Rayleigh-Benard convection and sensitivity analysis of magnetized couple stress water conveying bionanofluid flow with thermal diffusivities effect

Bionanofluids containing biological nanoparticles suspended in base fluids exhibit altered dynamics due to coupled effects between the nanoparticles and fluid properties. More efficient cooling can enhance medical technology performance, reduce energy usage, and provide safer, more sustainable healthcare solutions. This work overcomes previous research limitations by elucidating the combined impacts of microorganisms and couple stress properties on the behavior of water-based bionanofluids containing copper nanoparticles, under inclined magnetic fields. Governing equations for momentum, energy, concentration, and microorganisms are transformed into ordinary differential equations (ODEs) via similarity methods. The resulting ODE system is then solved semi-analytically using the Homotopy Analysis Method, revealing distinct profile behaviors. Additionally, quantitative indicators including skin friction for different values of M, λ,β, and Nr increased by 7.19%, 62.81%, 31.27%, and 21.32% respectively. Similarly Nusselt number for different values Qe, Ec, and Df decrease by 3.502 %, 2.5705%, and 2.447% respectively. Furthermore, Sherwood Numbers for different values of Sc, Kc, increased by 16.41%, and 4.133% respectively. Finally, Microorganisms for different values of Lb, Pe, and σ1 increase by 2.934%, 2.61%, and 1.172% respectively.