Dynamics of Oldroyd-B fluid with fractional derivative: A computational analysis

Non-Newtonian fluids have become increasingly popular over the years in various engineering fields. One form of non-Newtonian fluid is generalized Oldroyd-B fluid, which may be used to imitate the behavior of various dilute polymeric liquids. There is very little literature on the solution of this model, especially in two dimensions. Therefore, this study investigates the flow of a generalized Oldroyd-B fluid over a horizontal plate under the influence of a magnetic field. Velocity and temperature profiles are examined considering Newtonian heating, magnetic field effects, and viscous dissipation. A robust numerical framework is employed using the Crank–Nicolson method in conjunction with the L1 approximation for the Caputo derivative. The results reveal that the fluid velocity increases with increasing relaxation time but decreases with higher retardation time, magnetic parameter, and fractional order, indicating more pronounced damping in fractional and magnetized regimes. Furthermore, temperature significantly intensifies due to Newtonian heating and viscous dissipation. The Nusselt number rises with increasing relaxation time and retardation time, reflecting enhanced thermal transfer associated with both extended stress retention and delayed strain development.