Thermo-magnetic transport analysis of Williamson penta-hybrid nanofluid flow over a thin moving needle: Implications for targeted drug delivery

This study presents a numerical analysis of steady magnetohydrodynamic Williamson penta-hybrid nanofluid flow over a thin heated moving needle, incorporating thermal radiation, second-order slip, internal heat generation, and an inclined magnetic field. The governing equations are reduced via similarity transformations and solved using MATLAB’s bvp4c solver. The results are validated against benchmark data, showing excellent agreement. The findings indicate that penta-hybrid nanofluids enhance heat transfer, yielding a modest increase in the Nusselt number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>≈</mml:mo> <mml:mn>1.6</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> ), while mass transfer decreases ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>≈</mml:mo> <mml:mn>12</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> ) for nanoparticle-scale diffusion ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mi>c</mml:mi> <mml:mo>=</mml:mo> <mml:mn>100</mml:mn> </mml:math> ) due to boundary-layer thickening. For lower Schmidt numbers ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mi>c</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>10</mml:mn> </mml:math> ), representing small-molecule drugs, diffusion improves slightly. These results provide useful insights for magnetically assisted micro-injection and thermo-regulated targeted drug-delivery systems, highlighting a controllable trade-off between heat and mass transfer.