Temperature Distribution in the Flow of a Viscous Incompressible Non-Newtonian Williamson Nanofluid Saturated by Gyrotactic Microorganisms

The heat and mass transfer in magnetized non-Newtonian Williamson nanofluid flow, saturated by gyrotactic microorganisms due to a stretched sheet, is debated here. The rough sheet is subjected to uniform heat flux, and its velocity is proportional to its distance from the slit. Nanofluid viscosity and thermal conductivity are temperature-dependent, but microbe diffusivity and Brownian motion are concentration-dependent. Through similarity transformation, the system of modeled equations is reduced to dimensionless differential equations. We employed the shooting approach in conjunction with the Runge–Kutta scheme to obtain a solution for the physical model. For various combinations of the controlling parameters, some numerical results are found. When the generated results are compared to the existing literature, the highest settlement is found. According to numerical results, the skin-friction coefficient rises as the magnetic field and thermal conductivity parameters rise, while the opposite tendency is observed for both the slip velocity and viscosity parameters.