This study analyses the two-dimensional (2D) magnetohydrodynamics (MHD) boundary layer flow, heat/mass transfer, and bioconvection of a Sutterby tetra-hybrid nanofluid over a nonlinear porous stretching sheet with motile microorganisms. Copper, silver, ferrosoferric oxide, and zinc nanoparticles are dispersed in ethylene glycol, with effective properties evaluated through a sequential mixture rule, and rheology are captured by the Sutterby relation with Deborah's $ \Gamma $ and the power-law $ n $. Thermal radiation, Brownian motion, thermophoresis, chemical reaction, and motile microorganisms are included. Similarity reduces the problem to a ninth-order ordinary differential equation system, solved by collocation and validated against an independent method and three exact solutions, improving on Crane's benchmark to within $ 3.8\times10^{-10} $. Magnetic and porosity parameters increase the skin friction and decrease the Nusselt number; the Sutterby parameters soften the velocity gradient yet, once wall stress correction included, increase the reported skin friction. Increasing tetra-hybrid loading increases both the friction and Nusselt number by enhancing the conductivity. Radiation and thermophoresis alter the concentration field, and bioconvection Schmidt and Péclet numbers raise the density of microorganisms. The results are relevant to bio-nanofluid thermal systems such as microfluidic cooling and bioconvective coating.
Citation: R. T. Matoog, R. Sarathy, R. Revathi, Sultan Hassan Hakmi. MHD flow and thermal enhancement of Sutterby tetra-hybrid nanofluids over a nonlinear porous stretching sheet with motile microorganisms attributable to bioconvection effect[J]. AIMS Mathematics, 2026, 11(10): 35756-35794. doi: 10.3934/math.20261386
This study analyses the two-dimensional (2D) magnetohydrodynamics (MHD) boundary layer flow, heat/mass transfer, and bioconvection of a Sutterby tetra-hybrid nanofluid over a nonlinear porous stretching sheet with motile microorganisms. Copper, silver, ferrosoferric oxide, and zinc nanoparticles are dispersed in ethylene glycol, with effective properties evaluated through a sequential mixture rule, and rheology are captured by the Sutterby relation with Deborah's $ \Gamma $ and the power-law $ n $. Thermal radiation, Brownian motion, thermophoresis, chemical reaction, and motile microorganisms are included. Similarity reduces the problem to a ninth-order ordinary differential equation system, solved by collocation and validated against an independent method and three exact solutions, improving on Crane's benchmark to within $ 3.8\times10^{-10} $. Magnetic and porosity parameters increase the skin friction and decrease the Nusselt number; the Sutterby parameters soften the velocity gradient yet, once wall stress correction included, increase the reported skin friction. Increasing tetra-hybrid loading increases both the friction and Nusselt number by enhancing the conductivity. Radiation and thermophoresis alter the concentration field, and bioconvection Schmidt and Péclet numbers raise the density of microorganisms. The results are relevant to bio-nanofluid thermal systems such as microfluidic cooling and bioconvective coating.
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Figures(17) / Tables(5)
R. T. Matoog, R. Sarathy, R. Revathi, Sultan Hassan Hakmi. MHD flow and thermal enhancement of Sutterby tetra-hybrid nanofluids over a nonlinear porous stretching sheet with motile microorganisms attributable to bioconvection effect[J]. AIMS Mathematics, 2026, 11(10): 35756-35794. doi: 10.3934/math.20261386
Physical model and coordinate system for the MHD Sutterby tetra-hybrid nanofluid flow over a nonlinear porous stretching sheet with motile microorganisms
Flowchart of the residual-controlled $\texttt{bvp4c}$/collocation numerical solution procedure used to solve the governing boundary-value problem
Effect of the magnetic field parameter $ M $ on (a) velocity $ f'(\eta) $ and (b) temperature $ \theta(\eta) $
Effect of the porosity parameter $ \varepsilon $ on (a) velocity $ f'(\eta) $ and (b) temperature $ \theta(\eta) $
Effect of the Sutterby fluid parameter $ \Gamma $ on the velocity $ f'(\eta) $
Effect of the Sutterby power-law index $ n $ on the velocity $ f'(\eta) $
Effect of equal tetra-hybrid nanoparticle loading $ \varphi_i $ ($ i = 1 $–$ 4 $) on (a) velocity $ f'(\eta) $ and (b) temperature $ \theta(\eta) $
Effect of the thermal radiation parameter $ Nr $ on temperature $ \theta(\eta) $
Effect of the Brownian motion parameter $ Nb $ on (a) temperature $ \theta(\eta) $ and (b) concentration $ \phi(\eta) $, plotted to $ \eta = 20 $, over which every curve is confirmed to converge fully to its far-field value (Table 2)
Effect of the thermophoresis parameter $ Nt $ on (a) temperature $ \theta(\eta) $ and (b) concentration $ \phi(\eta) $, plotted to $ \eta = 20 $, over which every curve is confirmed to converge fully to its far-field value (Table 2)
Effect of the Schmidt number $ Sc $ on the concentration $ \phi(\eta) $, plotted to $ \eta = 20 $, over which every curve converges fully to zero
Effect of the chemical reaction parameter $ Kr $ on the concentration $ \phi(\eta) $, plotted to $ \eta = 20 $, over which every curve converges fully to zero
Effect of the bioconvection Schmidt number $ Sb $ on motile microorganism density $ \chi(\eta) $, plotted to $ \eta = 20 $, over which every curve converges fully to zero
Effect of the microorganism concentration difference parameter $ G $ on motile microorganism density $ \chi(\eta) $, plotted to $ \eta = 20 $, over which every curve converges fully to zero
Physical plane streamlines colored by magnitude of velocity for $ M = 0 $, $ 2 $, and $ 8 $ (base case values of all other parameters)
Bar chart of (a) the skin friction coefficient $ Re_x^{1/2}C_f $ and (b) Nusselt number $ Re_x^{-1/2}Nu_x $ for a varying magnetic field parameter $ M $
Bar chart of (a) the skin friction coefficient $ Re_x^{1/2}C_f $ and (b) Nusselt number $ Re_x^{-1/2}Nu_x $ for a varying tetra-hybrid nanoparticle loading $ \varphi_i $ ($ i = 1 $–$ 4 $, equal loading)
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