Solving heat transfer problems with phase change via smoothed effective heat capacity and element-free Galerkin methods

This paper presents a smoothed effective heat capacity model that is combined with element-free Galerkin (EFG) method, to solve heat transfer problems with phase change. The Sigmoid function is employed to build a continuous and smooth effective heat capacity function, so as to avoid possible error caused by the step-jump. The proposed numerical model is verified via numerical examples, and the effects of arrangement of EFG nodes and parameters relevant with Sigmoid function on the solutions are investigated. Satisfactory results are achieved in comparison with analytical solutions.