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Temperature Distribution in Solids with Variable Off-Axis of Anisotropy

ABSTRACT A model for the heat flow in the injection-molded fiber-reinforced plastics is presented. It is the anisotropic medium whose axis of anisotropy is changing with depth periodically. Its equation of heat conduction yields to a type of Hill's equation and the exact closed form solution is obtained. Numerical examples for the temperature contour are presented for three geometries: an infinite medium with a pair of heat source and sink, a semi-infinite medium with a heating edge, and a thick plate with heating and cooling edges. The shape of the contour for the lower temperature is greatly affected by the variation of the axis of anisotropy; however, that of the high temperature contour near the source is close to that in the anisotropic medium with uniform off-axis. The present temperature analysis gives some insights for the residual stress in the injection-molded fiber-reinforced plastics.