Convergence and Residual Error Analysis of Unsteady MHD Stagnation Flow Over a Cylindrical Surface With Streamline and Isotherm Visualization

ABSTRACT Melting phenomena are important in geothermal heat exchangers, magmatic crystallization, and future thermal energy storage systems. This study provides a detailed numerical study of the heat and mass transfer behavior of unsteady MHD Cross nanofluid flow over a stretching melting cylinder in a Darcy–Forchheimer porous medium. The transport model includes the effects of viscous dissipation and thermal radiation in the energy equation, and effects of activation energy, Brownian motion, thermophoresis, and chemically reactive species in the mass transport equations. Appropriate similarity transformations are used to transform the governing nonlinear partial differential equations into a system of coupled nonlinear ordinary differential equations. The resulting boundary value problem is then solved by the Parametric Continuation Method (PCM), with very strict convergence criteria. Grid‐autonomous solutions are confirmed by comprehensive grid independence testing with absolute residual errors below an ultra‐low operating floor of 10 −7 . The absolute percent error for code validation showed a very low error of 0.008123% at a Weissenberg number ( We = 0.5) against the literature. The flow field topologies in graphical form show that the Lorentz drag force significantly slows the flow and brings the stagnation streamline fields into close contact with the cylinder surface. However, the melting process is a localized fluid injection process that enlarges the thermal boundary layer, resulting in an outward swelling of the tracking isothermal layer, which is noticeable. A quantitative evaluation in tabular form shows that the local energy transmission rate can be improved up to 51.1556%, 21.5731%, and 19.5265% by systematically tuning the Prandtl number from 6.0 to 7.0, the thermophoresis factor from 0.3 to 0.7, and the Brownian diffusion factor from 0.3 to 0.7, respectively. Such broad information can provide actionable data for modeling, managing, and designing industrial thermal storage systems optimally for controlling complex non‐Newtonian transport phenomena.