Heat transfer characteristics of transient nanofluid flow with time-fractional derivative under buoyancy convection using a fast ADI scheme

This study introduces an efficient algorithm designed to investigate fluid flow behavior and heat transfer characteristics in a fractional-order buoyancy-driven system. Additionally, the study explores the influence of fractional parameters, buoyancy-driven convection, and other key physical factors on both steady-state and transient flow conditions, providing deeper insights into how fractional nanofluid dynamics evolve over time. The fast algorithm, integrated with the Alternating Direction Implicit (ADI) approach, is employed to solve the nanofluid system of equations, accounting for the appropriate initial and boundary conditions. The fractional derivatives are represented using the Caputo derivative. The behavior of fluid flow and thermal distribution under various parameters was examined at different time intervals. The numerical findings indicate that nanofluid flow and isotherms achieve initial development faster when the fractional parameter is lower. At the initial time t=0.001, both nanofluids show a higher heat transfer rate with a larger fractional parameter. As time progresses, however, a lower fractional parameter results in a slightly increased heat transfer rate. It is noticed that the lower fractional parameter leads to attaining a steady state sooner. With an increase in thermal radiation, there is a notable rise in the heat transfer rate and an intensification in the magnitude of streamlines and isotherms.