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    Radiation and gyrotactic microorganisms in Walter-B nanofluid flow over a stretching sheet
    (Elsevier BV, 2025-09) Muhammad Shaheen; Hakeem Ullah; Mehreen Fiza; Aasim Ullah Jan; Ali Akgül; A.S. Hendy; Samira Elaissi; Ilyas Khan; Mohsen Bakhori; N.F.M. Noor
    The present study investigates the flow characteristics of both homogeneous and heterogeneous Walter-B nanofluids induced by a stretching sheet. Special attention is given to the effects of melting and magnetic fields on the flow behavior. The distribution of motile microorganisms is modeled using a microbial conservation equation, incorporating key parameters such as the Lewis number, Peclet number, and the microorganism difference parameter. The influence of thermal radiation and the heterogeneous reaction parameter is also considered. To facilitate the analysis, the governing partial differential equations are transformed into a set of ordinary differential equations using similarity transformations. A convergent series solution is then obtained through the application of the Homotopy Analysis Method (HAM). The study further explores the effects of various physical parameters, including the Prandtl number, magnetic field intensity, radiation, thermophoresis, Brownian motion, bioconvection, Peclet number, and the microorganism difference parameter. Results indicate that the velocity field decreases with an increase in the magnetic parameter, while the temperature profile diminishes with higher values of the radiation parameter. Furthermore, the concentration of microorganisms is observed to decline with increasing Lewis number.