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Simulating convective-radiative heat sink effect by means of FEA-based Gaussian heat sources and its approximate analytical solutions for semi-infinite body

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Abstract

FEA-based Gaussian density heat source models were developed to study the effect of convective and radiative heat sinks on the transient temperature field predicted by the available analytical solution of the purely conduction-based Goldak’s heat source. A new complex 3D Gaussian heat source model, incorporating all three modes of heat transfer, i.e. conduction, convection and radiation, has been developed as an extension of the Goldak heat source. The approximate transient analytical solutions for this 3D moving heat source were derived and numerically benchmarked with the available measured temperature and weld pool geometry data. The calibrated transient temperature field generated by MATLAB programming was 5 to 6 times faster than by FEA-based simulation. The new complex 3D Gaussian heat source model and its approximate solution could significantly reduce the computing time in generating the transient temperature field and be an efficient alternative to extensive FEA-based simulations of heating sequences, where virtual optimisation of a melting heat source (i.e. used in welding, heating, cutting or other advanced manufacturing processes) is desirable for characterisation of material behaviour in microstructure evolution, melted pool, microhardness, residual stress and distortions.

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Availability of data and material

Measured transient temperature data and weld bead geometry of Nguyen et al.’s bead-on-plate data [Ref. 5] used to benchmark the Gaussian heat source are available upon request.

Code availability

The input file and Dflux user subroutines used for Abaqus FEA modelling; MATLAB codes for implementing the approximate analytical solutions for the complex Gaussian heat source developed in this work, i.e. simulating the transient temperature field for a bead-on-plate subjected to this heat source, are available upon request.

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Acknowledgements

Contribution of Mohammad Nasiri in earlier stage of this project for initial MATLAB codes implementing the heat convection effect was greatly appreciated. This project was purely volunteer research project, based on the tremendous efforts and endless time of the authors who have strong common interest and passion for advancing research in Gaussian heat sources, FEA-based simulation and its transient analytical solutions for potential industrial applications.

Funding

The second author gratefully acknowledges the financial support from the National Agency for Petroleum, Natural Gas and Biofuels (ANP)-PRH 18 and FINEP for the fellowship, not directly related to this project as he worked on this project voluntarily in addition to his work’s project.

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Authors and Affiliations

  1. HRL Technology, EMD Engineering and Materials, Melbourne, Australia

    Ninh Nguyen

  2. Programa de Engenharia Naval e Oceânica, Laboratório de Tecnologia Submarina COPPE/ UFRJ, Rio de Janeiro, Brazil

    John H. Chujutalli

Authors
  1. Ninh Nguyen
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  2. John H. Chujutalli
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Contributions

The first author has derived the new complex Gaussian heat source by extending the Goldak’s heat source to include all three modes of heat transfer (i.e. conduction, convection and radiation); derivation of approximate analytical solutions and give direction to Abaqus-based finite element modelling; and carried out MATLAB implementation of the analytical solutions for transient temperature field for bead-on-plate and manuscript.

The second author has carried out the Abaqus-based FEA modelling of the complex Gaussian heat source, heat source calibration, sensitivity study and manuscript.

Corresponding author

Correspondence to Ninh Nguyen.

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Appendix. Analytical solution of the complex heat source by MATLAB codes

Appendix. Analytical solution of the complex heat source by MATLAB codes

Figure 15 shows a captured screen of the MATLAB code run display at the end of the path 2 of the bead-on-plate GMAW simulation. The temperature contour surrounding the heat source is shown on the steel plate cross-section, cutting through the centre planes of the weld paths.

Figure 15
figure 15

Image of MATLAB transient run for 2 paths — inc. Temp. contours and weld pool size

Full size image

There are four small windows designated for the real-time display of the weld pool shapes, i.e. showing the real time sizes of the weld pool length, with and depth with constant iso-boundary temperature depicted at 1370°C.

The top two windows (left and right) showing the weld pool boundary due to heat conduction-only transient temperature solution for the Goldak’s heat source by Nguyen et al. [5], using calibrated heat source parameters. The bottom two windows (left and right) showing the effective weld pool shape geometry (i.e. pool length, width and depth), determined from the approximate analytical transient solution for the complex heat source which incorporated all three modes of heat transfer, i.e. heat conduction, convection and radiation.

The approximate transient analytical solution of the complex heat source model was implemented by written MATLAB codes, with calibrated Goldak’s heat source parameter [chf, chb ah bh ] = [10 20 10 1.5], typical heat convection film in quiet air h = 5 W/m2/°C, grey body of steel plate with emissivity of 0.67 and radiative correction factor of krad = 0.02 for temperature solution reduction, due to radiative heat sink as per the approximate analytical solution for the complex heat source equations, developed in this work.

The transient temperature depicted at three selected points A, B and C and its corresponding temperature reductions due to convective and radiative heat sinks are shown in Fig. 16a and 16b, respectively.

Figure 16
figure 16

Transient Temperature at 3 selected points and temperature reductions due to convection and radiation. (a) Transient temperature at the 3 selected points A, B and C. (b) Temperature reduction due to convective and radiative heat sink

Full size image

Figure 17 shows the calibrated transient temperatures, generated by Matlab codes for the point A, B and C, are compared reasonable well with the transient temperature data from Nguyen’s et al experiment [5]. The plot has demonstrated the validity of the approximate transient analytical solution of the complex heat source model that could be used as an efficient alternative for extensive FEA-based simulations of heating sequences, where virtual optimisation of a melting heat source (i.e. used in welding, heating, cutting or other advanced manufacturing processes) is desirable.

Figure 17
figure 17

Transient temperature by MATLAB codes was benchmarked with the measured temperature data [5] to obtain suitable heat source parameters for the complex heat source analytical solution

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Nguyen, N., Chujutalli, J.H. Simulating convective-radiative heat sink effect by means of FEA-based Gaussian heat sources and its approximate analytical solutions for semi-infinite body. Int J Adv Manuf Technol 117, 3717–3742 (2021). https://doi.org/10.1007/s00170-021-07699-8

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