Machine Learning and RBF Interpolation on Nanofluid Flow in a Rounded Corner Cavity

In this study, three machine learning techniques and RBF interpolation are compared on a heat transfer and fluid flow problem in a cavity having rounded corner through the left bottom corner. The two dimensional, time dependent dimensionless governing equations of the problem are numerically solved by the radial basis function (RBF) method for space derivatives and by the backward Euler method for time derivatives. The differentially heated cavity has straight hot left wall and cold right wall, the top wall is the adiabatic wall and the bottom wall involving the rounded corner is the insulated wall. The numerical results show that the presence of the rounded corner causes convective heat transfer to increase. A dataset involving inputs as Rayleigh number and the radius of the circular corner and output as the average Nusselt number along the hot left wall is collected from the numerical results. The machine learning techniques, neural networks, gaussian process regression and ensemble learning as well as RBF interpolation are deployed for modeling. Each modeling results in small mean squared error metric results, but the best modeling is found by RBF interpolation.