Modeling of Average Nusselt Number by Machine Learning and Interpolation Techniques

Abstract

In this study, an important heat transfer and fluid flow parameter, average Nusselt number Nu¯, is statistically modeled by using the data obtained from a numerical process. The two dimensional, time dependent dimensionless equations of natural convection flow either in the absence or in the presence of a uniform inclined magnetic field (MF) is numerically solved by using global radial basis function (RBF) method in spatial derivatives and the second order backward differentiation formula (BDF2) in time derivatives. Numerical simulations are performed in a set of combined dimensionless problem parameters. A data set with inputs Rayleigh number Ra, Prandtl number Pr and with output Nu¯ in the absence of MF, and a data set with inputs Ra, Pr, Hartmann number Ha, inclination angle gamma and with output Nu¯ in the presence of inclined uniform MF are saved. The obtained data is separated into train and test sets. Then, Nu¯ is firstly modeled by Neural Networks (NN). Secondly, interpolation is also examined. In terms of mean squared error metric, NN outputs give the best goodness of fit results comparing to curve fitting on test data. On the other side, it is shown that interpolation is also an alternative for modeling. This modeling issue enables one to get the desired result without making heavy numerical calculations many times.