Heat transfer analysis for magnetohydrodynamic peristalsis of Reiner–Philippoff fluid: Application of an artificial neural network

Abstract

Present communication explores a novel application of the computational intelligence technique, namely, the Levenberg–Marquardt scheme under a Backpropagated Neural Network (LM-BNN) to solve the mathematical model for the magnetohydrodynamic peristaltic transport of Reiner–Philippoff (R–Ph) pseudoplastic fluid considering the influences of Ohmic heating, mixed convection, and viscous dissipation through a symmetric channel. The R–Ph fluid model is used in this investigation to elucidate the non-Newtonian behavior of the fluid under consideration. The Reiner–Philippoff fluid model delineates the intricate relationship between stress and deformation rate within the fluid. There are a few studies available on the peristaltic transport of the Reiner–Philippoff fluid that do not incorporate Joule heating, mixed convection, and magnetic field effects. Therefore, a novel mathematical model is developed to employ an artificial neural network technique with a different approach that has not been examined before. The governing equations of the problem are simplified using long wavelength and low Reynolds number approximations, and the resulting system is numerically solved using the BVP4c scheme in MATLAB based on the shooting algorithm. Furthermore, a dataset is constructed through the BVP4c technique for the proposed LM-BNN, considering eight scenarios of peristaltic motion of the Reiner–Philippoff fluid model by varying the Bingham number, the Brinkman number, the Grashof number, the R–Ph fluid parameter, and the Hartmann number. The numerical dataset is divided into 15% for testing, 15% for training, and 70% for validation, which are utilized in LM-BNN to analyze the numerical solutions and Levenberg–Marquardt neural networks (LM-NNs) predicted results. The consistency and effectiveness of LM-BNN are validated through regression analysis, stresses at the wall, error histogram, correlation index, heat transfer, and mean squared error based fitness curves, which vary from 10−3→10−11. Variations in several flow parameters affecting temperature and velocity profiles are explained physically through graphs. Additionally, an analysis of heat transfer and stresses at the wall, including absolute errors, is provided through tables. The outcomes reveal that the improving Grashof number and the Hartmann number tend to increase the temperature profile. Tabular results indicate that rates of heat transfer improve when assigning higher values to the Hartmann number, the Brinkman number, and the Grashof number, whereas stresses at the wall decrease for the Reiner–Philippoff fluid parameter and the Bingham number. The error analysis of numerical simulations is a valuable step in determining whether the data obtained are reliable and accurate. In terms of absolute error, the disagreement between numerical solutions and those predicted by LM-NNs is approximately 10−5→10−11. It is clear from this error analysis that LM-NNs predicted results are consistent and reliable.