Heat and mass transfer in MHD-UCM nanofluid flow past a porous nonlinear stretching sheet with chemical reaction and bioconvection: a dual-method approach

Abstract The study aims to scrutinize the magneto-hydrodynamic (MHD) heat and mass transfer properties of an upper-convected Maxwell (UCM) nanofluid over a nonlinearly stretched porous sheet with gyrotactic microorganisms via numerical and semi-numerical approaches. The UCM nanofluid model encompasses the effects of thermal stratification, heat absorption, chemotaxis movement of microorganisms, velocity ratio and chemical reaction parameters. The prominent mathematical equations of continuity, momentum, energy, nanoparticle concentration and microorganism density are transformed into a self-similar system of coupled nonlinear ordinary differential equations (ODEs) by appropriate similarity variables. These equations were solved through numerical and semi-numerical techniques viz, Keller-box and Haar wavelet collocation methods. The attained results were successfully compared with the prevailing literature and are exemplified through graphs and tables. The exploration revealed that nanofluid velocity decelerates due to the rise in magnetic field, porosity and Deborah number because stronger magnetic forces, porous medium resistance and greater fluid elasticity together oppose the fluid motion. Thermal stratification noticeably reduces the thermal boundary layer thickness due to the lower temperature difference between surface and the ambient fluid. Additionally, motility increases with an increase in the Prandtl number, thermophoresis, and Peclet number, as reduced thermal diffusion and enhanced particle transport strengthen the microorganism accumulation near the surface. It confirms that the presence of gyro-tactic microorganisms enhances nanofluid stability by preventing nanoparticle agglomeration.