The study of magnetohydrodynamic (MHD) flows involving nanofluids has gained important attention due to its relevance in bioengineering, MHD power generation, and thermomedical treatment systems. In particular, the use of titanium dioxide ( \({\text{TiO}}_{2}\) ) dispersed in blood, which forms a biologically compatible nanofluid, has revealed great potential in enhancing thermal conductivity and enabling targeted drug delivery. This study investigates the combined effects of dissipative radiative heating, temperature slip condition, and thermodynamic irreversibility in the magnetohydrodynamic (MHD) flow of titanium dioxide ( \({\text{TiO}}_{2}\) ) nanofluid, with particular focus on the influence of curvature-induced geometric factors. This study explores the thermodynamic behavior of bio-nanofluid flows containing nanoparticles of various geometrical shapes, including bricks, cylinders, and platelets. To ensure accurate modeling of the system, the Hamilton–Crosser model is utilized to characterize the effective thermal conductivity of the nanofluid, and the governing equations are solved using the finite element method. The results show that entropy generation increases significantly with Brinkman number. A stronger magnetic field induces reverse flow near the tube walls and increases the fluid temperature. Thermal slip enhances heat distribution and raises the temperature field.
