Journal of the Textile Machinery Society of Japan

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The flow rate of a steady flow of viscoelastic fluid under a constant axial pressure gradient in a toroidal pipe of circular cross-section is analytically solved with the White-Metzner constitutive equation by a perturbation method. It is examined how the shear thinning viscosity and elasticity affect the flow rate of the fluid at high shear-rate to which former analyses could not be applied.
The analysis shows that the characteristics of the flow in a curved pipe are determined not only by the Dean number but also by the non-dimensional value W_e; /√<R> where W_e; is the Weissenberg number and R is the ratio of the toroidal radius to the pipe cross-sectional one. The results calculated for the ratio f_r; of the flow rate in a toroidal pipe to that in a straight pipe under the same axial pressure gradient at low Reynolds number are as follows:
(1) In the case of the Power law fluid in which W_e; is zero, f_r; decreases with increment of the Reynolds number R_e; and with decrement of the viscosity index n representing the shear thinning viscosity. Thus, the pipe resistance in a curved pipe is higher than that in a straight one.
(2) The larger W_e; gives the larger f_r; and thus the smaller pipe resistance.
(3) Large R_e; and small n give large increment of f_r; with increasing W_e; .
(4) The effect of the elasticity index s, representing the shear thinning elasticity, on f_r; is insignificant unless n is small.

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The heat transfer phenomenon of Polyethylene Terephthalate (PET) yarns is studied. As the stress change in a running yarn undergoing normal deformation depends upon the heating, it is possible to estimate the temperature to which the yarn has subjected.
Heat transfer rate to a yarn decreases as the yarn twist increases. When a yarn in false-twist texturing is given a twist on a heater, the yarn temperature increases faster than that of a yarn running without rotation. As the degree of twist on the heater increases, so does the apparent heat transfer coefficient. However, as the increase is extremly small, it is closely akin to the heat transfer coefficient of saturated twist yarns.

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