Research On Unsteady Stagnation-point Flow Of Fractional Viscoelastic Fluid

The stagnation point flow is widely applied in industry,such as glass blowing,extrusion production and continuous casting processes,among which stagnation point flow of viscoelastic fluid has attracted much attention.This paper studies the unsteady stagnation point flow of fractional Maxwell fluids and fractional Oldroyd-B fluids.The effects of dimensionless parameters on flow and heat transfer are analyzed,which can provide theoretical guidance for practical applications.Firstly,unsteady stagnation point flow and heat transfer of fractional Maxwell fluid are investigated.The fractional derivative of velocity is introduced into the momentum equation through the fractional Maxwell constitutive equation.Based on the characteristics of the pressure distribution in the boundary layer,the characteristics of stagnation point flow is introduced in the momentum equation,and it is introduced in the energy equation through the viscous dissipation.The generalized Fourier's law is considered in the energy equation,and the convective heat transfer boundary condition has made consequential amendments.A finite difference scheme for solving the model is established with the L1 algorithm,and a numerical example is constructed to verify the convergence of the scheme.The numerical results are used to analyze the effects of stagnation point parameter,fractional derivative parameter,and momentum Fourier numbers on velocity and temperature.The results show that the higher the momentum Fourier number is,the lower velocities are,but the case with temperature is opposite.All the temperature profiles increase at first and then decreases,which demonstrates that the fractional derivative in the generalized Fourier's law can reflect the memory characteristics of the fluid,that is,the Maxwell fluid has obvious thermal retardation.Secondly,unsteady stagnation point flow of fractional Oldroyd-B fluid towards a stretching plate is studied.Similar to the study in the first part,the fractional Oldroyd-B constitutive relationship is used to describe the relationship between fluid stress and strain.The influences of the stagnation parameter,the magnetic parameter and other parameter on the velocity are discussed.It is found that the velocity rises as stagnation parameter increases and magnetic field hinders fluid movement.Thirdly,the three-dimensional flow of fractional Maxwell fluid over a bidirectional stretching plate is discussed.The fractional Fourier's law and Fick's law are considered.The stretching speed of the stretching plate is not only power law dependent on time,but also a power exponential function of the distance in each spatial direction.The result showsthat the smaller the velocity fractional parameter is,the thinner the velocity boundary layer is when the power values in each space direction are same.Conversely,the greater the velocity fractional parameter is,the velocity reduces firstly then increases.Finally,the fractional differential is used to study the diffusion of volatile organic compounds(VOCs)in dry building materials.The influence of pore structure on VOCs emission in dry building material is considered.The spatial fractional diffusion model is established and the areal porosity is introduced in the convection mass transfer equation.By comparing with the integer order derivative diffusion model,it is found that the spatial fractional diffusion model can more accurately describe the diffusion process of VOCs.Taking the particleboard as an example,the parameters of the experimental data are estimated,and the formaldehyde release in the particleboard is predicted using the spatial fractional diffusion model.