Green element calculations of nonlinear heat conduction with a time-dependent fundamental solution

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Calculations of nonlinear transient heat conduction are carried out with a Green element formulation that incorporates the time-dependent Green's function derived from the diffusion differential operator. This formulation is different from the one that uses the logarithmic fundamental solution, and offers another viable approach at solving nonlinear heat transfer problems. Applying the formulation in 2D spatial domains, the integral equation arising from applying the singular integral theory is implemented from element to element with linear interpolation in space and time for the temperature field. The nonlinear discretized equations are solved by the Picard and Newton–Raphson algorithms with good convergence being achieved for all thermo-elastic relations examined, and the latter algorithm exhibiting slightly better convergence characteristics. Comparison of the current Green element formulation with the previous one that uses the logarithmic Green's function indicates that comparable accuracy are achievable from both formulations with the latter having an edge in terms of simplicity of formulation.