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Heat transfer during dry spinning of fibers

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Summary

Heat transfer to fibers formed in dry spinning has been subjected to fundamental analysis. Solutions of the equation of energy have been derived and tested with experimental data. Results were deemed satisfactory in view of the accuracy of the experimental data. The present work is believed to yield a good representation of the heat transfer in the dry spinning process.

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Abbreviations

h :

heat transfer coefficient, cal/cm2 °C sec

k :

thermal conductivity, cal/cm °C sec

r :

radial distance, cm

t :

time, sec

Z :

axial distance, cm

A :

surface area, cm2

A n :

\((T_0 - T)(a_n \pi )^{\tfrac{1}{2}} \frac{{\sin {\text{ }}a_n }}{{a_n^2 }} - \frac{{\cos {\text{ }}a_n }}{{a_n }};\) or n-th root of \({\text{tan }}a = \frac{{ak}}{{k + h}}\)

A 0 :

energy required for solvent evaporation, cal/sec cm3

C p :

specific heat cal/gm °C

J 0 :

Bessel function of first kind, order zero

J 1 :

Bessel function of first kind, order one

J 2 :

Bessel function of first kind, order two

N :

k/(R 2 ρC p V)

Q :

volumetric flow rate cm3/sec

R :

outside radius, cm

T :

point temperature, °C

T S :

surface temperature °C

T 0 :

initial fiber temperature °C

T ∞ :

ambient air temperature, °C

\(\bar T\) :

average fiber temperature, °C

\(\bar T\) 1 :

average fiber temperature of preceding segment, °C

V :

average fiber velocity relative to air strean, cm/sec

V r :

radial velocity component, cm/sec

V z :

axial velocity components, cm/sec

V θ :

θ direction velocity component cm/sec

W :

weight of solvent evaporated in a given fiber segment, gms

α n :

a solution of the equation J 0(X)=0

λ :

heat of vaporization of solvent, cal/gm

θ :

θ dimension

φ :

r/R

ρ :

density, gms/cc

References

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  4. Culpin, M. F. and D. M. Jones, J. sci. Inst. 36 (1959) 28.

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  5. Earl M. Seagrave, Personal Communication, Earl M. Seagrave Company, Charlotte, North Carolina.

  6. Bird R. B., W. E. Stewart and E. N. Lightfoot, Transport Phenomena, p. 319, John Wiley, New York, 1960.

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  7. Mickley, H. S., T. K. Sherwood and C. E. Reed, Applied Mathematics in Chemical Engineering, p. 262, McGraw-Hill, New York, 1957.

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  9. Griskey, R. G., Unpublished data.

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Author information

Author notes

  1. Siu Yuen Fok

    Present address: Chemistry Department, Clarkson College of Technology, Potsdam, New York, USA

Authors and Affiliations

  1. Department of Chemical Engineering, Virginia Polytechnic Institute, 24061, Blacksburg, Virginia, USA

    Siu Yuen Fok & Richard G. Griskey

Authors
  1. Siu Yuen Fok
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  2. Richard G. Griskey
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Fok, S.Y., Griskey, R.G. Heat transfer during dry spinning of fibers. Appl. Sci. Res. 16, 141–148 (1966). https://doi.org/10.1007/BF00384061

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  • DOI: https://doi.org/10.1007/BF00384061

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