Activity of motile microorganism in bioconvective nanofluid flow with Arrhenius activation energy

In this current article, we developed a theoretical model for the bioconvective microbial activities through the nanofluid flow. The appearance of activation energy and Arrhenius function are present in this model. The investigation of motile microorganisms with heat generation effects has not been studied yet to the best of our knowledge. The governing equations consist of the continuity equation, the energy equation, the solutal equation, and the concentration equation of microbes. The system of PDEs contained in the governing equation is transformed into a system of nonlinear ODEs by using suitable similarity transformation, and then solved numerically by applying the spectral quasilinearization method. MATLAB software has been used to plot the figures; residual error for this numerical technique and the effect of several fluid parameters are also been demonstrated graphically. Moreover, the skin friction coefficient, the heat transfer coefficient, the Sherwood number, and the density number of motile microbes are also discussed. It has been found that there is a good agreement between the current results with the previously published works. The microbes’ concentration boundary layer increases with the enhancement of the heat generation parameter. A high rate of chemical reaction parameters of microbes enhances the temperature of the system. In addition, the velocity profile increases with the increment of the bioconvection Schmidt number. The increment of the magnetic parameter from 0.1 to 0.5 reduces the Nusselt number by 28.36 % , but microorganism density increases by 3.53 % . When the bioconvection Brownian motion parameter varies from 0.1 to 1.2 , the Nusselt number almost decreases by 95.99 % , which will be significant for one of the physical interests of the investigation.