Solving natural convection heat transfer in turbulent flow by extending the meshless local Petrov-Galerkin method

This study extends the conventional meshless local Petrov-Galerkin method to enable the meshless technique to solve natural convection heat transfer in turbulent regimes. To do so, the Navier-Stokes and energy equations are expressed in terms of the stream function and vorticity formulation and are incorporated with the Spalart-Allmaras model which governs the turbulent viscosity. In this developed meshless numerical work, the fluid variables are approximated using the moving least squares interpolation, and the weighting function is given a unity value for the weak form of the governing equations. The proposed meshless technique is then applied to solve three conventional test cases of, the natural convection heat transfer in a square cavity, the natural convection heat transfer between two concentric cylinders of square outer and circular inner walls, and the natural convection heat transfer through a fluid bounded between two concentric circular cylinders. All the three test cases are solved for 0.71 Prandtl and different turbulent Rayleigh numbers. Based on the proposed extended method results and comparing them with those of the conventional numerical and experimental methods, the proposed technique shows to be amenable and accurate to solve turbulent natural convection heat transfer problems.