Modeling of Average Nusselt Number by Machine Learning and Interpolation Techniques

Abstract

In this study, an important heat transfer, fluid flow parameter, and average Nusselt number Nu¯ are statistically modeled by using the data obtained from a numerical process. The two-dimensional, time-dependent dimensionless equations of natural convection (NC) flow either in the absence or in the presence of a uniform inclined magnetic field (MF) are 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 dataset with inputs Rayleigh number Ra, Prandtl number Pr, and output Nu¯ in the absence of MF and a dataset with inputs Ra, Pr, Hartmann number Ha, inclination angle γ, and output Nu¯ in the presence of inclined uniform MF are saved. The obtained data are separated into train and test sets. Then, Nu¯ is first modeled by Neural Networks (NN). Second, interpolation is also examined. In terms of mean squared error (MSE) metric, NN outputs give the best goodness of fit results compared 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.