Determine number of chill rollers for cooling

[roldy]

I've been tasked to see if I could determine the number of chill rollers needed to cool down glue being extruded onto a fabric. I'm not sure if my method is valid. The roller has wall thickness d with contact area A. Water inside chill roller is at T₁ and glue is at T₂.

1) Calculate the rate of heat transfer of the first roller
2) Use the rate of heat transfer to calculate T_2t, temperature of glue after time t of roller contact
3) Find ΔT of the glue of the first roller.
4) Use ΔT to determine number of chill rollers to be used. Round answer accordingly

1) Q/t = kA(T₂-T₁)/d

2) T_2t = Qd/(tkA) + T₁

3) ΔT = T_2t - T₂

4) n = (T_req - T₂)/ΔT

 

[CWatters]

4) Use ΔT to determine number of chill rollers to be used. Round answer accordingly

I don't think the temperature delta won't be the same for each roller. I think you need to repeat steps 1-3 for each roller.

 

[roldy]

After re-reading my problem I realized that I do in fact have to repeat the steps. Although, I'm not all to certain these steps will work because when I back solve forT_2t I will get T₂.