The distinguishing thermophysical features of nanofluids make them possibly advantageous in enhancing transfer of heat. The applications of nanofluids in industrial cooling, cooling tower detection, imaging, microelectronic cooling, crossbreed motor proficiency, transparent sunscreen, crack-resistant paint, nuclear reactor cooling, thermal transport, enhanced oil recovery, and architecture have diversified extensively in recent years. Scientific research has shown an enormous spike in fascination with non-Newtonian nanofluids in the past few decades. The stress in non-Newtonian fluids varies nonlinearly with the rate of deformation. These fluids are used in material processing, bioengineering, polymeric fluids, oil reservoir design, and the chemical and nuclear industries. There have been several non-Newtonian models presented forth. The Williamson fluid model is one example of such a model that has a shear-thinning behavior. The current article explanate analysis of (3D) Williamson fluid flow considering various physical features which plays vital role to raise the heat transportation rate. Through transformations procedure the governing physical problem is simplified and then solved via bvp4c in MATLAB. Acquired data are tabulated and graphically presented, and the impacts of relevant parameters on concentration-microorganisms and temperature have been examined numerically. According to the accomplishments, the concentration profile is anticipated to decline as the stretching rate parameter and Brownian motion parameter values grow. By boosting the magnetic parameter, the microorganism profile advances, but the bioconvection Peclet number reveals an opposite tendency.
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