scholarly journals Heat transfer at nanometric scales described by extended irreversible thermodynamics

2016 ◽  
Vol 7 (2) ◽  
pp. 177-195 ◽  
Author(s):  
Hatim Machrafi
Keyword(s):  
Heat Transfer ◽  
Particle Size ◽  
Irreversible Thermodynamics ◽  
Considerable Influence ◽  
Flux Vector ◽  
Extended Irreversible Thermodynamics ◽  
Matrix Interaction ◽  
Heat Flux Vector ◽  
The Status ◽  
Independent Variable

AbstractThe purpose of this work is to present a study on heat conduction in systems that are composed out of spherical and cylindrical micro- and nanoparticles dispersed in a bulk matrix. Special emphasis is put on the dependence of the effective heat conductivity on various selected parameters as particle size and also its shape, surface specularity and density, including particle-matrix interaction. The heat transfer at nanometric scales is modelled using extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by a Copper-Silicium (Cu-Si) system. It is shown that all the investigated parameters have a considerable influence, the particle size being especially useful to either increase or decrease the effective thermal conductivity.

scholarly journals Effective Thermal Conductivity of Spherical Particulate Nanocomposites: Comparison with Theoretical Models, Monte Carlo Simulations and Experiments

2014 ◽  
Vol 13 (03) ◽  
pp. 1450022 ◽  
Author(s):  
Hatim Machrafi ◽  
Georgy Lebon
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Theoretical Models ◽  
Irreversible Thermodynamics ◽  
Flux Vector ◽  
Heat Flux Vector ◽  
The Matrix ◽  
The Status ◽  
Independent Variable ◽  
Good Agreement

The purpose of this work is to study heat conduction in systems that are composed out of spherical micro-and nanoparticles dispersed in a bulk matrix. Special emphasis will be put on the dependence of the effective heat conductivity on various selected parameters as dimension and density of particles, interface interaction with the matrix. This is achieved by combining the effective medium approximation and extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by three examples: Silicium-Germanium, Silica-epoxy-resin and Copper-Silicium systems. Predictions of our model are in good agreement with other theoretical models, Monte-Carlo simulations and experimental data.

scholarly journals An extended thermodynamic model of transient heat conduction at sub-continuum scales

2011 ◽  
Vol 467 (2135) ◽  
pp. 3241-3256 ◽  
Author(s):  
G. Lebon ◽  
H. Machrafi ◽  
M. Grmela ◽  
Ch. Dubois
Keyword(s):  
Heat Conduction ◽  
Thermodynamic Description ◽  
Type Equation ◽  
Transient Heat Conduction ◽  
Irreversible Thermodynamics ◽  
Extended Thermodynamic ◽  
Heat Flux Vector ◽  
The Status ◽  
Non Local ◽  
Ballistic Phonons

A thermodynamic description of transient heat conduction at small length and timescales is proposed. It is based on extended irreversible thermodynamics and the main feature of this formalism is to elevate the heat flux vector to the status of independent variable at the same level as the classical variable, the temperature. The present model assumes the coexistence of two kinds of heat carriers: diffusive and ballistic phonons. The behaviour of the diffusive phonons is governed by a Cattaneo-type equation to take into account the high-frequency phenomena generally present at nanoscales. To include non-local effects that are dominant in nanostructures, it is assumed that the ballistic carriers are obeying a Guyer–Krumhansl relation. The model is applied to the problem of transient heat conduction through a thin nanofilm. The numerical results are compared with those provided by Fourier, Cattaneo and other recent models.

Heat Flux Vector Potential in Convective Heat Transfer

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Vector Potential ◽  
Heat Convection ◽  
Two Dimensional ◽  
Flux Vector ◽  
Heat Function ◽  
Heat Flux Vector

The heat function concept introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) for two-dimensional (2D) heat transfer is being extended in this note to three dimensions. It is shown that a heat flux vector potential exists and can be used in three-dimensional (3D) heat convection problems. It is further shown that this heat flux vector potential degenerates to the heat function introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) when the heat convection is two-dimensional.

scholarly journals Effect of voids in a heat-flux dependent theory for thermoelastic bodies with dipolar structure

2020 ◽  
Vol 36 (3) ◽  
pp. 463-474
Keyword(s):  
Heat Flux ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
The Body ◽  
Flux Vector ◽  
Dependent Theory ◽  
Heat Flux Vector ◽  
Independent Variable ◽  
Initial Boundary Value

In our paper we formulate a theory for thermoelastic porous dipolar bodies in which we consider a new independent variable, namely the heat-flux vector. Furthermore, we add, to the differential equations that describe the behavior of the body, a new differential equation which is an equation of evolution which is satisfied by the components of the heat-flux vector. The basic system of the mixed initial-boundary value problem in this context consists of equations of the hyperbolic type. In order to ensure the consistency of the constructed theory, we formulate and prove an uniqueness result, with regards to the solution of the mixed problem.

scholarly journals A Miniaturized 3D Heat Flux Sensor to Characterize Heat Transfer in Regolith of Planets and Small Bodies

Sensors ◽  
2020 ◽  
Vol 20 (15) ◽  
pp. 4135
Author(s):  
Manuel Domínguez-Pumar ◽  
Jose-Antonio Rodríguez-Manfredi ◽  
Vicente Jiménez ◽  
Sandra Bermejo ◽  
Joan Pons-Nin
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Heat Flow ◽  
Thermal Environment ◽  
Heat Flux Sensor ◽  
Flux Vector ◽  
Small Bodies ◽  
Heat Flux Vector ◽  
Flux Sensor

The objective of this work is to present the first analytical and experimental results obtained with a 3D heat flux sensor for planetary regolith. The proposed structure, a sphere divided in four sectors, is sensible to heat flow magnitude and angle. Each sector includes a platinum resistor that is used both to sense its temperature and provide heating power. By operating the sectors at constant temperature, the sensor gives a response that is proportional to the heat flux vector in the regolith. The response of the sensor is therefore independent of the thermal conductivity of the regolith. A complete analytical solution of the response of the sensor is presented. The sensor may be used to provide information on the instantaneous local thermal environment surrounding a lander in planetary exploration or in small bodies like asteroids. To the best knowledge of the authors, this is the first sensor capable of measuring local 3D heat flux.

A Multipoint Flux Approximation of the Steady-State Heat Conduction Equation in Anisotropic Media

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Amgad Salama ◽  
Shuyu Sun ◽  
M. F. El Amin
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Heat Flux ◽  
Heat Conduction ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Anisotropic Media ◽  
Flux Vector ◽  
Conduction Heat Transfer ◽  
Heat Flux Vector

In this work, we introduce multipoint flux (MF) approximation method to the problem of conduction heat transfer in anisotropic media. In such media, the heat flux vector is no longer coincident with the temperature gradient vector. In this case, thermal conductivity is described as a second order tensor that usually requires, at least, six quantities to be fully defined in general three-dimensional problems. The two-point flux finite differences approximation may not handle such anisotropy and essentially more points need to be involved to describe the heat flux vector. In the framework of mixed finite element method (MFE), the MFMFE methods are locally conservative with continuous normal fluxes. We consider the lowest order Brezzi–Douglas–Marini (BDM) mixed finite element method with a special quadrature rule that allows for nodal velocity elimination resulting in a cell-centered system for the temperature. We show comparisons with some analytical solution of the problem of conduction heat transfer in anisotropic long strip. We also consider the problem of heat conduction in a bounded, rectangular domain with different anisotropy scenarios. It is noticed that the temperature field is significantly affected by such anisotropy scenarios. Also, the technique used in this work has shown that it is possible to use the finite difference settings to handle heat transfer in anisotropic media. In this case, heat flux vectors, for the case of rectangular mesh, generally require six points to be described.

Extended Irreversible Thermodynamics Versus Second Law Analysis of High-Order Dual-Phase-Lag Heat Transfer

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Hossein Askarizadeh ◽  
Hossein Ahmadikia
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Flow ◽  
Irreversible Thermodynamics ◽  
High Order ◽  
Second Law ◽  
Phase Lag ◽  
Dual Phase ◽  
Heat Transfer Equation ◽  
Extended Irreversible Thermodynamics

This study introduces an analysis of high-order dual-phase-lag (DPL) heat transfer equation and its thermodynamic consistency. The frameworks of extended irreversible thermodynamics (EIT) and traditional second law are employed to investigate the compatibility of DPL model by evaluating the entropy production rates (EPR). Applying an analytical approach showed that both the first- and second-order approximations of the DPL model are compatible with the traditional second law of thermodynamics under certain circumstances. If the heat flux is the cause of temperature gradient in the medium (over diffused or flux precedence (FP) heat flow), the DPL model is compatible with the traditional second law without any constraints. Otherwise, when the temperature gradient is the cause of heat flux (gradient precedence (GP) heat flow), the conditions of stable solution of the DPL heat transfer equation should be considered to obtain compatible solution with the local equilibrium thermodynamics. Finally, an insight inspection has been presented to declare precisely the influence of high-order terms on the EPRs.

scholarly journals Derivation of unifying formulae for convective heat transfer in compressible flow fields

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bo Zhao
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Driving Force ◽  
Potential Temperature ◽  
Reference Temperature ◽  
Driving Mechanism ◽  
Flux Vector ◽  
Heat Flux Vector

AbstractAlthough many theoretical and experimental studies on convective heat transfer exist, the consistent analytical expression of advection heat flux vector in convection as well as its reference temperature in the thermal driving force remains unclear. Here we show theoretically and experimentally the unifying formulae for three-dimensional (3D) heat flux vector of forced and natural convections for compressible laminar flows based on the first law of thermodynamics. It is indicated for a single-phase compressible fluid that advection is no other than heat transfer owing to mass flow in the forms of enthalpy and mechanical energy by gross fluid movement, driven by the temperature difference between the fluid temperature and the potential temperature associated with the relevant adiabatic work done. A simple formula for the total convective heat flux vector of natural convection is also suggested and reformulated in terms of logarithmic density difference as the thermal driving force. The theoretical calculations agree well with the laminar flow experiment results. Our discovery of advection heat transfer for compressible flows caused by the temperature differential in which the potential temperature is regarded as the unifying reference temperature represents a previously unknown thermal driving mechanism. This work would bring fundamental insights into the physical mechanism of convective heat transfer, and opens up new avenue for the design, calculation and thermal management of the 3D convection heat flux problems using the novel thermal driving force for compressible laminar and turbulent flows.

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