Numerical modeling of fractional viscoelastic non-Newtonian fluids over a backward facing step – Buoyancy driven flow and heat transfer. (1st March 2021) - Moosavi, Rouhollah; Moltafet, Reza; Lin, Cheng-Xian; Abel Chuang, Po-Ya
Highlights: Study of unsteady convection of fractional Maxwell fluid over a backward-facing step. The velocity and temperature layers increase with fractional derivative parameter α . The friction coefficient rises with increasing fractional derivative parameters α a n d β . The boundary layer of the Maxwell fluid is thicker than the Newtonian fluid. The Nusselt number of the Maxwell fluid is greater than the Newtonian fluid. Abstract: The unsteady flow and natural convection heat transfer of fractional Maxwell viscoelastic fluid over sudden expansion geometry such as vertical backward facing step is studied. The time–space fractional derivatives are calculated based on Caputo fractional derivative. The nonlinear governing equations are solved using finite difference method mixed with a L-1 algorithm. The step, upstream and downstream walls were set at a constant temperature. The range of step length is 0 ≤ S ≤ 0.5 and dimensionless temperature is 0.25 ≤ θ w ≤ 1 . The effects of velocity and temperature fractional derivatives ( α and β ) and various physical parameters, such as step length, dimensionless temperature, on Nusselt number, friction coefficient, profile of velocity and temperature, are investigated numerically. The results reveal that the fractional derivative parameters, the variation of wall temperature and step length have significant effects on the rate of heat transfer, the friction coefficient, the velocity and temperature of backward facing step. The average of Nusselt number variation increases with increasing of β and decreases of α parameters. The results show that the velocity and thermal boundary layer of the non-Newtonian fluid (ordinary Maxwell) is higher than Newtonian fluid. Also, the Nusselt number for the ordinary Maxwell fluid flow is greater than the Newtonian fluid flow. With the increase of the step length of backward facing step, the average Nusselt number, friction coefficient, velocity boundary layer, and temperature boundary layer increases. The obtained results can improve significantly the performance of the systems design that operate with the non-Newtonian fluids.