Unsteady Falkner-Skan flow of fractional Maxwell fluid towards a stretched wedge with buoyancy effects

Abstract The majority of researches for Falkner-Skan flow are dependent on the classical constitutive relations of viscoelastic fluids. Fractional Maxwell fluid model is introduced to depict Falkner-Skan flow innovatively in the paper. Moreover, the momentum equation studying the effects of buoyancy force is established. Analogy to constitutive relevance for fractional Maxwell fluid, fractional derivative is brought in Fourier's law and Fick's law. It is worth mentioning that heat source and chemical reaction are discussed. Finite difference method integrated with L1-algorithm is utilized to address the fractional governing equations, whose convergence is verified by constructing an example with accurate solution. Furthermore, the influences of pertinent physical parameters are analyzed diagrammatically. A fascinating phenomenon is discovered that all the velocity profiles initially rise to a maximal value due to the impact of buoyancy force and then decrease to the free flow velocity. Besides, the temperature and concentration distributions first increase slightly while decline significantly, which indicates the thermal relaxation and mass relaxation characteristic of Maxwell fluid.