Influence of Motile Microorganisms on MHD Squeezing Flow of Ree–Eyring Nanofluid with Hall and Heat Generation Effects

Abstract The study addresses the flow dynamics of an incompressible non‐Newtonian Ree‐Eyring nanofluid. It explores an innovative interaction of electromagnetic squeezing flow with microorganisms, including Hall current effects and nonlinear heat generation. The flow traverses a permeable region within a channel formed by two parallel plates, influenced by microorganisms, Hall currents, nonlinear heat sources, and a constant response rate. The thermal transfer due to Ohmic dissipation is also examined in the flow. The examination of the density of microorganisms and dispersion of nanoparticles under electromagnetic squeezing advances the knowledge of linked magneto‐bio‐convective nanofluid dynamics. The controlling equations are restructured as nonlinear ordinary differential equations by suitable similarity transformations. The theoretical analysis addresses the ordinary differential equations governing equations of motion via the Homotopy perturbation method. It is discovered that the middle of the channel is a vital point in fluid flow, and the impact of any parameter is reflected there, but the impact is similar near the edges. The heat broadcast gets better when all pertinent parameters increase, except for Hall parameter. Nanomaterials are condensed with the growth of most of their related parameters. Microbes almost diminish in density and decrease in existence with augmentation of their related parameters.