Electromagnetohydrodynamic flow of 3D Williamson nanofluid with bio-convection and motile microorganisms over an exponentially stretching sheet

This paper presents a novel model for the steady three-dimensional electromagnetohydrodynamic (EMHD) convective flow of Williamson fluid embedded with colloidal gold nanoparticles over an exponentially stretching surface. The flow is endorsed by factors such as thermal and soluble stratification, the motility of microorganisms, and the application of the Cattaneo-Christov heat and mass flux model. Transformer oil is considered as a base fluid. Gold nanoparticles, characterized by their uniform size and shape, are rapidly gaining traction in various fields, including electronics, photodynamic therapy, drug delivery, sensors, probes, catalysis, and diagnostics. To analyze the system, we utilize MATLAB’s bvp4c scheme to tackle the reduced dimensionless nonlinear ordinary differential equations. Detailed graphs are used to show how different physical parameters affect the flow behavior. Our findings are compared with existing literature, demonstrating the effectiveness of our approach. The results reveal that the heat transfer rate in the nanofluid is substantially higher than that of the conventional base fluid, highlighting the promising role of gold nanoparticles in enhancing thermal performance in fluid dynamics. The velocity rises while dominating electric parameters and drops with increasing values of the Weissenberg number (We) and magnetic parameter (M). The temperature declines with cumulative We, Prandtl number (Pr), and Deborah number De 1 . Meanwhile increases with increasing ϕ, Eckert number (Ec), magnetic parameter (M), stratification parameter, thermophoretic number (Nt), buoyancy number (Nb), and Schmidt number (Sc). concentration shrinkages with increasing De 2 , Schmidt number (Sc), heat generation parameters, and thermophoretic number (Nt). The motile density declines with increasing Schmidt number (Sc) and Peclet number (Pe), and shows quickening fluctuations with respect to the bio-convection Lewis number (Lb).