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The goal of the current study is to theoretically evaluate the heat and mass transfer behavior of magnetohydrodynamic Casson and Williamson fluids as they pass through a stretched sheet with Brownian and thermophoresis effects. The evolution of high-density heat devices necessitates efficient thermal transportation. For these requirements, the concept of nanofluid plays an active role. This article describes the effects of Cattaneo–Christov. This study introduces new concepts such as motile microorganism bioconvection, non-Fourier heat flux, and activation energy. A Runge–Kutta-based shooting procedure is used to solve the problem. The effects of the relevant parameters on velocity, thermal, concentration, and motile microorganisms are depicted graphically. The computed reduced Nusselt, Sherwood, and motile density numbers are displayed in tables in this study. When compared to the Williamson fluid, the thermal and concentration fields of the Casson fluid are heavily influenced by the parameters.