One-argument Lie scaling and sensitivity analysis of UCM liquid flow over a vertical wedge using response surface method

Wedge geometries are widely used in aerodynamics, heat exchangers, solar collectors, and chemical processing equipment. This study focuses on the combined impacts of thermal radiation, latent heat of fusion, Hiemenz flow, Joule heating, and electro-magnetohydrodynamic (EMHD) flows on the natural convection flow over a vertical wedge, which has not been examined previously. Due to the wide range of engineering applications involving wedge geometries, it is important to consider and discuss the effects of different thermophysical properties on the flow and heat transfer behavior. We examined upper-convected Maxwell (UCM) viscoelastic liquid flow in a permeable medium with phase change (melting effects). A one-argument scaling method has been introduced for transforming the developed equations of the liquid flow model into non-linear ordinary differential equations (ODEs). The numerical solution of the ODEs with boundary conditions is explored using the BVP4C technique, and the results are shown in graphs and analyzed. The velocity of the fluid increases with the magnetic field, porosity, electric field, Deborah number, suction, melting heat, and Hiemenz flow, while it decreases with higher Prandtl number. Similarly, the temperature distribution is enhanced by porosity, Prandtl number, melting heat, Hiemenz flow, as well as magnetic and electric field effects. The sensitivity analysis reveals that the melting heat parameter significantly enhances the Nusselt number (≈ 18.98%), establishing it as the most dominant factor in thermal energy transmission, while suction contributes moderately with a stable variation of ≈ 19.57%. In contrast, the Hiemenz parameter exhibits a negligible negative influence (nearly 200 times smaller), confirming its minimal role in affecting heat transfer performance.