Numerical study of nano-biofilm stagnation flow from a nonlinear stretching/shrinking surface with variable nanofluid and bioconvection transport properties

Abstract

Abstract A mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno’s two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter $$({c}_{2})$$ ( c 2 ) , thermal conductivity parameter (c 4 ), nano-particle mass diffusivity (c 6 ), micro-organism species diffusivity (c 8 ), thermophoresis parameter $$(Nt)$$ ( N t ) , Brownian motion parameter $$(Nb)$$ ( N b ) , Lewis number $$(Le)$$ ( L e ) , bioconvection Schmidt number $$(Sc)$$ ( S c ) , bioconvection constant (σ) and bioconvection Péclet number $$(Pe)$$ ( P e ) . Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter ( $${\mathrm{c}}_{2})$$ c 2 ) whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter ( $${\mathrm{c}}_{4})$$ c 4 ) whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter ( $${c}_{6}$$ c 6 ) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent ( $$m),$$ m ) , skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter ( $${\mathrm{c}}_{8}$$ c 8 ) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes.