Generalized Fourier law and anomalous Righi–Leduc effect in a ferromagnet

2018 ◽  
Vol 382 (42-43) ◽  
pp. 3115-3119 ◽  
Author(s):  
Qing-Lian Xu ◽  
Zhen-Gang Zhu ◽  
Gang Su
Keyword(s):  
Fourier Law ◽  
Generalized Fourier Law

scholarly journals First and second order dual phase lag equation. Numerical solution using the explicit and implicit schemes of the finite difference method

2018 ◽  
Vol 240 ◽  
pp. 05018 ◽  
Author(s):  
Ewa Majchrzak ◽  
Bohdan Mochnacki
Keyword(s):  
Thin Metal Film ◽  
Phase Lag ◽  
Dual Phase ◽  
Mathematical Form ◽  
Fourier Law ◽  
Delay Times ◽  
Left And Right ◽  
Explicit And Implicit Schemes ◽  
Theoretical Considerations ◽  
Generalized Fourier Law

In the paper the different variants of the dual phase lag equation (DPLE) are considered. As one knows, the mathematical form of DPLE results from the generalization of the Fourier law in which two delay times are introduced, namely the relaxation time τq and the thermalization one τT. Depending on the order of development of the left and right hand sides of the generalized Fourier law into the Taylor series one can obtain the different forms of the DPLE. It is also possible to consider the others forms of equation discussed resulting from the introduction of the new variable or variables (substitution). In the paper a thin metal film subjected to a laser pulse is considered (the 1D problem). Theoretical considerations are illustrated by the examples of numerical computations. The discussion of the results obtained is also presented.

Analysis of modified Fourier law in flow of ferromagnetic Powell–Eyring fluid considering two equal magnetic dipoles

2019 ◽  
Vol 97 (7) ◽  
pp. 772-776 ◽  
Author(s):  
M. Zubair ◽  
M. Ijaz ◽  
T. Abbas ◽  
A. Riaz
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Constitutive Relations ◽  
Flow Analysis ◽  
Thermal Relaxation ◽  
Fourier Law ◽  
Magnetic Dipoles ◽  
Flux Model ◽  
Layer Flow ◽  
Heat Flux Model

The target of the current study is to inspect theoretically 2D boundary layer flow of an Eyring–Powell ferromagnetic liquid over a flat plate. An external magnetic field due to two magnetic dipoles is applied. Modified Fourier law of heat flux model is employed. Constitutive relations for Eyring–Powell fluid are considered in the boundary layer flow analysis. Series results to the nonlinear formulation are derived and scrutinized by homotopic scheme. Characteristics of various parameters like magneto-thermomechanical (ferrohydrodynamic) interaction parameter, Prandtl number, and dimensionless thermal relaxation on temperature profile are displayed via graphs. It is noted that temperature field decays via thermal relaxation factor.

Anomalous Heat Conduction, Diffusion and Heat Rectification in Nanoscale Structures

2009 ◽  
Author(s):  
Gang Zhang ◽  
Nuo Yang ◽  
Gang Wu ◽  
Baowen Li
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Transport ◽  
Nano Materials ◽  
Fourier Law ◽  
Nanoscale Structures ◽  
Recent Developments ◽  
Theoretical Results ◽  
Good Agreement ◽  
Anomalous Heat

In this paper, we report the recent developments in the study of heat transport in nano materials. First of all, we show that phonon transports in nanotube super-diffusively which leads to a length dependence thermal conductivity, thus breaks down the Fourier law. Then we discuss how the introduction of isotope doping can reduce the thermal conductivity efficiently. The theoretical results are in good agreement with experimental ones. Finally, we will demonstrate that nanoscale structures are promising candidates for heat rectification.

Analytical solutions for heat diffusion beyond Fourier law

2017 ◽  
Vol 293 ◽  
pp. 423-437 ◽  
Author(s):  
K.V. Zhukovsky ◽  
H.M. Srivastava
Keyword(s):  
Analytical Solutions ◽  
Heat Diffusion ◽  
Fourier Law

scholarly journals Finite thermoelastoplasticity and creep under small elastic strains

2018 ◽  
Vol 24 (4) ◽  
pp. 1161-1181 ◽  
Author(s):  
Tomáš Roubíček ◽  
Ulisse Stefanelli
Keyword(s):  
Convergence Result ◽  
Large Strains ◽  
Gradient Plasticity ◽  
Fourier Law ◽  
Large Plastic Strain ◽  
Rate Dependent ◽  
Galerkin Approximations ◽  
Elastic Strains ◽  
Rigorous Mathematical Analysis ◽  
The Continuum

A mathematical model for an elastoplastic continuum subject to large strains is presented. The inelastic response is modelled within the frame of rate-dependent gradient plasticity for non-simple materials. Heat diffuses through the continuum by the Fourier law in the actual deformed configuration. Inertia makes the nonlinear problem hyperbolic. The modelling assumption of small elastic Green–Lagrange strains is combined in a thermodynamically consistent way with the possibly large displacements and large plastic strain. The model is amenable to a rigorous mathematical analysis. The existence of suitably defined weak solutions and a convergence result for Galerkin approximations is proved.

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