Numerical simulations of a third-grade fluid flow on a tube through a contraction

Carapau, Fernando; Correia, Paulo

doi:10.1016/j.euromechflu.2017.02.006

Cited by 12 publications

(2 citation statements)

References 31 publications

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“…Their applicability in mathematical models for which we cannot easily find exact solutions, namely those involving symmetry issues, the study of the stability of the approximate solutions is an open field of research. In particular, this work may be relevant in the study of the stability of the symmetrical flow of Newtonian and non-Newtonian fluids related to one-dimensional models obtained by Cosserat Theory associated with fluid dynamics (see [28,29]).…”

Section: Introductionmentioning

confidence: 99%

New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

2021

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In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.

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Section: Introductionmentioning

confidence: 99%

New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

2021

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“…Robertson [3] applied the nine-director theory on the modeling of the blood flow in walls of arteries, that are typical case of flexible wall and non-Newtonian liquid fluid structure interaction case. Carapau [4] used the director theory approach related to fluid dynamics for reduction of the nonlinear three-dimensional equations governing the axisymmetric unsteady motion of a non-Newtonian incompressible fluid to a one-dimensional system of ordinary differential equations depending on time and on a single spatial variable. Unfortunately, the model of unsteady friction is not as well described as the model of steady friction, and investigation in this area is still ongoing [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Influence of Second Viscosity on Pressure Pulsation

Himr

Fialová

2019

Applied Sciences

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A mathematical model of pulsating flow is proposed in the paper. The model includes more accurate description of energy dissipation, so it allows, for example, better stability analysis of water power plant control and more effective operation. Flow in a pipeline system is usually treated as a one-dimensional flow. This is also applied for more difficult cases of the Newtonian and non-Newtonian liquids simulations in the rigid or flexible pipes. Computational simulations of pressure pulsations in pipelines often predict lower damping than what the experimental results show. This discrepancy can be caused by neglecting one of the important damping mechanisms. The second viscosity describes the energy losses due to the compressibility of the liquid. Its existence and use in the computations specifies the real pulsations damping descriptions and predictions. A frequency dependent model of pressure pulsations including second viscosity is introduced. The second viscosity is determined from the system eigenvalue. The experiments were performed with water for low frequencies (from 0.1 to 1 kHz). This area is not fully covered by the current available research results.

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