Page 318 - Mechanics Analysis Composite Materials
P. 318
Chapter 7. Environrncwlal, special loading, and rnanufucturing e&ts 303
The same equation can be written for the ith layer, i.e.
The total heat flow through the laminate in the x-direction is
k
Substituting the foregoing results we arrive at
(7.4)
where h; = h;/h.
Now consider the heat transfer in the z-direction and introduce the apparent
thermal conductivity A, in accordance with the following form of Eq. (7.1):
Taking n = z and I. = 1.; for zi-l< z < ziin Eq. (7.3), using step-wise integration
and conditions T(z = 0) = TO?T(z = h) = G to find constants CI and C: we get for
the ith layer
The heat flow through the ith layer follows from Eqs. (7.1) and (7.6), i.e.
Obviously, q; = 4: (see Fig. 7.1), and with due regard to Eq. (7.5)
where as earlier, hi= h,/h.
Thus obtained results, Eqs. (7.4) and (7.7), can be used to determine the thermal
conductivity of a unidirectional composite ply. Indeed, comparing Fig. 7.1 with
