A nanofluid is a fluid containing particles with less than a nanometer diameter. These particles are referred to as nanoparticles dispersed in a base fluid. The viscoelastic Oldroyd-B nanofluid flow past a vertical stretching sheet with swimming gyrotactic microorganisms is investigated in this present analysis. Lorentz force characteristics are considered because the magnetic field is applied normally to the sheet. Viscous dissipation, Joule heating, and chemical reaction are combined inside the system. The resulting equations are converted into the dimensionless form using similar improvement and then explained by the bvp4c procedure. The effect of associated parameters on velocity, temperature, motile density profiles, and nanoparticle volume fraction has been reflected through physical justification over tables and graphs. Statistical analysis is applied to disclose the association of parameters with the physical characters. The temperature rises due to managing relaxing time in the current investigation. When the chemical destructive response rate increases, a constructive chemical reaction increases species concentration considerably; however, the species concentration drops when the reaction rate increases. The current and potential applications of bioconvection renewed the drive for theoretical research on synthesis and process control in biofuel cells and bioreactors.

An analysis is presented to study the unsteady, two-dimensional nanofluid flow of heat and mass transfer with vanishing nanoparticles flux at the wall in the presence of heat generation or absorption with viscous dissipation. In this analysis, it is assumed as nanoparticle flux is zero on the boundaries. The highly nonlinear differential equations governing the boundary layer flow, heat and mass transfer are numerically solved by spectral relaxation method and validated with MATLAB solver bvp4c. The results are obtained by some values of the physical parameters, namely, the Brownian motion parameter, the thermophoresis parameter, unsteadiness parameter, Eckert number, heat generation or absorption parameter, Prandtl number and Lewis number. Physical features for all relevant parameters on the dimensionless velocity, temperature, nanoparticles volume fraction and heat and mass transfer rates are analysed and discussed. The thermal boundary layer thickness increases with an increase in the thermophoretic parameter. The nanoparticle volume fraction profile significantly descends from the surface with an increase in Brownian motion parameter.