scholarly journals Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics

2021 ◽  
Vol 16 (5) ◽  
Author(s):  
Gao-Le Dai
Keyword(s):  
Fourier Law

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.

The Fourier Law at the Macro and Nanoscale

2013 ◽  
Author(s):  
Thomas Prevenslik
Keyword(s):  
Lag Time ◽  
Fourier Law ◽  
Speed Of Light ◽  
Carrier Mechanism ◽  
Acoustic Velocities ◽  
Carrier Velocity ◽  
Transient Thermal ◽  
Electron Carriers ◽  
Planck Energy ◽  
Fourier Equation

The Fourier law implicitly assumes transient thermal disturbances are carried throughout the solid at an infinite velocity while not defining the carrier mechanism. Paradoxically, the phonon and electron carriers on which the Fourier law is based are limited to acoustic velocities. At the macroscale, the paradox is resolved by the thermal BB photons of QM that carry the Planck energy E = kT of the atoms in the disturbance throughout the solid at the speed of light. BB stands for blackbody and QM for quantum mechanics. The traditional Fourier equation in lattice temperature is expressed in terms of the Planck energy E of the atoms to show infinite carrier velocity is reasonably approximated by BB photons at the speed of light, thereby avoiding the unphysical alternative that absent BB photons the Fourier law is required to rely on thermal disturbances travelling at infinite velocity. Practically, the effect of BB photons on the accuracy of the Fourier solution is insignificant as the BB transient response of the semi-infinite solid is shown identical to that which includes the lag time caused by the speed of light. Fourier’s law is not applicable at the nanoscale as by QM the Planck energy of the atom is not available to be carried through the solid by the BB photon.

scholarly journals Energy Balance Approach to Study the Role of Perspiration in Heat Distribution of Human Skin

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Aijaz Mir ◽  
Ibrahim M. Almanjahie ◽  
Javid Gani Dar
Keyword(s):  
Energy Balance ◽  
Human Skin ◽  
Subcutaneous Tissue ◽  
Thermal Conductance ◽  
Energy Balance Equation ◽  
Heat Radiation ◽  
Fourier Law ◽  
Bioheat Equation ◽  
Energy Balance Approach

This paper develops a model to identify the role of perspiration in temperature distribution of human skin. The model has been solved by using the energy balance equation on the surface of human skin. The role played by thermal conductance, convection, and heat radiation during heat transfer in human skin has been considered, and the relevant laws such as Fourier law for conduction, Newton’s Law for convection, and Stefan–Boltzmann’s law for radiation have been used in the model. Pennes’ bioheat equation has been employed to estimate the heat flow in the dermal region of skin including subcutaneous tissue.

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