Physics-informed neural networks approach for pollutant dispersion flow caused by magnetic dipole

Abstract

Abstract Research on the liquid flow and distribution of waste discharge concentration over cylindrical surfaces might lead to the growth of efficient waste management and pollution controlling strategies. In view of this, the pollutant concentration and magnetic dipole impact on the liquid flow through the cylinder with a porous medium are explored in the present analysis. Moreover, Fourier’s and Fick’s laws are considered to explore heat transport features. The governing partial differential equations (PDEs) of the present study are converted into non-dimensional ordinary differential equations (ODEs) utilizing similarity variables. Also, the current study proposes a novel implementation of neural networks based on physics knowledge for the liquid flow past a cylinder. The self-updating weights and bias facilitate the network to satisfy the minimization objective function and provide accurate results. Additionally, the solution obtained by Runge Kutta Fehlberg's fourth-fifth order (RKF-45) method is utilized to validate the physics-informed neural network (PINN) results, presenting mean squared errors from 10-9 to 10-11. Furthermore, it is found that the increase in temperature relaxation time parameter decreases the Nusselt number gradually at the rate of 1 to 5%. An upsurge in the values of the pollutant external source parameter and the pollutant external source variation parameter decreases the concentration profile.