Examining thermophoretic transport in Carreau fluids across vertical cylinders: A local non-similarity approach with ANN based estimates

A computational investigation is carried out for Carreau-type non-Newtonian flows past a vertically aligned cylinder. The rheological behavior of the Carreau fluid is captured through a set of boundary layer equations incorporating buoyancy, magnetic field effects, viscous dissipation and stretching. For accuracy and reliability, the resulting problem is solved using two independent numerical approaches: the shooting method coupled with a fifth-order Runge–Kutta scheme and Newton's method, as well as MATLAB's built-in boundary value solver. Flow and thermal characteristics are modeled using an artificial neural network trained with the Levenberg–Marquardt (LM) algorithm. The reliability of the predictions is verified through multiple validation metrics, and a comparison between the bvp4c scheme and the artificial neural network model reveals remarkable agreement. Results reveal how shear-thinning characteristics and magnetic field intensity jointly influence the momentum and thermal boundary layers. Graphical illustrations provide further insight into the evolving structure of the flow and temperature fields under various operating conditions. With an increasing curvature parameter and thicker momentum, thermal and concentration boundary layers are formed. By increasing the parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> <mml:mo>*</mml:mo> </mml:math> , the thermophoretic diffusion mechanism strengthens leading to a higher thermophoretic velocity. The impact of key physical parameters—including the power-law index, Weissenberg number, magnetic interaction parameter and Eckert number—on the wall shear stress and heat transfer rate is systematically explored.