Numerical investigations of ion slip and hall effects on Cattaneo-Christov heat and mass fluxes in darcy-forchheimer flow of Casson fluid within a porous medium, utilizing non-fourier double diffusion theories through artificial neural networks ANNs

Abstract

The current research focuses on harnessing the computational power of neural networks, notably the Levenberg-Marquardt backpropagation optimization algorithm (ANN-LMBOA), to simulate the behavior of magnetohydrodynamic (MHD) three-dimensional non-Newtonian Darcy-Forchheimer flow of Casson nanofluid over a stretching surface situated within a porous medium. The fluid flow is subject to the influence of Hall and ion slip forces, contributing to its behavior. Additionally, the Cattaneo–Christov heat flux model is incorporated to represent the temperature balance in the boundary layer accurately. Non-Newtonian fluids improve thermal transmission due to their shear-thinning propensity, increased turbulence, and more excellent convective heat transfer. The thermal conductivity of nanofluids is increased by the inclusion of nanoparticles, enabling more effective heat transmission. Buongiorno's model is used for the nanofluid phenomena that concentrate on thermophoresis and Brownian motion. To tackle the flow problem efficiently, the governing equations are transformed into non-linear differential equations using self-similar variables. The ANN-LMBOA algorithm is then employed to solve these equations, providing a practical and accurate approach to the simulation. To train and validate the ANN-LMBOA model, a dataset is generated using the bvp4c numerical method, which can easily handle highly non-linear coupled differential equations. The dataset is created for different scenarios of flow parameters, facilitating comprehensive training, testing, and authentication of the neural network. The accuracy of the ANN-LMBOA model is assessed through various statistical neural network tools, such as MSE, RP, CF graphs, and EH. The study thoroughly investigates flow model parameters related to momentum, energy, and concentration profiles, which are presented using visual representations to understand the system's behavior and characteristics comprehensively. The effects of various parameters of interest like Casson, ion slip, porosity, thermal relaxation, and magnetic parameters on velocity, temperature, and concentration distribution have been studied numerically via ANN-LMBOA networks. The absolute error of reference and target data is obtained in the range of 10−4 − 10−5which proves the best accuracy performance of ANN-LMBOA networks. By raising the Prandtl and Schmidt numbers, solutal, thermal, and diffusional variables, one can reduce the diffusion of mass and heat.

Keywords

• Nanofluid
• Porous medium
• Darcy-forchhiemer
• Bvp4c technique
• Levenberg marquardt
• Neural networks