulate the assembly line. At first I thought it would be a simple calculation but man, it's been over 20 years since using heat transfer and/or thermodynamics.

 

[georgeverghese]

Take a look at the differential equations on page 5-9 in the chapter on heat transfer in the 7th edn of Perry Chem Engg Handbook - suspect your case solution is an extension of one of these expressions. Note the heat transfer at the surface of the strand is the sum of convective and radiative components.