Analysis of viscoelastic non-Newtonian fluid over a vertical forward-facing step using the Maxwell fractional model

In this study, unsteady of the fluid flow and heat transfer of natural convection of viscoelastic non-Newtonian fluid have been investigated with the Maxwell fractional model on a vertical forward-facing step. Fractional derivatives are used to the fluid properties more accurate calculations. The fractional time derivative of the Caputo method and the fractional derivative of the velocity and temperature of the viscoelastic fluid are calculated using the finite difference numerical method by combining the L-1 algorithm. The effect of various factors such as parameters of velocity and temperature fraction derivative (α and β), buoyancy force, step length, and Prandtl number on velocity profile, the temperature of the viscoelastic fluid, Nusselt number and friction coefficient on a vertical forward-facing step are investigated. Numerical results show that with increasing α, β and step length, the coefficient of friction increases and also decreases with increasing Prandtl. With increasing α, the average Nusselt value decreases, and with increasing β, Prandtl, and step length increases. It is also observed that the thickness of the momentum and thermal boundary layer in viscoelastic fluids is higher than that of the Newtonian fluid boundary layer.