On the heat flux vector for flowing granular materials—Part I: effective thermal conductivity and background

2006 ◽  
Vol 29 (13) ◽  
pp. 1585-1598 ◽  
Author(s):  
Mehrdad Massoudi
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Flux Vector ◽  
Heat Flux Vector

PROPERTIES OF HEAT FLUX FUNCTIONS AND A LINEAR THEORY OF HEAT FLUX

1995 ◽  
Vol 09 (09) ◽  
pp. 1113-1122 ◽  
Author(s):  
LIQIU WANG
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Linear Function ◽  
Linear Theory ◽  
Strain Tensor ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Flux Vector ◽  
Heat Flux Vector

The symmetry and positive definiteness of thermal conductivity tensor K are used to derive some properties of heat flux functions ɸi (i=0, 1, 2). All ɸi are shown to be real-valued. Both ɸ0 and ɸ2 are found to be positive definite, and ɸ1 is constrained between −(ɸ0 + ɸ2) and (ɸ0 + ɸ2). By assuming heat flux vector q to be a linear function of temperature gradient ∇θ and velocity strain tensor D, ɸi reduce to three coefficients which are independent of D and ∇θ.

scholarly journals On the Heat Flux Vector and Thermal Conductivity of Slags: A Brief Review

Energies ◽  
2016 ◽  
Vol 9 (1) ◽  
pp. 27 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Jeongho Kim ◽  
Ping Wang
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Flux Vector ◽  
Heat Flux Vector

Numerical Study of a Non-Linear Model for the Heat Flux Vector for Granular Materials

2012 ◽  
Author(s):  
Hyunjin Yang ◽  
Nadine Aubry ◽  
Mehrdad Massoudi
Keyword(s):  
Heat Flux ◽  
Granular Materials ◽  
Volume Fraction ◽  
Numerical Study ◽  
Constitutive Relations ◽  
Flux Vector ◽  
Heat Flux Vector ◽  
Non Linear ◽  
Effects Of Radiation ◽  
The One

The two important constitutive relations needed for the study of flow and heat transfer in granular materials, where the effects of radiation are ignored, are the stress tensor and the heat flux vector. Massoudi [1, 2] derived a constitutive model that reflects the dependence of the heat flux vector on the temperature gradient, the density gradient and the velocity gradient, in an appropriate frame-invariant formulation. In this paper we use a simplified version of this model and consider the one dimensional fully developed flow of granular materials down a heated inclined plane, subject to a constant temperature boundary condition. The equations are made dimensionless and a parametric study is performed in order to examine the effects of the additional parameters on the heat flux vector. The derived governing equations are coupled non-linear second order ordinary differential equations which are solved numerically and the results are shown for the temperature, volume fraction and velocity profiles.

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.

Boundary-value problems in the kinetic theory of gases. Part 2. Thermal creep

1971 ◽  
Vol 45 (4) ◽  
pp. 759-768 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Kinetic Theory ◽  
Effective Thermal Conductivity ◽  
Half Space ◽  
Thermal Creep ◽  
Kinetic Theory Of Gases ◽  
Boundary Wall ◽  
Creep Velocity

The effect of a temperature gradient in a gas inclined at an angle to a boundary wall has been investigated. For an infinite half-space of gas it is found that, in addition to the conventional temperature slip problem, the component of the temperature gradient parallel to the wall induces a net mass flow known as thermal creep. We show that the temperature slip and thermal creep effects can be decoupled and treated quite separately.Expressions are obtained for the creep velocity and heat flux, both far from and at the boundary; it is noted that thermal creep tends to reduce the effective thermal conductivity of the medium.

A Transient Formulation of Newton's Cooling Law for Spherical Bodies

2000 ◽  
Vol 123 (1) ◽  
pp. 63-64 ◽  
Author(s):  
S. S. Sazhin ◽  
V. A. Gol'dshtein ◽  
M. R. Heikal
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Diesel Engine ◽  
Effective Thermal Conductivity ◽  
Spherical Body ◽  
Fuel Droplet ◽  
Transient Effects ◽  
Newton's Law ◽  
Initial Stage ◽  
Newton’S Law

Newton's law of cooling is shown to underestimate the heat flux between a spherical body (droplet) and a homogeneous gas after this body is suddenly immersed into the gas. This problem is rectified by replacing the gas thermal conductivity by the effective thermal conductivity. The latter reduces to the gas thermal conductivity in the limit of t→∞, but can be substantially higher in the limit of t→0. In the case of fuel droplet heating in a medium duty truck Diesel engine the gas thermal conductivity may need to be increased by more than 100 percent at the initial stage of calculations to account for transient effects during the process of droplet heating.

Evaluation of effective thermal conductivity of unsaturated granular materials using random network model

Geothermics ◽  
2017 ◽  
Vol 67 ◽  
pp. 76-85 ◽  
Author(s):  
Chulho Lee ◽  
Li Zhuang ◽  
Dongseop Lee ◽  
Seokjae Lee ◽  
In-Mo Lee ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Network Model ◽  
Random Network

Effective Thermal Conductivity of Submicron Powders: A Numerical Study

2016 ◽  
Vol 846 ◽  
pp. 500-505
Author(s):  
Wei Jing Dai ◽  
Yi Xiang Gan ◽  
Dorian Hanaor
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Gas Phase ◽  
Numerical Study ◽  
Transfer Model ◽  
Size Of Particles ◽  
Contact Unit

Effective thermal conductivity is an important property of granular materials in engineering applications and industrial processes, including the blending and mixing of powders, sintering of ceramics and refractory metals, and electrochemical interactions in fuel cells and Li-ion batteries. The thermo-mechanical properties of granular materials with macroscopic particle sizes (above 1 mm) have been investigated experimentally and theoretically, but knowledge remains limited for materials consisting of micro/nanosized grains. In this work we study the effective thermal conductivity of micro/nanopowders under varying conditions of mechanical stress and gas pressure via the discrete thermal resistance method. In this proposed method, a unit cell of contact structure is regarded as one thermal resistor. Thermal transport between two contacting particles and through the gas phase (including conduction in the gas phase and heat transfer of solid-gas interfaces) are the main mechanisms. Due to the small size of particles, the gas phase is limited to a small volume and a simplified gas heat transfer model is applied considering the Knudsen number. During loading, changes in the gas volume and the contact area between particles are simulated by the finite element method. The thermal resistance of one contact unit is calculated through the combination of the heat transfer mechanisms. A simplified relationship between effective thermal conductivity and loading pressure can be obtained by integrating the contact units of the compacted powders.

The Effective Thermal Conductivity of a Packing of Spheres

1990 ◽  
Vol 57 (3) ◽  
pp. 789-791 ◽  
Author(s):  
A. Jagota ◽  
C. Y. Hui
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Closed Form ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Upper Bound ◽  
Random Packing ◽  
Fabric Tensor ◽  
Mean Temperature

The anisotropic effective thermal conductivity of a random packing of spheres is derived. The conductivity is closely related to the fabric tensor of the theory of granular materials. The derivation involves a mean temperature field assumption which is shown to render the model an upper bound. Closed-form expressions for the conductivity are obtained in the isotropic and axisymmetric cases.

Sign in / Sign up

Export Citation Format

Share Document