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Abstract The addition of nanoparticles in the base fluid increases the thermal conductivity of the fluid but the stability of the fluid gets affected due to the presence of nanoparticles in the base fluid. The addition of motile microorganisms in the nanofluid increases the stability of the nanofluid by enhancing thermal conductivity as well as mass transport. In this perspective, the current investigation deals with the study of the behavior of microorganisms in bioconvection over the fluid variables in the non-Darcy background. A two-dimensional Prandtl-nanofluid moving along an inclined stretching flat surface subject to inlet and outlet rate of flow to the surface under the action magnetic drag force normal to the surface. The non-linear partial differential equations are transmuted to ODEs through appropriate similarity transformations. The MATLAB inbuilt bvp4c solver has been employed to generate the solution of the transformed ODEs. The stability of the finite difference scheme is demonstrated by a stability test, and the influence of various parameters on the nanofluid velocity, thermal as well as concentration, and density of motile microorganisms is depicted using graphs for each of them. Additionally, interested physical quantities, shearing stresses, rate of thermal diffusion, rate of mass diffusion, and rate of motile microorganism at the surface, have been plotted by varying the controlling parameters. Growth in the shear stress as well as the rate of thermal diffusion has been detected for the increasing values of δ and β . However, the Sherwood number decays for augmented values of δ . The findings could be utilized to increase the thermal efficiency of heat exchangers in order to maintain thermal balance management in small heat-density equipment and gadgets, as well as the thermal efficiency of microbial fuel cells, enzyme biosensors, and microfluidics devices. [ABSTRACT FROM AUTHOR]