The thermal conductivity of tin at low temperatures

1955 ◽  
Vol 229 (1179) ◽  
pp. 473-492 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Low Temperatures ◽  
Fluid Model ◽  
Accurate Method ◽  
Resistance Thermometers ◽  
Lattice Waves ◽  
Normal States ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Good Agreement

An account is given of an accurate method of measuring the thermal conductivity of metals between 0·2 and 4°K using carbon aquadag resistance thermometers. Experimental curves are shown for tin specimens of different crystal structure and of varying impurity contents in both superconducting and normal states, and they are analyzed on the basis of the two-fluid model of superconductivity. It appears that at low temperatures the conductivity is mainly due to the lattice, since the observed temperature variation for all specimens is consistent with a T 3 law at sufficiently low temperatures. Good agreement is obtained between the effective mean free paths of the lattice waves and the values expected from the rod dimensions and crystal sizes. The electronic contribution to the thermal conduction in the superconducting state falls very rapidly below T c , and, to a first approximation, the ratio of this contribution to that in the normal state is a function of temperature and not of impurity. The effects of magnetic fields on measurements of thermal conductivity are also briefly discussed and it is shown that the results may be complicated by frozen-in flux.

scholarly journals Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 810
Author(s):  
Jade Gesare Abuga ◽  
Tiri Chinyoka
Keyword(s):  
Finite Volume ◽  
Numerical Algorithm ◽  
Numerical Study ◽  
Fluid Model ◽  
Shear Banding ◽  
Numerical Algorithms ◽  
Viscoelastic Fluids ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Good Agreement

The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, we explore both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein the stress dynamics are coupled with concentration equations. We follow a computational analysis approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the Finite Volume Method (FVM) and it is implemented in the open-source software package, OpenFOAM. The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques, namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting (DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding results via both the Giesekus and Johnson-Segalman models show good agreement with existing literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with existing literature for the concentration and velocity profiles is also in good agreement.

scholarly journals Models results Comparison of different approaches to turbulence for flow past a heated flat plate

2021 ◽  
Vol 264 ◽  
pp. 01008
Author(s):  
Zafar Malikov ◽  
Dilshod Navruzov ◽  
Xikmatulla Djumayev
Keyword(s):  
Experimental Data ◽  
Flat Plate ◽  
Fluid Model ◽  
Fundamental Difference ◽  
Rans Models ◽  
Two Fluid Model ◽  
Almost All ◽  
Substance Transfer ◽  
Two Fluid ◽  
Good Agreement

This paper compares the results of the well-known Spalart-Allmares (SA) model and the two-fluid model for the flow around a heated flat plate. These models represent different approaches to the problem of turbulence. The SA model is a one-parameter model and a representative of the RANS models. This model is currently the most popular and is used to solve many practical problems. The advantage of this model is that its accuracy is quite good and simple for numerical implementation. Therefore, the SA model is included in almost all the codes of the software package. The two-fluid model used in this work has been developed recently [15]. In the pioneering works, it is shown that the basis for constructing this model is the possibility of representing a turbulent flow in the form of a heterogeneous mixture of two liquids. Therefore, this model is derived from the dynamics of two liquids. In these works, it is also shown that the developed two-fluid model is able to adequately describe complex anisotropic turbulences. The fundamental difference between these two models is that the SA model uses the substance transfer equation, while the two-fluid model uses the dynamics equation. To compare the two models, we compare their numerical results with the known experimental data. It is shown that the results of both models are close to each other and are in good agreement with the experimental data.

The thermal conductivity of lead at low temperatures

1958 ◽  
Vol 244 (1236) ◽  
pp. 85-100 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Plastic Deformation ◽  
Single Crystals ◽  
Superconducting State ◽  
Low Temperatures ◽  
Conductivity Measurements ◽  
Conduction Electrons ◽  
Lattice Waves ◽  
Normal States ◽  
Theory Of Superconductivity

Thermal conductivity measurements have been made upon a series of lead specimens between 1 and 4° K, in the superconducting and in the normal states. Both single crystals and polycrystals were studied, and also specimens containing various added impurities. The results in the superconducting state confirm the hypothesis that below about 1·4° K the thermal current is carried entirely by lattice waves, and that these are not scattered by conduction electrons. This conclusion is based upon three pieces of evidence: (1) the thermal conductivity K s is insensitive to the amount and species of impurity; (2) it depends upon the geometry of the specimen for sufficiently thin specimens; (3) it is sensitive to plastic deformation, which can be explained if the lattice waves are scattered by dislocations. A brief discussion is given of the possible significance of these results in the theory of superconductivity.

scholarly journals Natural modes of the two-fluid model of two-phase flow

2021 ◽  
Vol 33 (3) ◽  
pp. 033324
Author(s):  
Alejandro Clausse ◽  
Martín López de Bertodano
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Natural Modes ◽  
Two Fluid Model ◽  
Two Fluid

Self-consistent hydrodynamic two-fluid model of vortex plasma

2021 ◽  
Vol 33 (3) ◽  
pp. 037116
Author(s):  
Victor L. Mironov
Keyword(s):  
Fluid Model ◽  
Self Consistent ◽  
Two Fluid Model ◽  
Two Fluid

scholarly journals Mathematical study on two-fluid model for flow of K–L fluid in a stenosed artery with porous wall

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
R. Ponalagusamy ◽  
Ramakrishna Manchi
Keyword(s):  
Theoretical Study ◽  
Fluid Model ◽  
Porous Wall ◽  
Governing Equations ◽  
Rate Of Increase ◽  
Special Cases ◽  
Stenosed Artery ◽  
Flow Through ◽  
Two Fluid Model ◽  
Two Fluid

AbstractThe present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

Sign in / Sign up

Export Citation Format

Share Document