Research On The Flow And Heat Transfer Of Viscoelastic Fluid Due To The Stretching Sheet

The interests in flow and heat transfer of viscoelastic fluids are shown by numerous researchers in recent years for its various applications in industrial and people's daily life.It is a major breakthrough that fractional derivatives have been found to be quite flexible in describing viscoelastic behavior.That is to say,the generalized constitutive equations for viscoelastic fluids are modified by replacing the time derivative of an integer order with the fractional calculus operators.Therefore,some fractional viscoelastic fluid models have been proposed to depict stress-strain relationship of different viscoelastic fluid,The flow and heat transfer of the fiveparameter fluid model,the double-fractional-parameter Burgers fluid model and the generalized Oldroyd-B fluid model have been studied in this paper.In Chapter 2,we consider a viscoelastic fluids model with five parameters and obtain a new viscoelastic fluid constitutive model by paralleling Maxwell model and Kelvin model then with a damper in series.The flow of viscoelastic fluid due to double accelerating plates is discussed.We obtained the analytical solutions of velocity and shear stress by using the Laplace transform.Furthermore,we analyzed the influences of the slip and the magnetic field on viscoelastic fluid flow.On the basis of supposing the different fractional order derivative for the different dashpot,the governing equations of fractional viscoelastic fluid are reformulated in Chapter 3.We discuss the flow of Burgers' fluid with slip effect under the magnetic field.The analytical solution for velocity and shear stress can be obtained by using the Laplace transform.The behaviors of relevant interesting parameters of interest on the velocity fields and shear stress are shown graphically through different diagrams.In Chapter 4,the heat transfer of viscoelastic fluid is researched.Combining with fractional order Oldroyd-B fluid constitutive model,the fractional order momentum equation and energy equation of incompressible fluid are established.The numerical solutions for the velocity and temperature fields are obtained by the effective finite difference method.Moreover,the figures are plotted to show the effects of various relevant physical parameters on the flow and heat transfer.We studied the heat transfer and flow of viscoelastic fluid by fractional calculus in this paper,and extended the fractional viscoelastic fluid constitutive model.Using the analytical and numerical methods including Laplace transform and finite difference,the analytical and numerical solutions are obtained simultaneously.The influences of various relevant parameters on the flow and temperature field are elucidated through graphs.The developed model,the research method employed and the conclusion in paper are valuable for industrial production and scientific experiments.