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1D dynamics of a second-grade viscous fluid in a constricted tube

Fernando Carapau, Adélia Sequeira (2008)

Banach Center Publications

Using a one-dimensional hierarchical model based on the Cosserat theory approach to fluid dynamics we can reduce the full 3D system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible second-grade viscous fluid to a system of equations depending on time and on a single spatial variable. From this new system we obtain the steady relationship between average pressure gradient and volume flow rate over a finite section of a straight constricted tube, and the corresponding...

3-dimensional physically consistent diffusion in anisotropic media with memory

Michele Caputo (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Some data on the flow of fluids exhibit properties which may not be interpreted with the classic theory of propagation of pressure and of fluids [21] based on the classic D’Arcy’s law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and of the pressure of fluids the law of D’Arcy is here modified introducing a memory formalisms operating on the flow as well as on the pressure gradient which implies a filtering of the pressure...

A model of dense fluids

R. Streater (1998)

Banach Center Publications

We obtain coupled reaction-diffusion equations for the density and temperature of a dense fluid, starting from a discrete model in which at most one particle can be present at each site. The model is constructed by the methods of statistical dynamics. We verify that the theory obeys the first and second laws of thermodynamics. Some remarks on measurement theory for the position of a particle are offered.

A new model to describe the response of a class of seemingly viscoplastic materials

Sai Manikiran Garimella, Mohan Anand, Kumbakonam R. Rajagopal (2022)

Applications of Mathematics

A new model is proposed to mimic the response of a class of seemingly viscoplastic materials. Using the proposed model, the steady, fully developed flow of the fluid is studied in a cylindrical pipe. The semi-inverse approach is applied to obtain an analytical solution for the velocity profile. The model is used to fit the shear-stress data of several supposedly viscoplastic materials reported in the literature. A numerical procedure is developed to solve the governing ODE and the procedure is validated...

A regularity criterion for the 2D MHD and viscoelastic fluid equations

Zhuan Ye (2015)

Annales Polonici Mathematici

This paper is dedicated to a regularity criterion for the 2D MHD equations and viscoelastic equations. We prove that if the magnetic field B, respectively the local deformation gradient F, satisfies ∇ B , ∇ F ∈ L q ( 0 , T ; L p ( ℝ ² ) ) for 1/p + 1/q = 1 and 2 < p ≤ ∞, then the corresponding local solution can be extended beyond time T.

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