Isothermal and nonisothermal, laminar, inelastic, non-Newtonian tube-entrance flow following a contraction

Christiansen, E. B.; Kelsey, S. J.

doi:10.1016/0009-2509(73)80013-2

Cited by 12 publications

(4 citation statements)

References 21 publications

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“…There are hundreds of models belonging to this framework used in chemistry, biofluid rheology, geomechanics, food industry, etc. A discussion of various aspects of these models can be found in [87], with references to the chemical engineering and colloidal mechanics literature ( [28,35,99,106,114,116]), ice-mechanics and glaciology ( [71,91,119]), blood rheology ( [29,30,33,34,37,40,41,55,94,99,100,111,118,122] and [49]).…”

Section: Examples Of Implicit Constitutive Equationsmentioning

confidence: 99%

On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary

Bulíček,

Málek,

Maringová

2023

J. Math. Fluid Mech.

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Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of incompressible fluids is nowadays available not only for Navier–Stokes fluids but also for various fluid models where the relation between the Cauchy stress tensor and the symmetric part of the velocity gradient is nonlinear. The majority of such studies however concerns models where such a dependence is explicit (the stress is a function of the velocity gradient), which makes the class of studied models unduly restrictive. The same concerns boundary conditions, or more precisely the slipping mechanisms on the boundary, where the no-slip is still the most preferred condition considered in the literature. Our main objective is to develop a robust mathematical theory for unsteady internal flows of implicitly constituted incompressible fluids with implicit relations between the tangential projections of the velocity and the normal traction on the boundary. The theory covers numerous rheological models used in chemistry, biorheology, polymer and food industry as well as in geomechanics. It also includes, as special cases, nonlinear slip as well as stick–slip boundary conditions. Unlike earlier studies, the conditions characterizing admissible classes of constitutive equations are expressed by means of tools of elementary calculus. In addition, a fully constructive proof (approximation scheme) is incorporated. Finally, we focus on the question of uniqueness of such weak solutions.

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Section: Examples Of Implicit Constitutive Equationsmentioning

confidence: 99%

On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary

Bulíček,

Málek,

Maringová

2023

J. Math. Fluid Mech.

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“…On the other hand, for real-world problems, the advantage of considering the more general fluids of power-law type is not slight. In effect, as [35] describes, practitioners employed them to investigate problems in chemical engineering of colloids, suspensions, and polymeric fluids, see [49,48,52,4,9,41,44], in ice mechanics and glaciology, see [37,53,25], in blood-rheology, see [8,7,10,14,15,39,47,17], and also in geology, see [36], to name a few instances.…”

mentioning

confidence: 99%

Local null controllability of a class of non-Newtonian incompressible viscous fluids

Carvalho

Límaco

Menezes

et al. 2022

EECT

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<p style='text-indent:20px;'>We investigate the null controllability property of systems that mathematically describe the dynamics of some non-Newtonian incompressible viscous flows. The principal model we study was proposed by O. A. Ladyzhenskaya, although the techniques we develop here apply to other fluids having a shear-dependent viscosity. Taking advantage of the Pontryagin Minimum Principle, we utilize a bootstrapping argument to prove that sufficiently smooth controls to the forced linearized Stokes problem exist, as long as the initial data in turn has enough regularity. From there, we extend the result to the nonlinear problem. As a byproduct, we devise a quasi-Newton algorithm to compute the states and a control, which we prove to converge in an appropriate sense. We finish the work with some numerical experiments.</p>

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“…The idea was an extension of that originally proposed by Rabinowitsch, 1929 for Bingham fluids. Christiansen and Kelsey, 1973 using the popular stream-tube real-tube model investigated the simultaneously developing flow and heat transfer to Powell-Eyring fluids following a contraction. A temperature dependent consistency index was allowed for in their analysis.…”

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confidence: 99%

Forced convection heat transfer to a power‐law fluid in arbitrary cross‐section ducts

Lawal

Mujumdar

1984

Can J Chem Eng

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A numerical method is developed to predict the three‐dimensional forced convection laminar incompressible flow of a power law fluid in arbitrary cross‐section straight ducts. The continuity equation and boundary layer forms of the energy and momentum equations in rectangular coordinates are transformed into new orthogonal coordinates with boundaries coinciding with the coordinate surfaces. The resulting equations are solved using the finite difference technique. The numerical scheme is capable of handling different hydrodynamic and thermal entry boundary conditions but results are only presented for uniform inlet velocity and temperature profiles and isothermal wall. To demonstrate the wider applicability of the method local heat transfer coefficients and pressure drop in square, trapezoidal and regular pentagonal ducts are computed as functions of pertinent thermal and hydrodynamic parameters.

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Isothermal and nonisothermal, laminar, inelastic, non-Newtonian tube-entrance flow following a contraction

Cited by 12 publications

References 21 publications

On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary

On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary

Local null controllability of a class of non-Newtonian incompressible viscous fluids

Forced convection heat transfer to a power‐law fluid in arbitrary cross‐section ducts

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