Thermal and mass management of Walter-B nanoliquid with heat radiation and the Cattaneo–Christov double diffusion model incorporating microorganisms: convergence solution for stratified effect

This study examines heat and species-transport phenomena in a Darcy–Forchheimer porous framework that carries a stretching sheet onto which Walter’s-B nanofluid containing gyrotactic microbes is injected. The physical model combines radiative heat transfer, Brownian agitation, thermophoretic drift, chemical kinetics, and the Cattaneo–Christov double-diffusive formalism with thermal, solutal, and bioconvective stratification boundary conditions. After some similarity transformations, the primitive partial differential equations are transformed into a very nonlinear coupled ODE system, which we semi analytically using the homotopy analysis method, and convergence is verified by study of ℏ-curves and residual error tables. The results indicate that the velocity field decreases significantly with an increase of the Forchheimer inertia and the porosity parameter, which both increase the hydraulic resistance of the porous medium. On other hand, Walter’s-B viscoelastic parameter enhances the momentum diffusivity and thus speeds up flow. When thermal radiation, Brownian motion and thermophoresis increase, the temperature profiles widen noticeably; however, thermal stratification has the opposite effect, decreasing the thermal penetration depth by decreasing the wall-to-fluid temperature difference. The concentration distributions of the nanoparticles decrease significantly as the solutal stratification increases or the reaction rates increase—solutal stratification will reduce the driving concentration gradient, and the chemical reaction will consume the diffusing species. The microbial stratification factor and Péclet number are important for controlling bioconvection intensity, and their increase decreases the local population density for motile microorganisms. With the inclusion of wall shear, increments in the Darcy, Forchheimer, and viscoelastic parameters are shown to lead to an increase in the skin-friction coefficient, denoting improved interfacial momentum transfer. The effectiveness of heat transfer (Nusselt number) increases with the intensity of the radiative effects and decreases with the effects of thermophoresis, in which nanoparticles deviate away from the hot surface. Meanwhile, the density number for motile microorganisms increases with the bioconvection Lewis number, highlighting the important role of the diffusivity of microorganisms in the maintenance of the bioconvection flux. In conclusion, the present findings provide a clear understanding of the multi-physical control of heat, mass, and microbe transport in non-Newtonian nanofluidic systems.