Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Welding of thin steel plates: a new model for thermal analysis

  • 37 Accesses


A mathematical model for the transient heat flow analysis in arc-welding processes is proposed, based on a unique set of boundary conditions. The model attempts to make use of the relative advantages of analytical as well as numerical techniques in order to reduce the problem size for providing a quicker solution without sacrificing the accuracy of prediction. The variation of thermo-physical properties with temperature has been incorporated into the model to improve the thermal analysis in the weld and heat-affected zones. The model has been evaluated using a five-point explicit finite difference method for analysing the welding heat flow in thin plates of two different geometric configurations. The temperature distribution closer to the heat source, primarily in the weld zone and the heat-affected zones, are predicted by the numerical technique. The thermal characteristics beyond the heat-affected zone are amenable to standard analytical techniques. The behaviour of the boundary condition in the model has been investigated in detail.

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


q′ :

Rate of heat per unit thickness (Wm−1)

d :

Plate thickness (m)

v :

Velocity of source (m s−1)

t :

Time (s)

T :

Temperature value at the desired point (K)

T 0 :

Initial temperature (K)

K :

Thermal conductivity (W m−1 K−1)

ρ :

Density (kg m−3)

c p :

Specific heat (J kg−1 K−1)

α :

Thermal diffusivity (m2 s−1)

n :

\(\frac{{q\prime \upsilon }}{{4\pi \alpha ^2 \rho c_{\text{p}} {\text{(}}T_{{\text{A}}_{{\text{e3}}} } {\text{ - }}T_0 {\text{)}}}}({\text{m}}^{{\text{ - 1}}} )\)


Distance of point considered from the source (ξ=x−vt) (m)

K 0 :

Modified Bessel function of second kind and zero order

r :

Radial distance from the source (r=(x 2+y 2)1/2) (m)


Model width (m)

a :

Plate width (m)


Distance from the source ɛ=(ξ2+4 ×10−4)1/2 (m)

μn :

\(\left[ {1 + \left( {\frac{{\tau n2\alpha }}{{va}}} \right)} \right]^{1/2} \)


  1. 1.

    P. S. Myers, O. A. Uyehara andG. L. Borman,Weld. Res. Council Bull. 123 (1967) 1.

  2. 2.

    D. Rosenthal,Weld J. 20 (1941) 220-s.

  3. 3.

    Idem., Trans ASME 68 (1946) 848.

  4. 4.

    R. J. Grosh, E. A. Trabant andG. A. Hawkins,Q. Appl. Math. 13 (1955) 61.

  5. 5.

    D. T. Swifthook andA. E. F. Gick,Weld J. 52 (1973) 492-s.

  6. 6.

    K. Masubuchi, “Analysis of Welded Structures” (Pergamon Press, 1980) p. 60.

  7. 7.

    S. Kou, T. Kanevsky andS. Fyfitch,Weld J. 61 (1982) 175-s.

  8. 8.

    J. H. Argyris, J. Szimmat andK. J. William, “Numerical Methods in Heat Transfer” (Wiley, 1985).

  9. 9.

    P. Tekriwal, M. Stitt andJ. Mazumder,Metal Constr. 19 (1987) 559R.

  10. 10.

    T. Zacharia, S. A. David, J. M. Vitek andT. Debroy,Metall Trans. 20A (1989) 957.

  11. 11.

    A. S. Oddy andM. J. Bibby,Trans CSME (1983) 25.

  12. 12.

    B. V. Kumar, PhD thesis, IIT Kharagpur (1990).

  13. 13.

    M. Jacob, “Heat Transfer” (Wiley, 1956) p. 322.

  14. 14.

    H. S. Carslaw andJ. C. Jaegar, “Conduction of Heat in Solids” (Oxford University Press, 1959) p. 266.

  15. 15.

    C. J. Smithells, “Metals Reference Book”, 5th Edn (Butterworths, 1976) p. 940.

  16. 16.

    E. Kreyszig, “Advanced Engineering Mathematics” (Wiley Eastern, 1983) p. 848.

  17. 17.

    C. M. Adams,Weld. J. 37 (1955) 18-s.

  18. 18.

    S. V. Patanker, “Numerical Heat Transfer and Fluid Flow” (McGraw-Hill, 1980) p. 57.

  19. 19.

    O. R. Myhr andO. Grong,Acta Metall. Mater. 38 (1990) 449.

  20. 20.

    P. Jhaveri, W. G. Moffatt andC. M. Adams,Weld J. 41 (1962) 12-s.

  21. 21.

    M. F. Ashby andK. E. Easterling,Acta Metall. 32 (1984) 1935.

  22. 22.

    I. S. Sokolinkoff, “Advanced Calculus” (McGraw-Hill, 1939) p. 58.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kumar, B.V., Mohanty, O.N. & Biswas, A. Welding of thin steel plates: a new model for thermal analysis. J Mater Sci 27, 203–209 (1992). https://doi.org/10.1007/BF00553857

Download citation


  • Welding
  • Thermal Analysis
  • Heat Flow
  • Finite Difference Method
  • Numerical Technique