Heat Transfer Applications of Meshless Local Petrov-Galerkin (MLPG) Method during Plasma Spray

In this work, a compact computational formulation is established based on the truly meshless method MLPG, and is firstly used to solve steady and transient heat conductions of the plasma spray. The unknown function of temperature distribution is approximated by moving least square approximation functions. These approximants are constructed by using a weight function, a polynomial basis and a set of non-constant coefficients. A cubic spline function selected as the weight of the moving least-squares approximation and a penalty technique is introduced to enforce the essential boundary conditions. The effect of scaling and penalty parameters on this numerical algorithm is discussed in detail. FORTRAN code is developed to obtain the MLPG results. For comparison, finite element method is conducted to evaluate the accuracy and efficiency of this formulation; moreover, experiments of plasma spray are also designed and carried out. It is shown that MLPG solutions of a steady and transient heat conduction problems exhibit higher accuracy and reliability compared with the FEM and is in good agreement with that from the empirical results in plasma spray experiments, suggesting that the MLPG method is feasible and efficient and therefore applicable to heat conduction problems during the plasma spray process.