Mathematical analysis for Brownian motion of nonlinear thermal bioconvective stagnation point flow in a nanofluid using DTM and RKF method

Abstract

Abstract 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.