Lewis number

Quantum mechanics

Magnetic field

Turbulence

Sherwood number

Nusselt number

Heat transfer

Statistics

Magnetohydrodynamics

Materials science

Brownian motion

Reynolds number

Plasma

Classical mechanics

Thermophoresis

Mass transfer

Physics

Mathematics

Flow (mathematics)

Magnetohydrodynamic drive

Environmental science

Nanofluid

Mechanics

Alexandria Engineering Journal

The main purpose of the current study is to invetigate the influence of Brownian motion and thermophoresis diffusion in non-Newtonian Williamson fluid flow through exponentially stretching sheet with the effects of thermal radiation and the bioconvection of microorganisms. For this purpose, similarity functions are involved to transmute partial differential equations to corresponding ordinary differential equations. Then Runge–Kutta method with shooting technique is hired to evaluate the desired findings with utilization of MATLAB script. The fluid velocity becomes slow against strength of magnetic parameter and it boosts with mixed convection. The temperature rises with parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruence’s.

Impact of activation energy and MHD on Williamson fluid flow in the presence of bioconvection