Prediction of Entrance Length for Magnetohydrodynamics Channels Flow using Numerical simulation and Artificial Neural Network

This paper focuses on using the numerical finite volume method (FVM) and artificial neural network (ANN) in order to propose a correlation for computing the entrance length of laminar magnetohydrodynamics (MHD) channels flow. In the first step, for different values of the Reynolds (Re) and Hartmann (Ha) numbers (600 Re 1100 and 4 Ha 10), FVM was carried out and the values of entrance length were obtained. The hybrid and central differencing schemes were used for the convective and diffusive terms, respectively. Also, the SIMPLE algorithm was selected for solving the pressure field. In the second step, a feed-forward back-propagation ANN was trained. Then, the trained ANN was applied to develop the datasets for a wide range of Re and Ha. In the last step, using a fitting tool, the correlations for computing the MHD entrance length of channels were obtained. It was shown that by increasing of Ha, the MHD entrance length declined. However, when Re increases, the MHD entrance length is increased. In additions, with the increase of Ha, the velocity profile gets flatten and consequently, the entrance length becomes shorter. Further, the effect of Ha on the Lorentz force was discussed. It was shown that with increasing of Ha, FL increases.