The quasi stationary-state solution of the two-dimensional Rosenthal equation for a moving heat source using the meshless element free Galerkin method is studied in this article. Node-based moving least square approximants are used to approximate the temperature field. Essential boundary conditions are enforced by using Lagrange multipliers. A Gaussian surface heat source is used for the modeling of the moving heat source. The results obtained for a two-dimensional model are compared with the results of the finite-element method.
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Xuan-Tan Pham (2013) studied this question.
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