Application of the homotopy perturbation method to the Jeffery–Hamel flow of nanofluids between two non-parallel planar walls

• A modified Homotopy Perturbation Method (HPM) combined with Chebyshev Npseudospectral techniques is proposed to solve nonlinear MHD Jeffery–Hamel nanofluid flows. • The effects of Hartmann number (Ha), Reynolds number (Re), nanoparticle volume fraction (ϕ), and nanoparticle type (Al₂O₃, TiO₂, Cu) on velocity and shear profiles are investigated. • Analytical HPM solutions show close agreement with numerical Boundary Value Problem (BVP) results using RKF45, validating the robustness of the method. • Magnetic fields (higher Ha) stabilize flow and reduce shear, while higher Re enhances inertial effects and may induce flow reversal. • Nanoparticle concentration accelerates velocity decay and alters shear recovery, with Cu producing the strongest inertial effects and TiO₂ yielding the most stable profiles. • The proposed method demonstrates improved efficiency and convergence compared to standard HPM, offering a reliable tool for nonlinear MHD nanofluid modeling. This work applies a modified Homotopy Perturbation Method (HPM) to analyze magnetohydrodynamic (MHD) Jeffery–Hamel nanofluid flow between two non-parallel planar walls. The governing nonlinear boundary value problem incorporates the effects of Hartmann number (Ha), Reynolds number (Re), nanoparticle volume fraction (ϕ), and nanoparticle type (Al₂O₃, TiO₂, Cu) on velocity and shear profiles. The proposed modification integrates the standard HPM with Chebyshev pseudospectral techniques to improve computational efficiency and convergence. Analytical solutions obtained via HPM are compared with numerical results from the Boundary Value Problem (BVP) approach using the RKF45 method in Maple. The results show that increasing Ha stabilizes the flow, reduces shear, and delays flow reversal due to Lorentz forces; increasing Re amplifies inertial effects, steepens gradients, and may cause overshoot or reversal; higher ϕ enhances momentum diffusion, accelerates velocity decay, and alters shear recovery; and nanoparticle material significantly affects flow behavior, with Cu showing the strongest inertial and reversal effects, and TiO₂ producing the most stable profiles. Across all cases, HPM results closely match BVP solutions, with minor deviations in high-gradient regions, confirming the accuracy and robustness of the proposed method for nonlinear MHD nanofluid modeling. Key parameters, including nanoparticle concentration, Reynolds number, Hartmann number, and channel angle, are analyzed for their effects on velocity, temperature, skin friction, and Nusselt number. Results indicate that increasing nanoparticles improves heat transfer but may reduce flow velocity, while higher Hartmann numbers suppress the velocity field, providing practical insights for thermal performance optimization.