Three-dimensional thermodynamic analysis of micropolar hybrid nanofluid stagnation point flow with thermal non-equilibrium phase disparities and grid convergence uncertainty over a rotating stretching disk

This study presents a numerical study of the three-dimensional (3D) optimized non-equilibrium boundary layer flow, heat transfer and irreversibility characteristics of a hybrid nanofluid (MoS 2 -SiO 2 /KO) over a spinning disk under the presence of an inclined magnetic field and microstructural rotational resistance. A powerful shooting optimization method is used to solve the coupled, highly non-linear boundary-value problem with spatial step size ( \(Δ η = 0.01\) ), and far-field edge ( \(η ₘₐₓ = 6.0\) ). By 99.92% the maximum residual errors reach the order of 10 −7 with a strict grid independence validation up to a mesh grid ( \(300 × 300\) ) nodes, which guarantees the numerical convergence of the solution. The computed time step ( \(Δ τ ₘₐₓ \) ) equals \(2.45 × 10⁻⁶\) , which is the absolute convergence tracking below a global tolerance limit of \(1.0 × 10⁻⁷\) . The thermal properties are carefully analyzed with a Non-Equilibrium Two-Temperature Framework that describes the thermal slip gap between the fluid matrix and solid nanoparticle clusters. Increasing the thermal radiation parameter from 0.0 to 1.2 increases thickness of thermal core layer, which leads to a 36.98% increase in the fluid Nusselt number in the hybrid suspension. On the other hand, setting the inter-phase heat transfer coefficient to 1.0 reduces the local convective currents, leading to a decay trend of 11.45% and approaching total temperature equilibrium of the system. The results of volumetric entropy generation analysis reveal that increasing applied magnetics parameter, from 0.0 to 4.0 induces a powerful Lorentz drag that leads to a significant increase in Ohmic dissipation entropy of 64.19% and a significant rise in skin friction. Moreover, a rise in Brinkman number (Br) results in an increase of the fluid friction exergy destruction over the increase in thermal irreversibility, so that the Bejan number decreases smoothly in a completely stable non-negative range i.e. ( \(0 ≤ Be ≤ 1\) ) with the rise in Br.