Numerical and Levenberg-Marquardt backpropagation neural networks computation of ternary nanofluid flow across parallel plates with Nield boundary conditions

The impact of the inclined magnetic field toward a flat parallel plate by operating incompressible suspension of three diverse types of oxide nano-sized particles in water-based ternary hybrid nano-liquid is investigated numerically. Flow is theoretically to be unstable squeezing the laminar flow of ternary nanofluid between infinite parallel plates with Nield boundary conditions with the help of neural networks computation taken. The surface is subjected to a steady fully developed free stream velocity with Cattaneo-Christov heat and mass flux used to mathematical model with the governing equations in the form of partial differential equations of flow, and thermal profile, including the boundary conditions. The entailed similarity solution to the problem changed into a system of ordinary differential equations and resolved to utilize RKF 45 with shooting technique. The impact of these processes' sensitivity of the liquid parameterized by different non-dimensional parameters has been discussed on usual profiles along with Sherwood number and Nusselt number with the characteristics with the support of plots and tables. The study reveals that for squeezing parameter (S-1 < 0) velocity profile decays and is enhanced for (S-1 > 0). Increasing the magnetic effect decreases the velocity profile, whereas increasing the inclination angle increases the velocity profile. The developed ANN model was proved to be trustworthy due to its excellent accuracy throughout the training, validation, and testing processes.

Automated summary

The numerical investigation focuses on the impact of an inclined magnetic field on a flat parallel plate using an incompressible suspension of three types of oxide nano-sized particles in a water-based ternary hybrid nano-liquid. Neural networks computation is used to analyze the theoretical instability of the laminar flow and the Nield boundary conditions. The governing equations in the form of partial differential equations are transformed into a system of ordinary differential equations and solved using the RKF 45 method with shooting technique. The study shows that the velocity profile decreases with a negative squeezing parameter (S-1 < 0) and increases with a positive squeezing parameter (S-1 > 0), while the magnetic effect decreases the velocity profile and the inclination angle increases it. The developed ANN model demonstrates excellent accuracy throughout the training, validation, and testing processes.