Narrow Results

The heterogeneous fluid model is expressed for the nanofluid flow to study the significance of the Fourier’s and Fick’s laws. The magnetohydrodynamics couple-stress bioconvective nanofluid flow is considered across an extending surface with the effect of exponential heat source/sink and stratified boundary conditions. The solid nanoparticulates and concentrations of motile microorganisms are added to the nonlinear system of differential equations conveying the non-Newtonian nanoliquid flow model. Moreover, the combined effect of the heat flux and thermal radiation is also evaluated. 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 Levenberg Marquardt Back-propagation optimization algorithm is employed to solve these equations. To authenticate the outcomes, 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 Artificial Neural Network. The accuracy of the model is estimated through numerous statistical tools (histogram, curve fitting, regression measures, and performance plots). The outcomes are presented through the table and figures. It has been noticed that the couple-stress nanofluid flow declines with the influence of magnetic field and mixed convection. The couple-stress nanofluid temperature augments with the enhancement 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${}^{-6}$ that proves the exceptional precision of the results.