A series expansion and an approximation have been derived for the temperature in the general case of transient heat conduction in a thin layer with a surface heat flux between two semi-infinite media at different uniform initial temperatures. Their temperature accuracy has been evaluated for two test cases in the field of thermoplastic shaping of polymers. The series enables quick yet fairly accurate thermal analysis of compression molding (CM) and injection molding (IM) and its vitrification rate and of fused deposition modeling™ (FDM) and its bead welding and vitrification rate.

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