Significance of Cattaneo-Christov heat flux and bioconvection in magnetized Jeffrey nanofluid inside an extendable cylinder: Advanced in cooling system

• Investigated Jeffrey nanofluid flow with Cattaneo–Christov heat flux over a stretchable cylinder. • Explored effects of Brownian motion, thermophoresis, and buoyancy forces on heat and mass transfer. • Bioconvection of motile microorganisms analyzed for enhanced mixing and transport stability. • Numerical simulations validated with published results using MATLAB bvp4c solver. Owing to the exceptional thermal properties of non-Newtonian nanofluids, nanomaterials have reported widespread use in numerous fields such as mechanical engineering, cooling technologies, solar energy systems and industrial processes. This work aims to scrutinize the thermal behavior of Jeffrey nanofluids under the impact of bioconvection caused by gyrotactic microorganisms, with specific attention on the flow over a elongating cylinder. Non-Fourier heat conduction is modeled using the Cattaneo–Christov formulation instead of Fourier’s law. Appropriate similarity functions are applied to renovate the governing equations into transformed ordinary differential equations. Numerical simulations are carried out using bvp4c solver via MATLAB, and the outcomes are compared with published studies to authenticate accuracy. Graphical illustrations are used to estimate the inspiration of key fluid parameters such as magnetic parameter 0.2 ≤ M ≤ 2.2 , curvature parameter 0 ≤ γ ≤ 0.8 , Jeffrey fluid 0.5 ≤ β ≤ 2.5 , Lewis number 1.2 ≤ L e ≤ 2.0, buoyancy ratio parameter 0.5 ≤ N r ≤ 2.5 , thermophoresis 0.1 ≤ N t ≤ 1.0 and bioconvective Lewis number 0.2 ≤ L b ≤ 1.0 . It is witnessed that the velocity distribution rises with the curvature parameter and decreases with the Jeffrey, buoyancy ratio parameter and magnetic parameters. The thermal profile drops with growing thermal relaxation parameters, while it rises with both the magnetic parameter M and thermophoresis parameter N t . The concentration and density profiles reduce with improving values of the Lewis number L e and bioconvective Lewis number L b , respectively.