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This paper is concerned with the investigation of variable viscosity bioconvection flow of nanofluid containing motile gyrotactic microorganisms over a nonlinear stretching sheet in the presence of nonlinear thermal radiation, chemical reaction, internal heat source, and suction/injection effects. The homotopy analysis method has been developed for solving the governing nonlinear differential equations of the boundary layer flow of nanofluid over a stretching sheet. The scaling group transformation (a special form of Lie group transformation) has been applied to find the similarity variable $\eta $. Figures are drawn by using Mathematica software to analyze the results that correspond to some important physical parameters and bioconvection parameters on velocity, temperature, nanoparticle concentration, and density of gyrotactic microorganisms. It is found that the influence of variable viscosity on velocity profiles showed that there is an increase in the velocity profiles of nanofluid and the reverse effect is observed on its temperature distribution. It is seen that the thermal radiation parameter increases the temperature distribution, whereas it decreases the nanoparticle concentration distribution. It is also found that the inverse Darcy number reduces the velocity profile, whereas it enhances the temperature distribution. This work may find applications in advanced nanomechanical bioconvection energy conversion devices, bio-nanocoolant systems, etc.

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In the present paper, bioconvective stagnation point flow of nanofluid containing gyrotactic microorganisms over a nonlinearly stretching sheet embedded in a porous medium is considered. The scaling group transformation method is introduced to obtain the similarity transformation to convert the governing partial differential equations to a set of ordinary differential equations. The reduced governing nonlinear differential equations are then solved numerically with Runge–Kutta–Fehlberg method. Differential transform method is employed to justify the results obtained by the numerical method. It is found that both the results matched nicely. It is noticed that the density of motile microorganism distribution grows high with an increase in the values of the bioconvection Peclet number. Further, the rate of heat transfer and the rate of mass transfer increase rapidly with an increment in the thermophoresis parameter, heat source parameter, chemical reaction parameter, and Brownian motion parameter, respectively. This work is relevant to engineering and biotechnological applications, such as in the design of bioconjugates and mass transfer enhancement of microfluidics.

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Abstract:We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.