Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating

Abstract Nanofluids have many applications in industries as well as engineering such as biomedicine, manufacturing, and electronics. Nanofluid is used for improvement of thermal and mass transmission. Based on the aforementioned applications, in the present study, a two-dimensional Maxwell nanofluid with thermal radiation effect on the existence of motile microorganisms over a vertically stretchable surface is explored. The consequence of heat absorption, the efficiency of heat flux in a porous medium, viscous dissipations, and Joule heating impacts are considered. The Brownian and thermophoretic diffusion effects have been evaluated. In addition, the binary chemical reaction is taken into account to evaluate the magnetohydrodynamics (MHD) mixed convection flow. Graphene nanoparticles are suspended in so-called engine oil (base fluid). The proposed liquid model depends on the governing nonlinear equations of velocity, temperature, the concentration of nanoparticles, and motile gyrotactic microorganisms. In order to transform highly nonlinear partial differential equations into nonlinear ordinary differential equations, an appropriate similarity transformation is exploited. For the solution of the present study, the homotopy analysis method-technique in Mathematica-12 is used. The fluctuation of velocity, temperature, concentration, and gyrotactic microorganisms’ characteristics for numerous flow parameters is discussed in detail. Some important fallouts of the existing study are that the Maxwell liquid parameter, Eckert number, and magnetic parameter lessen the nanoliquid velocity. But the fluid temperature becomes higher for growing estimates of the Brownian motion and thermophoretic factors. The radiation and chemical reaction parameters have declining impacts on the solutal profile. The motile microorganism profile shows a decrement in bioconvection Lewis and Rayleigh numbers. The nanofluid thermal profile is improved but the nanofluid velocity declined through the augmentation of volume fraction. Also, the coefficient of skin friction and Nusselt number are obtained versus various flow parameters.