Transient free convective flow of viscoelastic nanofluids governed by fractional integrodifferential equations under Newtonian heating and thermal radiation

Abstract

The transient free convective flow of incompressible nanofluids past a vertical infinite plate with mass diffusion and Newtonian heating is investigated under the influence of thermal radiation. The fractional integrodifferential governing equations are first formulated from the generalized Maxwell constitutive relationship with dual fractional-order parameters. Some important physical quantities relevant to engineering, including the modified skin friction factor, Nusselt number, and Sherwood number, which are suitable for nanofluids, are also deduced. Then the dimensionless boundary layer equations of momentum, energy and concentration subject to the appropriate initial and boundary constraints, are solved numerically using the L1 formula and weighted-shifted Grünwald–Letnikov scheme. Some numerical illustrations are provided to demonstrate the impact of the key variables on the momentum, heat and mass transport properties for different nanofluids. The simulation findings reveal that both increasing the velocity fractional-order derivative parameter and decreasing the fractional-order integral parameter lead to a thicker momentum boundary layer. The inclusion of nanoparticles enhances fluid heat transfer performance. This study offers significant insight into the applicability of the fractional-order integrodifferential equations for characterizing the momentum, heat and mass transport properties of nanofluids.