EFFECT OF CURLING IRONS 243 OT 02T Ot - ot -- (Eq. 7) Ox 2 where T and t represents the temperature and time, respectively. The thermal diffusivity, ix, of the solid can be calculated using the following relationship: k tx- (Eq. 8) p'cp in which case the thermal conductivity (k), density (p), and specific heat capacity (cp) of the material are assumed to be constant throughout the heating process. Solution of Equation 7, with respect to the initial and final boundary conditions, provides the following relationship (34): •c T- T o 2 f 2X/• . t e-? du (Eq. 9) -- -- 0-T,-To 1 o where u is a dummy variable for the integration, T o is the initial hair temperature, T, is the surface temperature of the heat source, and T(x,t) is the temperature of hair as a function of distance (x) and time (t). For the sake of algebraic convenience, the dependent variable T(x,t) has been normalized, resulting in the single variable, 0. The results of the calculations, in the form of a plot of 0 as a function of the dimensionless distance parameter, are presented in Figure 2. We also performed calculations for a fiber arrangement in the form of a hexagonal lattice in which the composite consisted of fiber (91%) and air (9%). In comparison to the cubic arrangement, the hexagonal formation results in a smaller contribution of air, resulting in decreased thermal diffusitivity and, consequently, a slower rate of heat transfer. ACKNOWLEDGMENTS The authors acknowledge useful discussions with J. Kosiek and K. Krummel. REFERENCES (1) C. Robbins, Chemical and Physical Behavior of Hair, 3rd ed. (Springer-Verlag, New York, 1994), pp. 120-152. (2) M. L. Garcia, J. A. Epps, and R. S. Yare, Normal cuticle-wear patterns in human hair, J. Soc. Cosmet. Chem., 29, 155 (1976). (3) E. Hoting and M. Zimmermann, Photochemical alterations in human hair. Part III: Investigations of internal lipids,J. Soc. Cosmet. Chem., 47, 201 (1996). (4) C. Pande and J. Jachowicz, Hair photodamage--Measurement and prevention, J. Soc. Cosmet. Chem., 44, 109 (1993). (5) P. Milczarek, M. Zielinski, and M. Garcia, The mechanism and stability of thermal transitions in hair keratin, Colloid Polym. Sci., 270, 1106 (1992). (6) R. Crawford, C. Robbins, and K. Chesney, A hysteresis in heat dried hair,J. Soc. Cosmet. Chem., 32, 27 (1981). (7) L. Rebenfeld, H. Weigmann, and C. Dansizer, Temperature dependence of the mechanical properties of human hair in relation to structure, J. Soc. Cosmet. Chem., 17, 525 (1966). (8) W. Humphries, D. Miller, and R. Wildnauer, The thermomechanical analysis of natural and chemi- cally modified human hair, J. Soc. Cosmet. Chem., 23, 359 (1972).

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