Heuristic based physics informed neural network (H-PINN) approach to analyze nanotribology for viscous flow of ethylene glycol and water under magnetic effects among parallel sheets

Abstract

In this article, we have conducted the study for the flow and thermal transfer of magneto-hydrodynamic squeezing nanofluid in the middle of two collateral plates extending to infinity using artificial neural network (ANN). The fluid employed in this research is a combination of Ethylene Glycol and water, and we delve into the utilization of a hybrid nanoparticle consisting of Fe₃O₄ and MoS₂ particles. To solve the governing differential equations, we used unsupervised heuristic based physics informed neural network (H-PINN) based fitness function$.$ In this research, the weights and biases of neural network were optimized using a hybridization of heuristic algorithms to achieve high accuracy. The fitness values obtained from proposed approach ranging from${10}^{-05}$ to${10}^{-08}$. The optimal results were then compared with numerical solutions obtained by using Runge-Kutta order-4 method through BVP4c tool as a reference solution, demonstrating the effectiveness of the unsupervised ANN method. The absolute error between the reference solution and proposed heuristic based physics informed neural networks approaches are ranging from$2.36\times {10}^{-04}\text{to}3.46\times {10}^{-06}$, $2.77\times {10}^{-05}\text{to}1.20\times {10}^{-05}$ and$1.10\times {10}^{-06}\text{to}6.53\times {10}^{-07}$. Our findings demonstrate a strong agreement with the numerical approach, with the maximum discrepancy in the profiles of flow speed and energy profiles. Notably, we observed that an increase in the squeeze number and the Hartman number resulted in a reduction in the velocity profile.