Darcy-Forchheimer nanofluid flow and heat transfer with convective boundary conditions: Insights from differential transform method

Abstract

In this work, we use the sophisticated differential transform method (DTM) to derive solutions to the complicated momentum, heat, and mass transfer equations that characterize Darcy-Forchheimer nanofluid flow over a stretching surface with convective boundary conditions. The investigation includes the nuanced effects of heat sources and chemical reactions and also addresses the synergistic effects of Brownian motion and thermophoresis. By applying an appropriate similarity transformation, the governing partial differential equations (PDEs) are gracefully transformed into an elegant system of nonlinear coupled ordinary differential equations (ODEs), a problem that is ingeniously solved using DTM. The veracity of our results is underpinned by a careful validation against previous scientific work that illuminates the path to scientific clarity. As the mathematical tapestry unfolds, the enchanting interplay of physical parameters on fluid dynamics is revealed, manifesting in visually captivating graphs and illuminating tables. Of particular note is the transformative influence of the magnetic parameter, which stages a ballet in which an increase in skin friction and the Nusselt number causes a diminuendo. Meanwhile, the solutal concentration decreases as the Brownian motion, Lewis number, and chemical reaction parameters increase, while it waltzes in reverse harmony with the thermophoresis parameter. Beyond equations and diagrams, this investigation promises to cast a luminous beacon on practical realms, imparting invaluable insights for industries ensconced in the realm of heat exchangers, the alchemy of lubricant refining processes, and the grand tapestry of scientific and engineering domains.