Transition of thermally induced flow in a square cavity using an iterative predictor–corrector meshfree approach

Abstract

AbstractThis paper aims to propose a new approach based on meshfree method to solve the dimensionless steady nonlinear natural convection equations. The solution methodology uses the moving least squares (MLS) shape functions to discretize the weak form of the governing equations and the Newton–Raphson algorithm to compute the nonlinear solution. Parametric studies of natural convection concerning closed two‐dimensional (2D) cavity with different operating conditions filled with air is used to assess the impact of the proposed approach on the performance of computed solutions. The cavity is formed by adiabatic and isothermal walls. For that, in all considered cases, the vertical sidewalls of the enclosure are heated differentially and maintained at hot and cold temperatures. The horizontal top and bottom walls are considered thermally insulated. The thermophysical properties of the working fluid are assumed to be constant except the density variations causing a body force term in the momentum equation. No‐slip boundary condition is applied at all enclosure boundaries and all internal body boundaries. The considered cases are described and analyzed in detail to check the validity of the proposed method. A comparison is performed between the results obtained from the present computer code and those available in the literature. The influence of various controlling parameters is analyzed and discussed graphically through the obtained streamlines, isotherms, and (maximum and average) Nusselt number. The numerical results computed by the proposed method are found to be in good agreement with the reference data.