Research On Oblique Stagnation-Point Flow Of Unsteady Fractional Maxwell Fluid And Oldroyd-B Fluid

The oblique stagnation-point flow of viscoelastic fluid exists widely in practical production and life,such as polymer extrusion process,the manufacture of plastic film,blood flow at the junction of anterior cerebral artery and anterior communication artery,etc.The unsteady oblique stagnation-point flow of viscoelastic fluids is studied based on the fractional constitutive models of Maxwell fluids and Oldroyd-B fluids.The effects of dimensionless parameters on velocity,temperature and concentration are analyzed,which provides theoretical guidance on practical problems.Firstly,unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid are discussed.The fractional material derivative is introduced to the constitutive equation of Maxwell fluid.A method to determine the pressure term is proposed.Analogy to the constitutive equation of fractional Maxwell fluid,the modified Fourier’s law is proposed to describe the heat transfer characteristics of fluid.The numerical solutions are acquired by virtue of the finite difference method combined with L-1 algorithm.It turns out to be convergent through constructing numerical example.Results show that both velocity and temperature decrease as the order of the fractional derivative increases.The temperature tends to increase first and then decrease near the plate due to the boundary conditions of convective heat transfer.Secondly,unsteady oblique stagnation-point flow,heat and mass transfer of fractional Oldroyd-B fluid are studied.The upper convective fractional derivative is introduced into the constitutive equation of Oldroyd-B fluid.The pressure term is analyzed according to the idea of the first part.Furthermore,fractional derivative is introduced to Cattaneo-Christov double diffusion model to depict heat and mass transfer.The numerical solutions are obtained by using finite difference-spectral method,which provides a new idea for solving the problem of oblique stagnation-point flow.And the convergence of discrete scheme is verified.Results show that velocity,temperature and concentration distribution appear intersection with the variation of fractional derivative respectively,reflecting that the model of fractional viscoelastic fluids can demonstrate the memory characteristics of fluids.The velocity is accelerated obviously with the enlargement of retardation time,which embodies retardation characteristics of Oldroyd-B fluid.Finally,unsteady stagnation-point flow of fractional Burgers fluid is researched based on the finite difference-spectral method.The space terms of governing equation are discretized by spectral method,finite difference method combined with L-1 algorithm and L-2 algorithm separately discretizes time terms of governing equation.Different discrete schemes are given according to the range of fractional derivative.The finite difference-spectral method and the finite difference method are used to obtain the numerical solution respectively in the section of verifying the convergence of discrete formats.By calculating the maximum error between the numerical solution and the analytical solution,it can be seen that the finite difference-spectral method has a higher convergence accuracy than the finite difference method.Results show that the velocity distribution appears intersection at different fractional derivative respectively,which reflects the memory properties of fluids.The smaller Reynolds number intensifies fluid viscosity,which speeds up fluid velocity.