Research On Flow And Heat Transfer Of Fractional Viscoelastic Fluid

The study of fractional viscoelastic fluid flow and heat transfer has provided theoretical guidance for the rational characterization of complex fluid constitutive relations,improved production and transport efficiency.In this paper,the flow and heat transfer of the fractional viscoelastic fluid due to an accelerated plate and driven by the pressure gradient in a rectangular pipe are investigated,respectively.The contents of the study are as follows:1)The flow and heat transfer of incompressible generalized burgers' magnetohydrodynamic over an exponential accelerating plate is studied.The fractional constitutive equation of Burgers' fluid is introduced into the energy equation by considering the effect of viscous dissipation.The improved implicit finite difference method and the G1 algorithm are used to solve the equations.The numerical solutions of velocity,temperature and shear stress are obtained,and a numerical example is constructed to analyze the error of the numerical method.The effects of relaxation time,retardation time,slip parameters and the order of fractional derivative on the flow,temperature and shear stress are discussed.2)The two-dimensional flow model of fractional Maxwell fluid driven by variable pressure gradient in a rectangular pipe is established.For the partial differential equation with fractional derivative orders distributed in the interval(0,2),the analytical solution of the velocity is derived by applying the method of fractional separation variable.The numerical solutions are obtained by using fractional predictor-corrector method and finite difference method,respectively.The stability and convergence of the finite difference scheme for two-dimensional partial differential equation are elucidated.Based on the numerical result,the influences of fractional order parameter,Hartmann number and relaxation time on the velocity distribution of fluid in a rectangular pipe are analyzed in detail.3)The flow and heat transfer model of fractional Maxwell magnetic nanofluid film over a stretching plate are investigated based on fractional divergence and fractional Cattaneo heat transfer model,and the effect of Marangoni on fluid flow is presented.Poly vinyl alcohol(PVA)-water was selected as the base fluid and nanoparticles were added the fluid to enhance its thermal conductivity.The governing equations are formulated by combining the constitutive model of time fractional Maxwell fluid with the space fractional momentum and energy equations.The finite difference method was applied to establish the Crank-Nicolson difference scheme with high accuracy and good stability of the equations to obtain the effects of relevant property parameters on the flow and heat transfer.In this paper,the theory of fractional viscoelastic fluid and the numerical analysis method,which can lay the foundation for investigate on the flow and heat transfer problems of fractional viscoelastic fluid.The validity of the finite difference method used in the paper is proved by the error analysis and stability analysis of a constructive numerical example,which provides a useful method for solving nonlinear fractional partial differential equation withconvection term in other research fields.