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Flow Dynamics of PTT and FENE-P Viscoelastic Fluids in Circular and Flat Ducts: An Analytical Study

  • Research Article-Mechanical Engineering
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Abstract

The main aim of this research work is to establish, under fully developed conditions, an analytical solution for viscoelastic fluids flow obeying the constitutive Phan–Thien–Tanner (PTT) and Finely Extensible Nonlinear Elastic-Peterlin (FENE-P) models. In fact, a unified formulation for laminar, stationary and fully developed flow in the cases of circular and flat ducts geometries is obtained for velocity profile involving PTT and FENE-P models. In this investigation, the effect of pressure gradient on velocity profile, shear stress, shear rate and shear viscosity is explored. Effects of pressure gradient and Weissenberg number on normal stress are also studied and discussed.

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Abbreviations

A :

Constant

\( F \) :

Stress coefficient function of PTT model

\( f \) :

Fanning friction factor

\( G \) :

Dimensionless pressure gradient

\( L^{2} \) :

Extensibility parameter of the FENE-P model

\( H \) :

Half-flat height (m)

\( K \) :

Form factor

\( p \) :

Pressure (Pa)

\( R \) :

Half-circular height (m)

\( u \) :

Dimensional velocity (m/s)

\( U \) :

Dimensionless fluid velocity

\( U_{\text{N}} \) :

Dimensionless velocity of the Newtonian fluid

\( u_{\text{m}} \) :

Average fluid velocity (m/s)

\( u_{\text{Nm}} \) :

Average velocity of the Newtonian fluid (m/s)

\( x \) :

Coordinate in the axial direction (m)

\( y,r,j \) :

Coordinates in the vertical direction (m)

\( Y \) :

Dimensionless vertical coordinate

\( Z \) :

Stress coefficient function of FENE-P model

\( {\text{Re}} \) :

Reynolds number

Wi:

Weissenberg number

\( \dot{\gamma } \) :

Dimensionless shear rate

\( \dot{\gamma }^{*} \) :

Shear rate (s−1)

\( \delta \) :

Characteristic dimension of the duct (m)

\( \varepsilon \) :

Elongation parameter of the PTT model

\( \eta_{\text{p}} \) :

Polymer viscosity (Pa s)

λ :

Relaxation time (s)

\( \rho \) :

Fluid density (kg/m3)

\( \tau \) :

Dimensionless shear stress

\( \tau^{ *} \) :

Shear stress (Pa)

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Authors and Affiliations

  1. Mechanical Engineering Department, University of Skikda, El Hadaiek Road, B.O. 26, 21000, Skikda, Algeria

    Salah Latreche & Mohamed Kezzar

  2. Laboratory of Industrial Mechanics, University of Badji Mokhtar of Annaba, B.O. 12, 23000, Annaba, Algeria

    Mohamed R. Sari

  3. Department of Mathematics, Faculty of Science, New Valley University, El-Kharga, Al-Wadi Al-Gadid, 72511, Egypt

    Mohamed R. Eid

  4. Department of Mathematics, Faculty of Science, Northern Border University, Arar, 1321, Saudi Arabia

    Mohamed R. Eid

Authors
  1. Salah Latreche
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  2. Mohamed R. Sari
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Correspondence to Mohamed R. Eid.

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Latreche, S., Sari, M.R., Kezzar, M. et al. Flow Dynamics of PTT and FENE-P Viscoelastic Fluids in Circular and Flat Ducts: An Analytical Study. Arab J Sci Eng 46, 2783–2792 (2021). https://doi.org/10.1007/s13369-020-05307-7

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