Modelling of forced convection using a stabilized meshless method

Modeling of coolant flow is increasingly important in the problems of heat treatment. Variation of the coolant characteristics is not possible to present, as a boundary condition at the appropriate level of detail. This paper presents a solution of the heat transfer equation with a convective term and a Navier-Stokes equation for forced flow, which is characteristic for a hardening process. These equations are solved by means of a meshless method. The emerging models for solving thermal processes in coolants require a stable numerical method. In this paper a stabilization of the numerical models for the generalized finite difference method for both temperature and fluid flow models are proposed. The results obtained with software implementations of the proposed models are compared with the an analytical solution and with the numerical benchmarks.