Three-dimensional analysis of motile-microorganism and heat transportation of viscoelastic nanofluid with nth order chemical reaction subject to variable thermal conductivity

The most important condition of modern industrial activities is excellent refrigeration performance for conventional buildings. The Buongiorno relation assessment identifies nanofluid's thermal and mass efficiency, which inspires us to specify different properties of random motion and thermophoretic diffusion. Non-Newtonian nanofluids are used in a variety of fields, including thermal exchangers, solar liquid boiler, and heat control in vehicles. Nanoparticles can significantly enhance a fluid's thermal conductivity and heat transfer properties. This makes nanofluids attractive in cooling systems for electronic devices, such as computer chips and LED lights, and in various industrial applications where efficient heat transfer is important. The proposed thermos-electric system depends on nanomaterial heat flow, fractional volume of nanomaterial, density, and motile microorganisms. Because of their numerous applications, ferromagnetic nanoparticles have become extremely popular in biotechnology. Numerous mathematical and technical constraints are considered to generate more useful data. Using the shooting scheme, evaluating numerically by MATLAB function bvp4c to transform expressions. Some observations about the bio-convection procedure its different exclusive characteristics are elaborated in the literature. The graphs show how multiple flows influence non-dimensional quantities. The present theoretical model could be applied to engineering methods, heat transfer improvements, and thermal energy.