Simulating non-Newtonian fluid free convection heat transfer through the meshless method

Abstract

Solving free convection heat transfer for non-Newtonian fluids through the meshless local Petrov-Galerkin (MLPG) method is the aim of this study. A mathematical elaborated computer program is developed to extend the application of the mesh-free method to address the two-dimensional laminar incompressible (mechanically incompressible, and thermally compressible) power-law fluids encompassing the entire spectrum of its rheological model indices. In the extended scheme the vorticity-stream function form of the governing equations is expressed, and a unity weighting function is secured. The proposed method takes the interpolation scheme of moving least square (MLS) to estimate the field variables. The newly application extension of the MLPG method considers three different geometrical benchmark cases which are addressed by the mesh-based analyses in the available (if there exist any) literature for validation purposes. The test cases are fluid within a square cavity, fluid within the annulus of two concentric circular cylinders, and fluid within the annulus of two concentric cylinders of circular inner and square outer walls. The comparison of the meshless to the mesh-based methods illustrates the accuracy, flexibility, and veracity of the offered extended MLPG application to addressing the free convection heat transfer for the non-Newtonian fluids for the very first time.