Nano-bio-film flow of Williamson fluid due to a non-linearly extending/contracting surface with non-uniform physical properties

Abstract

The major goal of this paper is to investigate a conceptual framework for nano-biofilm of Williamson fluid over an enlarging/compressing sheet. The impact of activation energy, magnetic field, and bioconvection are studied. Here, the analysis is carried out with varying physical properties such as viscosity, microorganism diffusivity, and thermal conductivity to be depending upon the concentration of nano-particles. The fluid's changing transport properties, dynamic viscosity, heat conductivity, and nano-particle mass diffusivity are calculated. This work's outcomes have applications in dense thermal transit devices such as heat exchangers, nuclear plants, and electronics. Non-linear systems of partial differential equations are transformed into non-linear fundamental differential equations via a similarity transformation. The shooting approach and RK-4 techniques are used to generate observations. The visual depictions of the impacts of various fluid transport characteristics and distinguishing factors on patterns of velocity, temperature, the concentration of nanoparticles, and motile density. Variable transit parameters , , and enhance dispersions of velocity, temperature, concentration and motile density. As the power law index m goes up, the fluid velocity improves, while the heat, concentration and motile intensity profiles decline. This work is useful in devices of dense thermal transportation such as nuclear plants, electronics, and heat exchangers.