non-equilibrium heat revolution bvph 2.0 unlocks al₂o₃-mos₂/blood hybrid nanofluid dynamics under mhd porous constraints

Hybrid nanofluids (hnfs) comprising al2o3-mos2 nanofillers in blood exhibit high thermal conductivity, which is beneficial for magnetic drug targeting and for porous heat exchangers. the non-newtonian williamson rheology under mhd (magnetohydrodynamics), local thermal non-equilibrium (ltne), and porous media remains unaddressed. this paper focuses on the 2d steady williamson nanofluid flow over a permeable stretching sheet. it aims to quantify the effects of mhd, porosity, viscous dissipation, and interphase heat transfer on the velocity and temperature profiles and the engineering coefficients. the boundary-layer pdes (partial differential equations) resulting from the application of similarity transformations are reduced to nonlinear ordinary differential equations (odes) that are solved semi-analytically using the homotopy analysis method (ham) in bvph 2.0/mathematica (with a convergence set to 10-5). the ltne (local thermal non-equilibrium) models the fluid and solid under isothermal conditions and accounts for separable darcy resistance and lorentz forces. an increasing williamson parameter (wp) and the mhd (magnetohydrodynamics) parameter (m) are shown to thicken the velocity boundary layer through lorentz drag and shear-thinning. an increase in the eckert number (ec) and the heat-generation parameter (q) elevates the temperature due to viscous heating, whereas a higher interphase coefficient yields a more uniform temperature profile. the porosity-modified conductivity ratio (γ) favours solid conduction. an increase in skin friction of 125% (m: 0.01→1.2) and nusselt number (nu) increase of 50% (ε: 0.5→0.8) establishes the superiority of hnfs. bvph 2.0 converges 20 times faster than the fdm (finite-difference method). the findings are beneficial for magnetic hyperthermia applications (tumour ablation at 42-45°c) and mhd porous exchangers by providing optimal design directions.