In this paper, the bioconvective nanofluid flow in a porous square cavity containing gyrotactic microorganisms in the presence of heat generation/absorption is investigated. The bioconvection flow in porous medium is formulated based on Darcy model of Boussinesq approximation. Galerkin finite elements method is employed to solve the governing equations. The numerical results are obtained and discussed the effect of parameters such as Rayleigh number Ra, bioconvection number Rayleigh number Rb, Peclet number Pe, Lewis number Le, Brownian motion Nb, Thermophoresis Nt, Schmidt number Sc, Prandtl number Pr, heat generation/absorption Q and buoyancy ratio Nr. Also, the average Sherwood number, average Nusselt number and average density number are discussed. The present solutions are validated with existing studies under limited cases. It is found that Peclet number and buoyancy ratio show a significant increasing effect on the streamlines, isotherms, isoconcentrations of nanoparticles and microorganisms. The heat generation/absorption reverses the patterns of the flow, temperature distribution and isoconcentrations of nanoparticles and microorganisms.

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The current article investigates the effect of inclination angle on thermo-bioconvection within the porous-square shaped cavity filled with gyrotactic type microorganisms and nanofluid. The Darcy law with Boussinesq estimation is used for the momentum equation in porous media. The transformed governing equations are solved by Galerkin’s method of finite elements. The effect of inclination angle in the square cavity is interpreted by varying the angle from [Formula: see text] to [Formula: see text]. The effect of inclination on different quantities, for instance, Rayleigh number, bioconvective Rayleigh number, Peclet number, Brownian motion, heat source/sink, and ratio of buoyancy, is discussed. Further, the mean quantities of Nusselt number [Formula: see text], Sherwood number [Formula: see text], and density number [Formula: see text] are analyzed at vertical walls. A quantitative outcome of the study is that the maximum values of [Formula: see text], [Formula: see text], and [Formula: see text] are found for the angle [Formula: see text] and [Formula: see text].

This research explored the influences of entropy generation on bioconvected nanoliquid flow through the porous cavity filled with nanofluid and gyrotactic microbes. The porosity term in the momentum equation is summarized by the implementation of Darcy’s formula through Boussinesq estimation. The novelty of this study is to investigate entropy generation in cavity by augmenting the convection generated by the phenomenon of Brownian motion, thermophoresis of nanofluid flow and the bioconvection due to swimming of microorganisms. The governing partial differential equations (PDEs) are highly nonlinear and are nondimensionalized through the suitable similarity constraints. The transformed PDEs are tackled via implementation of finite difference method (FDM). The reaction of entropy generation and Bejan number against various quantities like bioconvection Rayleigh number ([Formula: see text]–100), Rayleigh number ([Formula: see text]–100), Peclet number ([Formula: see text]–0.9) and ratio of buoyancy ([Formula: see text]–1) are reported and visualized. The entropies by the liquid friction, heat transportation, mass transmission and microorganisms are focused. Upsurge in Nr (0.3–0.5) and Pe (0.1–0.15) accelerated the maximum of entropy due to microorganism by 7% and 44%, respectively. Here, an increment in Ra, Rb, Pe and Nr affects the distribution pattern of total entropies and Bejan number consistently. The higher Lewis number caused a decrement in the total entropy by liquid friction.