Axisymmetric stagnation-point flow of a fractional Oldroyd-B hybrid nanofluid over a vertical cylinder by improved Buongiorno's model

Abstract

This paper investigated the unsteady axisymmetric stagnation-point flow, heat and mass transfer of Oldroyd-B hybrid nanofluid over a vertical cylinder by using Caputo time fractional derivatives for the first time, with the consideration of second-order velocity slip conditions. Improved Buongiorno's model was adopted to build the governing equations and finite difference combined with L1-algorithm was employed to solve the numerical solutions. Effects of key physical parameters on velocity, heat and mass transfer were presented graphically and discussed in detail. Outcomes show that the fractional derivatives are capable to describe the memory effect and thermoelasticity of viscoelastic nanofluids. Both Brownian motion and thermophoresis, especially Brownian motion, improve the heat transfer on the cylinder wall. In addition, the sensitivity of average Nusselt (or Sherwood) number to velocity fractional derivates α and β rises with increasing α and β, while the sensitivity to temperature fractional derivate γ declines with increasing γ. When γ increases from 0.2 to 0.3, the relative growth rate of average Nusselt number is about 9.26 %. This study provides a reference for exploring the stationary-point flow of fractional order nanofluids on vertical cylinders.