NEURAL NETWORK AND INTERPOLATION PROCESSES ON A THERMOPHYSICAL PROBLEM IN A POROUS MEDIUM

Abstract

In this study, the average Nusselt number (Nu) in a natural convection (NC) flow problem arising inside a porous square cavity under the effect of a uniform inclined magnetic field (MF) is modeled by interpolation and neural networks. The data for modeling are obtained from the numerical simulation of the problem in different problem parameter combinations, which are the Rayleigh (Ra) and Hartmann (Ha) numbers, and the inclination angle of MF (y). The inputs are grouped into three different cases depending on problem parameters. In the first case, input is only Ra; in the second case, Ra, Ha; and in the third case, Ra, Ha, y. The output Nu is considered as functions of these parameters in each case. The fitted and modeled Nu is tested on test data separated from the original data, and good fit results are found in terms of mean squared error and R-squared error measures. In the first and second cases, interpolation surpasses trilayer neural networks (TNN). In the third case, TNN is also as good as interpolation. The obtained models are also checked on out-of-range data. In that case, interpolation predictions are found to be better than TNN results. As a result, modeling of important heat transfer characteristics enables one to interpret the enhancement in convective heat transfer immediately in some parameters instead of performing numerical calculations many times.