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Abstract Microorganism movement may boost the convective transfer of heat by stirring the fluid to encourage mixing. Engineers may improve heat dissipation and maintain temperatures in electrical devices, engines, and industrial machinery by varying microbe proportion and quality. This research aims to gain insight into the rheological effects of an Eyring–Powell nanofluid and the movement of gyrotactic microorganisms on the surface of the Riga plate. The propagation of linear and non‐linear mixed‐convection nanofluid through a Riga plate is also studied. The primary goal of this work is to accelerate the heat transfer rate of nanofluid. The efficiency of heat transport and the ability to postpone boundary layer separation are both influenced by the magnetohydrodynamic force produced by the Riga plate. Regulating problem is converted into dimensionless form using suitable transformations, and the resulting equations are then resolved numerically using the MATLAB program “bvp4c”. The simulations are run for various variables, such as Prandtl numbers, mixed convection parameters, Hartmann numbers, Reynold numbers, Peclet numbers, and Lewis numbers. The outcomes are presented both tabularly and visually. This evaluation shows an increment in the Eyring–Powell fluid and mixed convection parameters, which causes the velocity profiles to rise. However, the reverse is true for an escalation in the magnetic parameters. In addition, the activation energy parameter increases the concentration profile. On the other hand, the Eyring–Powell fluid parameter causes the thermal field to contract. The skin friction at is 45.13% and decreased by 24.07% when for the linear case, while for the quadratic case, it is 43.69% at and deceased 25.58% when . A comparison against an earlier study is also performed to determine the accuracy of the proposed model. An outstanding agreement between current findings and formerly existing solutions shows the legitimacy of the present discoveries.
Awan et al. (Sat,) studied this question.