A proceeding to numerical study of mathematical model of bioconvective Maxwell nanofluid flow through a porous stretching surface with nield/convective boundary constraints

Abstract

Abstract Nanofluids become significant in the mass and heat transfer models, especially in engineering problems. Current proceedings focused on the bioconvective Maxwell nanofluid flow passing through the permeable stretchable sheet contingent to nield boundary conditions involving effects of activation energy and thermal radiation. Various physical quantities are involved in this mechanism like magnetic field, thermophoresis, and Brownian motion. The main objective of the study is to report the heat and mass transport in the existence of motile microorganisms. In a mathematical perspective, this structured physical model is going to govern with the help of partial differential equations (PDEs). These governing PDEs are then converted into dimensionless ordinary differential equations form by utilizing appropriate similarity transformations. For numerical results, the shooting technique with ‘bvp4c’ built-in package of MATLAB was implemented. Computed results are then visualized graphically and discussed effects of involving physical variables on the nano-fluid flow profiles are comprehensively. From results, it has been concluded that the fluid flow velocity, temperature, concentration, and microorganism density profiles show escalation on increasing the numeric values of porosity, thermophoresis, buoyancy ratio, bioconvection Rayleigh, Peclet number parameters and decrement reported due to increasing the counts of Prandtl number, magnetic field, radiation, Brownian motion, Lewis number as evident from figures. The numerical outcomes observed by fixing the physical parameters as $$0.1 < \lambda < 3.0$$ 0.1 < λ < 3.0 , $$0.1 < M < 1.5$$ 0.1 < M < 1.5 , $$0.1 < Nr < 6.0$$ 0.1 < N r < 6.0 , $$0.1 < Rb < 1.5$$ 0.1 < R b < 1.5 , $$0.1 < Nb < 6.0$$ 0.1 < N b < 6.0 , $$0.1 < Nt < 1.0$$ 0.1 < N t < 1.0 , $$2.0 < \Pr < 2.9$$ 2.0 < Pr < 2.9 , $$0.1 < Rd < 0.4$$ 0.1 < R d < 0.4 . Magnetic field and Brownian motion create retardation impact due to the liquid momentum. In tables, the numerical values of Skin friction, Nusselt number, Sherwood number, and microorganisms density number are presented and also comparison table of our computed results and already published results is included for the validation.