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|Annular flow of viscoelastic fluids: Analytical and numerical solutions
|Ferrás, Luís Jorge Lima
Afonso, A. M.
Alves, M. A.
Nóbrega, J. M.
Pinho, F. T.
Slip boundary conditions
|Journal of Non-Newtonian Fluid Mechanics
|Ferrás, L.L., Afonso, A.M., Alves, M.A., Nóbrega, J.M., Pinho, F.T., Annular flow of viscoelastic fluids: Analytical and numerical solutions, Journal of Non-Newtonian Fluid Mechanics, Vol 212, pp. 80-91, 2014.
|This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem
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|IPC - Artigos em revistas científicas internacionais com arbitragem
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