The meshless analog equation method for solving heat transfer to molten polymer flow in tubes

In this paper, we proposed a meshless analog equation method (MAEM) to solve a heat transfer problem of molten polymer flow, which is considered to be a generalized Newtonian viscous flow. The MAEM, free from mesh generation and numerical integration, is a powerful meshless method. The numerical solutions are expressed by a linear combination of the derived radial basis functions (RBFs). This paper considers two different viscosity models for the molten polymer; one is temperature-independent power-law model and the other is temperature-dependent power-law model. The viscous dissipation term is included in the energy equation to capture the relevant physical phenomena. From the comparisons of numerical simulation, the meshless solutions are in good agreement with some analytical solutions and other finite element solutions. Moreover, the MAEM uses much less CPU-time and computer memory to simulate molten polymer flows. Therefore, it is believed that the RBF-based meshless method of the MAEM is a promising and flexible numerical scheme for molten polymer flow simulation.