Analysis of natural convection in a nanofluid-filled triangular enclosure induced by cold and hot sources on the walls using stabilised MLPG method

A stabilised meshless local Petrov-Galerkin (MLPG) method with unity as the test function is extended to simulate the buoyancy-driven fluid flow and heat transfer in a right-angled, triangular enclosure filled with a nanofluid composed of a mixture of Al2O3 spherical nanoparticles in water. A cold source with a constant temperature T-c and a hot source with a constant temperature T-h are placed along the left and bottom walls of the cavity, respectively, with a differential temperature difference between T-c and T-h so that T-h>T-c. The simulations performed in this study are based on the stream function-vorticity formulation. The moving least-squares interpolations of the field variables are employed in these MLPG numerical calculations. A streamline upwind technique is employed to obtain stable solutions for high Rayleigh numbers. A parametric study is performed, and the effects of the Rayleigh number, the locations of the cold and hot sources on the respective cavity walls, and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the cavity are investigated. The results show that the average Nusselt number is generally an increasing function of the volume fraction of the nanoparticles. Moreover, it is concluded from the results that the locations of the cold and hot sources on the respective cavity walls have a significant effect on the flow and temperature fields inside the enclosure. In general, the maximum average Nusselt number occurs when the centres of the cold and hot sources are at Y-s=0.167 and X-s=0.167, respectively, while the average Nusselt number is minimum for Y-s=0.833 and X-s=0.833.