Study of bioconvective couple-stress nanofluid flow subject to stratified conditions by using numerical and Levenberg Marquardt back-propagation algorithms

Abstract

The heterogeneous fluid model is expressed for the nanofluid flow to study the consequence of Fourier's and Fick's laws. The magnetohydrodynamics couple-stress bioconvective nanofluid flow is considered across an extending surface with the impact of heat source/sink and stratified boundary conditions. The solid nano particulates and concentrations of motile microorganisms are added to the nonlinear system of differential equations conveying the non-Newtonian nanoliquid flow model. The similarity transformations are employed to transfigure the system of partial differential equations into the lowest order of ordinary differential equations. The artificial neural network (ANN) based on the LMBP (Levenberg Marquardt Back-propagation) algorithm is employed to solve these equations. The dataset is formed using the MATLAB package bvp4c. The dataset is created for diverse circumstances of flow factors, as well as validation and testing of the ANN. The accuracy of the problem is assessed through numerous statistical results (histogram, curve fitting, regression measures, and performance plots). The relative percent error between present outcomes and published studies is 0.00486 % at Pr = 2.0 (Prandtl number), where it gradually decreases up to 0.00069 % at Pr = 7.0. The outcomes are presented through the table and figures. It has been noticed that the Couple-stress nanofluid (CSNF) flow drops with the effect of the magnetic field. The CSNF temperature augments with the improvement of the thermophoresis effect, buoyancy ratio factor, Rayleigh number, and thermal radiation. Moreover, the concentration curve lessens under the impact of the Lewis number while enriched with the outcome of the concentration stratification parameter. The absolute error of reference and targeted date is attained within 10⁻³–10⁻⁶ which proves the exceptional precision of the results.