Study On Flow, Heat And Mass Transfer Of Fractional Viscoelastic Fluid Due To An Accelerating Plate

Viscoelastic fluids are widely applied in food processing,biomedicine and energy engineering.The existing research shows that the fractional derivative constitutive model is more consistent with the actual situation than the integer derivative constitutive model,and can better describe the creep,relaxation and other complex rheological behavior of viscoelastic fluid.In this paper the flow,heat transfer and mass transfer model based on fractional derivative is established for Maxwell fluid and Burgers fluid.A finite difference scheme is established based on numerical algorithm is established for solving the model,and whose convergence is confirmed by an example.The influence of the parameters on the flow,heat transfer and mass transfer of the fractional Maxwell fluid and the fractional Burgers fluid are obtained.The first part studies the flow and heat transfer of fractional Burgers fluid due to a periodic oscillating plate with the effects of periodic heating plate.Meanwhile the first order velocity slip and the second order velocity slip are considered,and the fluid model based on fractional derivative is established.A numerical difference scheme based on G1 algorithm for solving the control equations is established,and whose convergence is confirmed by a numerical example.The effects of fractional derivative,the Prandt number,the oscillation angle frequency and other parameters on the velocity and temperature of the fluid are discussed.The second part studies the flow and heat transfer of the fractional Maxwell fluid due to a power function accelerating plate.Considering the first order velocity slip and the convective heat transfer boundary condition,the fractional derivative is introduced into the energy equation by the viscous dissipation term.The flow and heat transfer model is formulated with multi-term time fractional derivatives.A finite difference scheme is established based on L1-algorithm,whose convergence is confirmed by constructing an example.The effects of fractional derivative,the first order velocity slip parameter,the Nusselt number,Reynolds number and other parameters on the flow and heat transfer of the fluid are analyzed.The third part studies the flow,heat transfer and mass transfer of three-dimensional fractional Maxwell fluid due to an exponential function accelerating plate with the effects of exponential heating plate and the first order chemical reaction.Meanwhile the magnetic field is taken into consideration.The model of fluid based on the fractional Fourier' law and fractional Fick' law is established.The numerical solutions of velocity,temperature and concentration are obtained by using fractional finite difference method.The effects of Prandtl number,magnetic field parameter and first order chemical reaction parameter on velocity,temperature and concentration are explored.