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The current work examines the heat and mass transfer phenomenon for time-dependent magnetohydrodynamic (MHD) flow of Williamson nanofluid in the presence of a motile gyrotactic microorganism. The energy equation is remodeled by interpolating radiation effects. The flow is actuated by a wedge which is assumed to be porous. The physical formulation for both static and moving are taken into account. Various physical and geometrical conditions have been included to yield more effective results. The original flow equations are converted into ordinary differential equations by using similarity functions. The numerical solution for these transmuted equations has been established by using the shooting technique. Various aspects of involved physical quantities like velocity, temperature, nanoparticle concentration, motile microorganism density, wall shear stress, effective local Nusselt number, and motile organism density number are discussed and sketched in view of different emerging parameters. The bioconvection induced by the microorganisms stabilized the nanoparticles, which resulted in efficient thermal distribution. A convincible accuracy of achieved results has been reported when compared with existing literature. The present theoretical computation may be beneficial in manufacturing processes, the enhancement of transport of energy, and heat resources.

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