ANN‐Based Validation of Periodic Magnetohydrodynamic Boundary‐Layer Flow of a Third‐Grade Fluid: A Study of Bejan's Flow Visualization

ABSTRACT The authors of this paper study the impact of a wavy or sinusoidal spatially periodic magnetic field on flow of a non‐Newtonian third‐grade fluid from a vertical plate through the application of two different mathematical techniques: the Crank–Nicholson stable time‐marching method and an artificial neural network (ANN). In the current study, a wavy magnetic field is used instead of a steady‐state magnetic field and thus the conducting fluid flowing past the plate will experience a series of push–pull magnetic forces that will greatly affect its velocity and heat transfer. As the current governed equations are complex and coupling nature, a stable time‐marching method (Crank‐Nicolson) has been chosen to find solutions to the equations. The researchers have studied how the wavy magnetic field influences the flow‐related quantities. Graphical representations of the results were obtained through plots of temperature, velocity distributions, and friction factor coefficients. The results indicate that as the third‐grade parameter amplifies, the maximum value of the velocity decreases and the temperature increases. These results are attributed mainly to increased resistance due to the more intense collisional interactions between third‐grade fluid particles. In addition to examining the effects of the Lorentz force, produced by applied magnetic field, on the local skin‐friction coefficients and the local Nusselt numbers, this study also demonstrates how the magnetic field influence in decrease of both parameters. Also, the authors show how the extent to which these parameter change is affected by the strength of the considered magnetic field. The suppression of convective transport by increasing Hartmann number causes the heatlines to drift off the heated plate, and this is a sign of decreased heat transfer at the plate. A substantial deviation of flow variables from the heated wall is observed. An artificial neural network (ANN) model is formed to distinguish the ensuing alterations in the system, that is, a Back Propagation Neural Network (BPNN). Comparing the numerical results with the ANN‐predicted values showed that there was a great degree of correlation between the two. The results reveal that the ANN‐based method is not only valid and efficient but also a convenient tool used to simulate the heat transfer processes and fluid flow over vertical plates in the presence of magnetic fields.