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

Latreche, Salah; Sari, Mohamed Rafik; Kezzar, Mohamed; Eid, Mohamed R.

doi:10.1007/s13369-020-05307-7

Cited by 8 publications

(6 citation statements)

References 25 publications

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“…The existence of the scaling parameter () for the FENE-P (sPTT) models in SSSF was also shown by Oliveira, Coelho & Pinho (2004) and Latreche et al. (2021). A recent study by Yamani & McKinley (2022) showed, analytically, that the SSSF response of the FENE-P model scales with the dimensionless parameter , which differs from the parameter used in this study, .…”

Section: Resultssupporting

confidence: 60%

“…The equivalence of these two models was first noted in the study of Cruz, Pinho & Oliveira (2005), who derived analytical solutions for fully developed pipe and channel flows with the FENE-P and sPTT models. Latreche et al (2021) also established analytical solutions for steady, fully developed, flows of the FENE-P and sPTT models in flat and circular ducts using the aforementioned substitution of parameter values. Davoodi et al (2022) then investigated the FENE-P and sPTT models for a range of steady and homogeneous flows, as well as unsteady and inhomogeneous flows.…”

Section: Introductionmentioning

confidence: 99%

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A comparison between the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear

John,

Poole,

Kowalski

et al. 2024

J. Fluid Mech.

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The finitely extensible nonlinear elastic with Peterlin closure (FENE-P) and simplified Phan-Thien–Tanner (sPTT) viscoelastic models are used widely for modelling of complex fluids. Although they are derived from distinct micro-structural theories, these models can become mathematically identical in steady and homogeneous flows with a particular choice of the values of the model parameters. However, even with this choice of parameter values, the model responses are known to differ from each other in transient flows. In this work, we investigate the responses of the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear (LAOS). In steady shear, the shear stress scales with the non-dimensional group $Wi/(aL)$ ( $Wi\,\sqrt {\epsilon }$ ) for the FENE-P (sPTT) model, where $Wi$ is the Weissenberg number, $L^2$ is the limit of extensibility in the FENE-P model ( $a$ being $L^2/(L^2-3)$ ), and $\epsilon$ is the extensibility parameter in the sPTT model. Our numerical and analytical results show that in LAOS, the FENE-P model shows this universality only for large values of $L^2$ , whereas the sPTT model shows it for all values of $\epsilon$ . In the strongly nonlinear region, there is a drastic difference between the responses of the two models, with the FENE-P model exhibiting strong shear stress overshoots that manifest as self-intersecting secondary loops in the viscous Lissajous curves. We quantify the nonlinearity exhibited by each constitutive model using the sequence of physical processes framework. Despite the high degree of nonlinearity exhibited by the FENE-P model, we also show using fully nonlinear one-dimensional simulations that it does not shear band in LAOS within the range of conditions studied.

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Section: Resultssupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

A comparison between the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear

John,

Poole,

Kowalski

et al. 2024

J. Fluid Mech.

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“…The adopted homotopy technique is deployed to ensure the series solutions (analytical) of transformed problem defined by Eqs. ( 9), ( 17), (18) under conditions at boundary (11), (12) and (19). In this regard, the base functions η k exp(−cη)/k ≥ 0, c ≥ 0 have been chosen.…”

Section: Analytical Solution Via Homotopic Techniquementioning

confidence: 99%

“…The study concludes that higher Weissenberg number depicts reversal flow trend through converging/diverging channel. Latreche et al 19 disclosed the flow behavior of diverse viscoelastic liquids through flat and circular ducts. Here, PTT and FENE-P liquids become identical when pressure gradient parameters approaches to 1.…”

Section: Introductionmentioning

confidence: 99%

Double-diffusive Hamel–Jeffrey flow of nanofluid in a convergent/divergent permeable medium under zero mass flux

Shafee

Farooq

2023

Sci Rep

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In the recent era, the nanofluid's transportation due to the Jeffrey–Hemal flow phenomenon (i.e., carrying fluid through a converging/diverging channel) has significant applications in numerous engineering and science technologies. Therefore, multi-disciplinary evolution and research motivated us to present current attempt. The aim of this attempt is to present Jeffrey–Hamel mechanism of the nanofluid through non-parallel channel under thermally balance non-Darcy permeable medium impacts. The nanomaterial is represented using the Buongiorno nanofluid model. The investigation also includes zero mass flux impacts as well as variable rheological fluid properties. The influences of temperature jump are also encountered in the current analysis. The governing flow expressions under the Jeffrey–Hemal analysis are made dimensionless utilizing the similarity variables. The dimensionless equations are then solved using the analytical scheme (homotopy method) and the obtained series solutions are convergent. The influences of the involved parameters on concerned profiles are investigated through graphs. Force of drag, Nusselt and Sherwood numbers are elaborated graphically. In this analysis, intensification in Prandtl number enhances the heat transfer rate whereas decrement is seen in heat transfer rate for larger thermal slip parameter. Further, mass diffusivity parameter adversely affects the mass transfer rate. The current analysis incorporates numerous industrial and technological processes including transportation, material synthesis, microfluidics, high-power Xrays, biomedical, solid-state lighting, microelectronics, scientific measurement, medicine, molten polymers extrusion via converging dies, cold drawing operation related to polymer industry etc.

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“…23 He analyzed that because of rise in the stretching limitations, the heat transport rate increases nearby the walls of the channels. In stretchable–shrinkable channels, the thermal radiation analysis on magneto hydrodynamic Nano fluid flow Dogonchi and Ganji 24 elaborates and finds that fluid velocity increases due to stretchable parameters. The analytical solution for MHD copper involved water Nano fluid flow over dual non-similar converging diverging channels using the RVI procedure was provided by Azimi and Riazi 25 and find that, the number of Nusselt boosts with the large value of Eckert number.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation for heat and mass transport of non-Newtonian Carreau rheological nanofluids through convergent/divergent channels

Hashim

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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Recent studies on fluid flows have shown that the non-Newtonian fluid flows through convergent/divergent channels with heat and mass transport analysis of nanofluids has triggered many researchers because of their occurrence in biomedicine, cavity flow model, flow through canals, and cold drawing operations. Moreover, heat enhancement during fluid flow plays an important role in different engineering applications, which can be achieved by improving fluid thermal physical properties. Therefore, the present study aims at providing a novel mathematical model for non-Newtonian Carreau rheological fluid flow through convergent/divergent channels by employing Buongiorno’s nanofluids model. The governing system of partial differential equations for Carreau fluid flow is formulated via basic conservation laws, for the first time in literature. The dimensionless variables are introduced to get the non-dimensional forms of the governing equations. The resultant system of ordinary differential equtions (ODEs) is numerical integrated using Runge-Kutta Fehlberg method with shooting technique, which is an efficient numerical technique to determine the numerical solutions of ODEs. The varying patterns of non-dimensional velocities, temperature, and concentration fields along with skin-friction, Nesselt and Sherwood numbers are simulated for various eminent physical parameters with converging and diverging walls. The underlying flow physics and thermal behavior are explored in terms of pertinent parameters, for instance, Reynolds number, channel angle, Prandtl number, Brownian motion parameter and thermophoresis parameter. From the present numerical simulations, we have concluded that the Reynolds number has an opposite effect on dimensionless velocity for convergent and divergent channels. It is recognized that the fluid velocity increases with higher values of Weissenberg number for convergent channel. Moreover, the temperature distributions enhance for larger Brownian motion parameter.

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

Cited by 8 publications

References 25 publications

A comparison between the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear

A comparison between the FENE-P and sPTT constitutive models in large-amplitude oscillatory shear

Double-diffusive Hamel–Jeffrey flow of nanofluid in a convergent/divergent permeable medium under zero mass flux

Numerical simulation for heat and mass transport of non-Newtonian Carreau rheological nanofluids through convergent/divergent channels

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