Effect of Melting Heat and Activation Energy on MHD Williamson Fluid Flow Over Parabolic and Plane Surfaces: A Numerical Approach

The complex relationship between fluid motion and curved surfaces significantly affects flow dynamics, yielding intricate patterns and phenomena. Fluid flow over curved geometries, specifically on parabolic geometries, is a crucial phenomenon in multiple engineering disciplines. Parabolic surfaces, characterized by their continuous curvature, are ubiquitous in nature and industrial applications, ranging from aerodynamic wing designs to hydroelectric power plants and biomedical devices. This study delineates the complex interactions among several critical factors like activation energy and melting heat accounting for supplementary factors such as mixed convection, heat source and Cattaneo-Christov formulation. The primary goal of this research paper is to investigate the combined effects of melting heat, activation energy, and magnetic fields (MHD) on the flow, heat transfer, and mass transfer characteristics of a Williamson non-Newtonian fluid over parabolic and plane surfaces. Solutions are derived numerically by employing Matlab's built-in bvp4c function and illustrated graphically for parabolic and plane geometries. Validation exercises reveal a high degree of consistency between numerical results and published data. Parabolic flow exhibits a rapid temperature escalation compared to plane flow. Parabolic flow demonstrates a pronounced concentration drop than in plane flow. A novel comparative scrutiny is carried out on parabolic and plane surfaces in the context of Williamson fluid. This study delineates the complex interactions among several critical factors like activation energy and melting heat, This research seeks to advance understanding in applications such as materials processing, polymer manufacturing, and energy systems. It is evinced that the parabolic surface demonstrates superior skin friction and heat transmission accompanied by reduced mass transport compared to plane surfaces.