Skip to main content
SpringerLink
Log in

A new energy conservation scheme for the numeric study of the heat transfer in profile extrusion calibration

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

In this work, a new second-order conservative finite volume scheme using the cell-to-vertex interpolation is proposed to solve the heat transfer problem involving discontinuous solution and discontinuous materials properties. We apply the method to a thermoplastic extrusion process where a dry calibration is used to cool down a polymer tape. One of the major difficulties in the modelling is to prescribe the adequate value for the heat transfer coefficient between the polymer and the calibrator. To this end, we define an optimization procedure coupled with the new finite volume method to evaluate the heat transfer coefficient at the polymer–calibrator interface from experimental data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Michaeli W (2003) Extrusion dies for plastics and rubber 3E: design and engineering computations. Hanser, Munich

    Book  Google Scholar 

  2. Sastrohartono T, Jaluria Y, Esseghir M, Sernas V (1995) A numerical and experimental study of the three-dimensional transport in the channel of an extruder for polymeric materials. Int J Heat Mass Transf 36:1957–1973

    Article  Google Scholar 

  3. Rauwendaal C (2014) Polymer extrusion 5E. Hanser, Munich

    Book  Google Scholar 

  4. Rauwendaal C (2010) Understanding extrusion 2E. Hanser, Munich

    Google Scholar 

  5. Mousseau P, Delaunay D, Lefvre N (2009) Analysis of the heat transfer in PVC profiles during the extrusion calibration/cooling step. Int Polym Process 24:122–132

    Article  Google Scholar 

  6. Carneiro OS, Nóbrega JM, Mota AR, Silva C (2013) Prototype and methodology for the characterization of the polymer-calibrator interface heat transfer coefficient. Polym Test 32(6):1154–1161

    Article  Google Scholar 

  7. Nóbrega JM, Carneiro OS, Covas JA, Pinho FT, Oliveira PJ (2004) Design of calibrators for extruded profiles. Part I: modeling the thermal interchanges. Polym Eng Sci 44(12):2216–2228

    Article  Google Scholar 

  8. Mitsoulis E, Vlachopoulos J, Mirza FA (1984) Finite element analysis of flow through dies and extruders channels. SPE ANTEC Tech Pap 30:53–58

    Google Scholar 

  9. Gupta M, Kown T, Jaluria Y (1992) Multivariant finite element for the three-dimensional simulation of viscous incompressible flows. Int J Numer Meth Fluids 14:557–585

    Article  MATH  Google Scholar 

  10. Yu Y, Luo X (2015) Estimation of heat transfer coefficients and heat flux on the billet surface by an integrated approach. Int J Heat Mass Transf 90:645–653

    Article  Google Scholar 

  11. Murashov MV, Panin SD (2015) Numerical modelling of contact heat transfer problem with work hardened rough surfaces. Int J Heat Mass Transf 90:72–80

    Article  Google Scholar 

  12. Versteeg H, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method, 2nd edn. Pearson Education, ISBN:978-0-13-127498-3

  13. Xue S-C, Barton GW (2012) Implementation of boundary conditions and global mass conservation in pressure-based finite volume method on unstructured grids forfluid flow and heat transfer simulations. Int J Heat Mass Transf 55:5233–5243

    Article  Google Scholar 

  14. Reséndiz-Flores EO, García-Calvillo ID (2014) Application of the finite pointset method to non-stationary heat conduction problems. Int J Heat Mass Transf 71:720–723

    Article  Google Scholar 

  15. Reséndiz-Flores EO, Saucedo-Zendojo FR (2015) Two-dimensional numerical simulation of heat transfer with moving heat source in welding using the finite pointset method. Int J Heat Mass Transf 90:239–245

    Article  Google Scholar 

  16. Costa R, Clain S, Machado GJ (2014) New cell-vertex reconstruction for finite volume scheme: application to the convection–diffusion–reaction equation. Comput Math Appl 68:1229–1249

    Article  MathSciNet  MATH  Google Scholar 

  17. Costa R, Clain S, Machado GJ (2014) Finite volume scheme based on cell-vertex reconstructions for anisotropic diffusion problems with discontinuous coefficients. In: 14th international conference in computational science and its applications—ICCSA (2014) Guimares, Portugal, 30 de junho a 3 de julho de 2014. Lecture Notes in Computer Science 8579:87–102

  18. Uffrecht W, Heinschke B, Günther A, Caspary V, Odenbach S (2015) Measurement of heat transfer coefficients at up to 25,500 g—a sensor test at a rotating free disk with complex telemetric instrumentation. Int J Therm Sci 96:331–344

    Article  Google Scholar 

  19. Rausch RD, Batina JT, Yang HTY (1991) Spatial adaptation procedure on unstructured meshes for accurate unsteady aerodynamic flow computation, AIAA Paper 91–1106

  20. Frink NT (1991) Three-dimensional upwind scheme for solving the Euler equations on unstructured tetrahedral grids, Ph. D Dissertation, Virginia Polytechnic Institute and state university

  21. Frink NT (1992) Upwind scheme for solving the Euler equations on unstructured tetrhedral meshes. AIAA J 1:70–77

    Article  MATH  Google Scholar 

  22. Frink NT (1994) Recent progress toward a three-dimensional unstructured Navier–Stokes flow solver, AIAA Paper 94–0061

  23. Mavriplis DJ (2003) Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes, NASA/CR-2003-212683 NIA Report No. 2003 06

  24. Chandrashekar P, Garg A (2013) Vertex-centroid finite volume scheme on tetrahedral grids for conservation laws. Comput Math Appl 65:58–74

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was financed by FEDER Funds through Programa Operacional Factores de Competitividade — COMPETE and by Portuguese Funds through FCT — Fundação para a Ciência e a Tecnologia, within the Projects PEst-OE/MAT/UI0013/2014, PTDC/MAT/121185/2010, and UID/CTM/50025/2013. The second author was also financed by project FCT-ANR/MAT-NAN/0122/2012.

Author information

Authors and Affiliations

  1. Centre of Mathematics, University of Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    Filipe Marques, Stéphane Clain & Gaspar J. Machado

  2. Institute for Polymers and Composites/I3N, University of Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    Bruno Martins, Olga S. Carneiro & João M. Nóbrega

  3. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062, Toulouse, France

    Stéphane Clain

Authors
  1. Filipe Marques
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stéphane Clain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gaspar J. Machado
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bruno Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Olga S. Carneiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. João M. Nóbrega
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gaspar J. Machado.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marques, F., Clain, S., Machado, G.J. et al. A new energy conservation scheme for the numeric study of the heat transfer in profile extrusion calibration. Heat Mass Transfer 53, 2901–2913 (2017). https://doi.org/10.1007/s00231-017-2023-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-017-2023-6

Keywords

Search

Navigation