MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid

In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell(UCM)constitutive equation.A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed.The complete free surface stress conditions are employed.The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method.The resulting equations are solved by the finite difference method on a 3D-staggered grid.By using an exact solution for fully developed flow inside a pipe,validation and convergence results are provided.Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

The present study examines the effect of induced magnetic field and convectiveboundary condition on magnetohydrodynamic(MHD)stagnation point flow and heat transfer dueto upper-convected Maxwell fluid over a stretching sheet in the presence of nanoparticles.Boundary layer theory is used to simplify the equation of motion,induced magnetic field,energyand concentration which results in four coupled non-linear ordinary differential equations.Thestudy takes into account the effect of Brownian motion and thermophoresis parameters.Thegoverning equations and their associated boundary conditions are initially cast into dimensionlessfonm by similarity variables.The resulting system of equations is then solved numerically usingfourth order Runge-Kutta-Fehlberg method along with shooting technique.The solution for thegoverning equations depends on parameters such as,magnetic,velocity ratio parameter B,Biotnumber Bi,Prandtl number Pr,Lewis number Le,Brownian motion Nb,reciprocal of magnetic Prandtl number A,the thermophoresis parameter Nt,and Maxwell parameter β.The numerical results are obtained for velocity,temperature,induced magnetic field andconcentration profiles as well as skin friction coefficient,the local Nusselt number andSherwood number.The results indicate that the skin friction coefficient,the local Nusseltnumber and Sherwood number decrease with an increase in B and M parameters.Moreover,local Sherwood number-φ'(O)decreases with an increase in convective parameter Bi,but the local Nusselt number-φ'(0)increases with an increase in Bi.The results are displayed both ingraphical and tabular form to illustrate the effect of the governing parameters on thedimensionless velocity,induced magnetic field,temperature and concentration.The numericalresults are compared and found to be in good agreement with the previously published resultson special cases of the problem.

Numerical Calculation of the Horizontal Stress Difference of Viscous-Elastic Fluid Acting on the Residual Oil in Micro Pore

In order to analyze the microscopic theory of viscous-elastic fluid flooding residual oil, the flow equation of polymer solution in the micro pore can be derived by selecting upper-convected Maxwell constitutive equation, continuity equation and motion equation. Then, the flow velocity field and stress field can be calculated under the boundary condition, and with the theory of stress tensor, the horizontal stress difference of polymer solution acting on the residual oil can be calculated. The results show that the greater the elasticity of viscous-elastic fluid is, the wider the flow channel is, the greater the horizontal stress difference is. The force acting on residual oil by viscous-elastic fluid can be increased by increasing the concentration of the polymer solution.

Flow behavior of UCM viscoelastic fluid in sudden contraction channel

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential upper-convected Maxwell (UCM) fluid through a contraction channel has been chosen as a prototype example. The conservation and constitutive equations are solved using the finite volume method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.

FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell （UCM） fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method （FVM） in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number （We）, further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweeo efficiency.