Thermodynamic optimization of magnetic hyperthermia via elasticity tuning in non-Newtonian blood flow

The Weissenberg number ( We ) quantifies the relative dominance of elastic over viscous forces in tangent‐hyperbolic fluids such as blood and is classically divided into three regimes—low to moderate elasticity ( We ≈ 0.01–0.1), transitional elasticity ( We ≈ 0.1–1.0), and high elasticity ( We ≈ 1.0–2.0). A unified analysis reveals that average velocity decreases by 0.17 %, 1.82 %, and 2.27 % across these regimes (from 0.0968 to 0.0927), skin friction intensifies by 0.23 %, 2.43 %, and 3.10 % (from –1.1616 to –1.0957), Nusselt number rises by 0.06 %–0.86 % (from –5.6063 to –5.5192), entropy‐generation rates grow by 0.14 %–2.08 % (from 0.0233 to 0.0242), and temperature distributions shift by less than 0.05 %. Progressive viscoelasticity restructures velocity profiles via boundary‐layer thinning and 0.17–2.27 % velocity reduction; coupled radiation–magnetic effects leave temperature invariant (<0.05 % variation); skin friction and Nusselt number respond through amplified shear and thermal gradients (increasing by 0.23–3.10 % and 0.06–0.86 %, respectively); entropy generation rises by 0.14–2.08 % with viscous dissipation dominating beyond We ≈ 1.0; the critical We for irreversibility shift is ≈1.0; and entropy minimization in magnetic hyperthermia is achieved in the low elasticity regime ( We ≤ 0.1). The novelty of the governing equations necessitates validation via residual error assessment of the computational solutions.