Study On Unsteady Stagnation Point Flow Of Fractional Viscoelastic Fluid

The stagnation point flow of viscoelastic fluid is extensively used in actual manufacture and life,such as plastic extrusion,geothermal system,crude oil exploitation,heat exchanger and blood flow measurement technology.The emergence of fractional calculus provides a more novel direction for the development of fluid mechanics.By integrating the stagnation point flow characteristics with fractional calculus,the stagnation point flow model of fractional viscoelastic fluid under unsteady conditions is established in this paper,and the numerical solution is investigated.Firstly,according to the characteristics of stagnation point flow,the flow of fractional Oldroyd-B fluid on the wall with time-dependent stretched velocity is analyzed.Based on the constitutive relationship of fractional Oldroyd-B fluid,the velocity equation of external potential flow is coupled with the momentum equation.Moreover,the fractional Fourier law with thermal relaxation-retardation time is integrated with the energy equation for the first time.The fractional derivative term in the model is dispersed by L1 algorithm and the numerical solution of the equation is obtained.The results display that the larger relaxation parameters will hinder fluid flow,while the delay parameters show the opposite trend.All temperature distributions in the flow increase firstly and then gradually diminish,which reflects the thermal retardation characteristic of Oldroyd-B fluid.Secondly,the flow of fractional Maxwell fluid around a wedge with time-dependent drawing velocity is studied for the first time.The fractional Maxwell fluid constitutive model is coupled with the velocity control program.Heat source and chemical reaction effect are lead into the temperature and concentration equations respectively.The outcomes display that all the velocity profiles initially rise to a maximal value due to the impact of buoyancy force and then decrease to the free flow velocity.The distribution of temperature and concentration always increases slightly and then decreases significantly,which shows the characteristics of thermal relaxation and mass relaxation of Maxwell fluid.Finally,the stagnation point flow of fractional Oldroyd-B fluid on a wedge in porous media is discussed with unsteady boundary conditions.Momentum equations are obtained by using the constitutive model of fractional Oldroyd-B fluids.The generalized Fourier law is coupled with temperature equation,and the thermal radiation effect is also considered.The outcomes show that with the raise of wedge angle parameter value,the buoyancy of the fluid increases,resulting in the acceleration of the velocity.The temperature distribution in the fluid increases marginally then decreases evidently,which indicates that Oldroyd-B fluid has thermal retardation characteristics.