A kind of analytical model of arc welding temperature distribution under varying material properties

Abstract

Nonlinear partial differential equation of temperature distribution with material properties varying was linearized by choosing appropriate linearization coefficient and solved through Green's function and Fourier transform methods. According to these results deduced, analytical model of arc welding temperature distribution under material properties varying condition was obtained. To verify precision of the analytical model obtained, temperature distribution of semi-infinite body under moving spot heat source was calculated through three different methods, including analytical model with and without considering material characters varying and finite element model. By comparing weld pool size calculated through the three methods, results got from analytical model of this paper were found more close to which got from finite element method. Conclusion was that, by taking material properties varying into account, analytical model deduced in this paper had higher precision, especially near the area of weld pool where temperature gradient was very great in welding process.

On the integral-balance approach to the transient heat conduction with linearly temperature-dependent thermal diffusivity

“…There exist several approaches to solve Eq. (1a), among them: orthogonal collocation method [6], Green function method [9], perturbation method [8,10,11], variational iteration method [8], homotopy-perturbation method [8], direct variational method [12], the least squares method [13], Networks models [14], iterative solutions with the solution of the linear problem as initial approximation [15], Finite difference solutions [5], Lattice Boltzmann method [16], numerical solutions [17], etc.…”

“…If the thermal diffusivity is non-linear and expressed as a power-law a = a p T m (m > 0), corresponding to degenerate diffusion problems) then Eqs. (6b) and (8) take the forms [25] The integral relations presented by (9) and (10) will be used further in this work in the development of the problems at issue. The application of both HBIM and DIM to the case with a(T ) = a 0 (1 + βT ) is demonstrated in the next section (see Sects.…”

Simulating Convective-Radiative Heat Sinks Effect by means of FEA-based Gaussian Heat Sources and Its Approximate Analytical Solutions for Semi-Infinite Body

“…As the need for more efficient and accurate 3D heat source modelling has arisen, the researchers continue to improve the current conduction-only analytical solutions to include the temperature dependent material properties [7][8] and effects of heat convection and radiation [9][10] as well.…”

“…Guo and Dai [7] and Wenji et al [8] included temperature-dependent properties, i.e., thermal conductivity, density and specific heat, in their attempt to improve current conduction-only analytical solutions for transient temperature field, that were derived for the constant material properties, due to moving Gaussian heat source.…”