Research Papers: Conduction

Transient Heat Conduction in a Thin Layer Between Semi-Infinite Media in Polymer Shaping

[+] Author and Article Information
Leendert van der Tempel

Philips Lighting Research,
Eindhoven 5656AE, The Netherlands
e-mail: Leendert.van.der.Tempel@Philips.com

Willem Potze

Royal Philips,
Eindhoven 5656AE, The Netherlands
e-mail: W.Potze@Philips.com

Jeroen H. Lammers

Royal Philips Research,
Eindhoven 5656AE, The Netherlands
e-mail: Jeroen.H.Lammers@Philips.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 21, 2017; final manuscript received August 9, 2017; published online December 27, 2017. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 140(4), 041301 (Dec 27, 2017) (8 pages) Paper No: HT-17-1222; doi: 10.1115/1.4038198 History: Received April 21, 2017; Revised August 09, 2017

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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Grahic Jump Location
Fig. 2

Laplace-transformed temperature distribution (9) multiplied by s in the IM and FDM test cases (Tables 2 and 3)

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Fig. 3

Relative error at zero depth of geometric series expansion (16) and rational approximation (18) in the IM and FDM test cases (Tables 2 and 3)

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Fig. 4

Temperature evolution and cooling rate-dependent glass transition in the IM and FDM test cases (Tables 2 and 3)

Grahic Jump Location
Fig. 5

Depth profile of the vitrification rate in the IM and FDM test cases (Tables 2 and 3)

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Fig. 6

Absolute maximum temperature error versus the computational work, i.e., number of function evaluations in the IM and FDM test cases (Tables 2 and 3)

Grahic Jump Location
Fig. 7

Relative truncation error of the temperature series (19) and approximation error of approximation (22) at zero depth in the IM and FDM test cases (Tables 2 and 3). Figure 3 shows the Laplace-transformed counterpart.

Grahic Jump Location
Fig. 8

Surface temperature evolution in the FDM test case (Table 3) and in case of a 0.8 mm thick bead with 300° C and 110° C initial temperatures



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