A pulsatile movement of an annular Ree-Eyring nanofluid with gyrotactic motile microorganisms and time-varying conditions

This work aims to investigate the Ree-Erying (RE) pulsation of an incompressible nanofluid inside a cylindrical annulus containing motile microorganisms that fluctuate in response to the buoyancy-driven force. Additionally, the impacts of the temperature, heat source, thermal radiation, and chemical reactions are reflected. The combinations of temperature and concentration on the boundary conditions (BCs) that change with time are applied. The motivation behind this study is concerned to many applications in the human body, particularly the pulsating movement in the veins, arteries, and digestive tracts, in pathological conditions. The required physical functions are split into two parts; the steady as well as the periodic ones. The Homotopy perturbation method (HPM) is analytically employed to analyze the system. It is concluded that the flow decays with the rise of the accumulation of nanoparticles and microbes as noted from the effect of buoyancy terms on the velocity. It is found also that the nanomaterials are concentrated with the rise of the Brownian coefficient and nanomaterial oscillating amplitude. Furthermore, Microbes' existence decreases with the augmentation of the Lewis, bio-conductivity, and Peclet measures. This investigation has produced important conclusions that may be helpful in many medical and industrial applications that concern nanofluids and microorganisms fluctuation.