Study On The Analytical Solutions Of Viscoelastic Fluids For Helical Flow Model

Paints,plastics,rocks,concrete,blood and other materials related to chemical,bio-logical,civil engineering,medicine and other fields are mostly polymer polymers.Under certain stress conditions,it not only shows limited deformation,but also shows limited or infinite flow.Its stress and strain response depend on time and strain rate,and is related to the history of load and deformation.Therefore,the stress and strain do not satisfy the linear relationship and are viscoelastic fluids.Based on this background,this thesis mainly studies the velocity field and shear stress of the helical flow for viscoelastic fluid.First of all,this article mainly introduces the research background of the subject,the current research status at home and abroad,and the theoretical basic knowledge used in this article and the derivatives and integrals of several special functions.We obtain the derivative formula of Bessel functions J1(rrn),Y1(rrn),J0(rrn),Y0(rrn),the derivative formula of transcendental function BN(rrn),and the integral formula of functions J1(rrn),Y1(rrn),r2 J1(rrn),r2Y1(rrn),rJ0(rrn),rY0(rrn),rlnrJ0(rrn),rlnrY0(rrn).It provides a correct theoretical basis for the subsequent calculation of the finite Hankel transformation.Secondly,three kinds of flows for generalized Maxwell fluid and generalized Oldroyd-B fluid are studied in this article.The first type is the unsteady flow of generalized Maxwell fluid and generalized Oldroyd-B fluid with pressure gradient,that is,the flow is caused by the rotation of two infinitely long straight cylinders and oscillating pressure gradient.The second type is the helical flow of generalized Maxwell fluid and generalized Oldroyd-B fluid,that is,the flow caused by the inner and outer cylinders rotating around the axis of symmetry at different angular frequencies and sliding along the axis of symmetry at different linear velocities.The third type is the unsteady helical flow of generalized Maxwell fluid and generalized Oldroyd-B fluid,that is,the flow caused by the torsion of the inner cylinder and the time-dependent,longitudinal shear stress.Finally,in the study of the above three types of flow conditions,this thesis uses the fractional differential operators for time instead of the integral derivatives of time,and constructs fractional constitutive models of generalized Maxwell fluid and generalized Oldroyd-B fluid.Combined with the momentum conservation equation and the initial boundary conditions of fluid motion,Laplace transform and finite Hankel transform are used to obtain the exact solutions of velocity field and shear stress of these three types of fluid motion.