Computation of stagnation coating flow of electro-conductive ternary Williamson hybrid [Formula: see text] nanofluid with a Cattaneo–Christov heat flux model and magnetic induction

Modern smart coating systems are increasingly exploiting functional materials which combine multiple features including rheology, electromagnetic properties and nanotechnological capabilities and provide a range of advantages in diverse operations including medical, energy and transport designs (aerospace, marine, automotive). The simulation of the industrial synthesis of these multi-faceted coatings (including stagnation flow deposition processes) requires advanced mathematical models which can address multiple effects simultaneously. Inspired by these requests, this study investigates the interconnected magnetohydrodynamic non-Newtonian movement and thermal transfer in the Hiemenz plane's stagnation flow. Additionally, it explores the application of a transverse static magnetic field to a ternary hybrid nanofluid coating through theoretical and numerical analysis. The base fluid (polymeric) considered is engine-oil (EO) doped with graphene [Formula: see text] , gold [Formula: see text] and Cobalt oxide [Formula: see text] nanoparticles. The model includes the integration of non-linear radiation, heat source, convective wall heating, and magnetic induction effects. For non-Newtonian characteristics, the Williamson model is utilized, while the Rosseland diffusion flux model is used for radiative transfer. Additionally, a non-Fourier Cattaneo–Christov heat flux model is utilized to include thermal relaxation effects. The governing partial differential conservation equations for mass, momentum, energy and magnetic induction are rendered into a system of coupled self-similar and non-linear ordinary differential equations (ODEs) with boundary restrictions using appropriate scaling transformations. The dimensionless boundary value problem that arises is solved using the bvp4c built-in function in MATLAB software, which employs the fourth-order Runge–Kutta (RK-4) method. An extensive examination is conducted to evaluate the impact of essential control parameters on the velocity [Formula: see text] , induced magnetic field stream function gradient [Formula: see text] and temperature [Formula: see text] is conducted. The relative performance of ternary, hybrid binary and unitary nanofluids for all transport characteristics is evaluated. The inclusion of verification of the MATLAB solutions with prior studies is incorporated. Fluid velocity is observed to be minimized for the ternary [Formula: see text] –[Formula: see text] –[Formula: see text] nanofluid whereas the velocity is maximized for the unitary cobalt oxide [Formula: see text] nanofluid with increasing magnetic parameter ([Formula: see text] Temperatures are elevated with increment in thermal radiation parameter (Rd). Streamlines are strongly modified in local regions with greater viscoelasticity i.e. higher Weissenberg number [Formula: see text] . Dimensionless skin friction is significantly greater for the ternary hybrid [Formula: see text] –[Formula: see text] –[Formula: see text] nanofluid compared with binary hybrid or unitary nanofluid cases.