A WILLIAMSON NANOFLUID WITH MOTILE MICROORGANISMS ACROSS A VERTICAL EXPONENTIALLY STRETCHING POROUS SHEET WITH VARYING THERMAL CHARACTERISTICS

The present work demonstrates a boundary layer movement of an incompressible non-Newtonian Williamson nanoliquid. The boundary layer is around an exponentially stretching permeable vertical surface. Moving motile microorganisms are implicated in the movement throughout a permeable medium considering modified Darcy law. The buoyancy-driven flow is presumed, where the density is expressed as being multiplied by gravity and chosen as a linear function of heat, nanoparticle, and microorganism concentrations. Analogous to the exponentially stretching sheet, an exponential variable magnetic strength is taken normal to the surface. Variable thermal conductivity and mass diffusivity are considered together with chemical reactions. The motivation for this study arises from the involvement of microorganisms in the flow and the contribution of its density equation with the velocity, temperature, and nanoparticles system of equations with suitable boundary restrictions. The fundamental governing scheme of nonlinear partial differential equations (PDEs) is transferred to ordinary ones (ODEs) by employing convenient similarity transforms. These equations are analyzed by the homotopy perturbation method (HPM). Therefore, a major objective graphical formation of the distributions is concluded to recognize the impacts of the produced nondimensional physical factors. Some important physiognomies are concluded from the results. The nanoparticle distribution enhances most of the effective parameters and in turn improves heat transmission, which is a good finding that can be useful in several applications. Microorganisms tend to collect with the growth of the Lewis number and infinity value, whereas its condensation damps with the rise of the bioconductivity and the Peclet number. Those results can be useful in identifying factors that help to get rid of microbes, viruses, and harmful bacteria from surfaces.